”31': ammoammom‘ “mama - ‘ . Jo wsaamun Aavum , A313)!!!" .ElKELEY i 'UBRARY UNWERSWY Of ' V CAU‘C‘V‘JH ARCHITECTURE LIB . ARCHITECTURAL DICTIONARY, CONTAINING A CORRECT NOMENCLATURE AND DERIVATION THE TERM S EMPLOYED BY ARCHITECTS, BUILDERS, AND WORKMEN. EXHIBITING, IN A PERSPICUOUS POINT OF VIEW, THE THEORY AND PRACTICE OF THE VARIOUS BRANCHES 0F ARCHITECTURE, IN CARPENTRY, JOINERY, MASONRY, BRICKLAYING, AND THEIR DEPENDENCE ON EACH OTHER; THE SCIENCES NECESSARY TO BE UNDERSTOOD; AND THE LIVES OF THE PRINCIPAL ARCHITECTS. THE WHOLE FORMING 921 complete @1111: to the game 0F flRCHITECTURE flJV'D THE flRT 0F BUILDINGI IN TWO VOLUMES. ooooooooooooooooooooooooo oltrllvootoolltu ooooooooo BY PETER NICHOLSON, ARCHITECT. flunUun : PRINTED BY J. BARI‘IELD, ‘VARDOUR-STREET, PRINTER TO HIS ROYAL HIGHNESS THE PRINCE REGENT. + 1819. ARCHITECTURE LIB. ARCHITECTURAL DICTIONARY. . AN 4: FAC PAL ‘5— FABRIC (from the Latin, fabrica, originally a smith’s shop, or forge) the structure or construction ofany thing, particularly of a building. In Italy, the word is applied to any considerable building; in France, it rather signifies the man- ner of building. FACADE, or FACE (from the Latin facies, the front) that portion of the surface of a body which presents itself to the eye. to any side of a building, and sometimes only to the principal front. FACE, or FACIA (from the Latin) a vertical mem- ber in the combination of mouldings, having a vtary small projection, but considerable breadth; such as the bands of an architrave. See FASCIA. FACE MOULD, in the preparation of the hand-rail ofa stair, a mould for drawing the proper figure on both sides of the plank; so that when cut by a saw, held at a certain inclination, the two sur- faces of the rail—piece will be every where per- Itis frequently applied . A pendicular to the plan, when laid in their in-' tended position. FACE or A STON E, the surface intended for the front of the work. The face is easily known when the stone is scalped, as being opposite to the back, which is rough as it comes from thequarry. The surface of the splitting grain ought always to be perpendicular to the face. FAClA, See FASCIA. ' FACING, in enginery, a small thickness of com- mon earth, soil, or stufi'ofa canal, laid in front of the side-lining or puddle on the sloping sides. It is of use to hold up the puddle while‘working and chopping, in the act of puddling, and after- wards to guard the puddle from being penetrated by the hitchers and poles used by the barge-men. FACING, FAcAnE, or REVETEMENT, in 'fortifiéa- tion, the portion of masonry, or rather building, VOL. 11. given to ramparts, with a View to prevent the soil of which they are composed’ from crumbling or giving way. When the wall is of masonry, it should be five feet thick at the top, with tresses, called counterforts, at about fifteen feet apart, to strengthen the facing. In order to prevent es- calade, the facing is generally made full twenty- seven feet high, from the bottom of the ditch to the cordon. Vth the facing is carried up as high as the soles of the embrasures, it is called a whole revetement; but when confined to the ditch only, it is called a half revetement. These must depend upon the nature of the soil, the facility of obtaining materials, the time that can be al- lowed, the importance of the post, 8Lc. ‘Vhen difficulties occur, as also in temporary works, the facings are made with turf, in which case they are said to be gazoned. For field-works, and par- ticularly in the conducting of sieges, fascines, or faggots, made of various materials, are very generally employed, and answer the intention. ' FACINGs, in joinery, all those fixed parts of wood- work which cover the rough work of the interior of walls, and present themselves to the eye in the completion. ’ ~FACTABLING, see COPING. FAIR CURVE, in ship-building, a winding line, used in delineating ships, whose shape is varied according to the part of the ship which it is in- tended to describe. FALL, see MEASURE, and WEIGHTS AND MEA- SURES. ' FALLING MOULDS, the two moulds which are applied to the vertical sides of the rail—piece, one to the convex, the other to the concave side, in order to form the back and under surface of the rail, and finish the squaring. - FALLING-SLUICES, in enginery, gates con- B / ,, 351 IEEA trived to fall down of themselves, and enlarge the water-way, on the increase of a flood, in a mill- dam, or the pond of a river navigation. FALSE ROOF, of a house, that part between the upper room and the covering. FANUM, among the Romans, a temple con- secrated to some deity. The deified mortals, among the heathens, had likewise theirfana : even the great philosopher Cicero erected one to . his daughter Tullia. Mem. Acad. Inscript. Vol. I. p. 488, et seq. .FANUM Jovrs, a temple of Jupiter, in Asia Minor, near the Thracian Bosphorus and the Syrntean promontory. FASCIA, FACIo, or FACE (from the Latin,fascia) a vertical member, of considerable height, but with a small projection, used in architraves and pedestals. In the Grecian Doric, the architrave under the band consists only of a single face; as does also the Ionic on the temple of the Illysus, in Attica. The Ionic on the temple of Erech- theus, at Athens, has three fasciee; as have several celebrated examples of the latter order. Vitru- vius allows only a single face to the Tuscan and Doric orders; that is, he makes it all plain, with- out any divisions or cantoning into parts or fasciae. In brick buildings, the jutting out of the bricks beyond the windows in the several stories, except the highest, are called fascias or fascia, These are sometimes plain, and sometimes moulded; but the moulding is only a sima reversa, or an ogee, with two plain courses of brick over it, then an astragal, and lastly, a boultine. 'FASCINERY, in enginery, wattled wood or hedge work, for groins, Sec. to retain the pebbles or beach, and break the waves on the shore. Smea- ton’s Reports, Vol. I. p. ’271. FASTIGIUM (Latin, a top or ridge) the same as PEDIMENT; which see. FATHOM (from the Saxon) a long measure of six feet, taken from the extent of both arms, when stretched in a right line. It is chiefly used in measuring the depth of water, quarries, wells, and pits. FAVISSA (Latin) a hole, pit, or vault underground, to keep something of great value. FEATHER-EDGED BOARDS, those of a trape- zoidal section; that is, thicker on one edge than on the other: they are used in the facing of wooden walls, and sometimes for the covering of to FIG an inclined roof, by lapping the thick edge of the upper board upon the thin edge of the lower one: boards of this description are also employed in fence walls," but are then most frequently placed vertically. FEATHER-EDGED COFING, see COPING. FEEDER, in cnginery, a cut or channel, sometimes called a carriage or catch drain, by which a stream or supply of water is brought into a canal: some- times the stream of water itself thus supplied is called a feeder. FEEDING—HOUSE, or SHED, a building in a farm, for the purpose of fattening neat cattle. It should have a dry warm situation, capable of free ventilation, and be well supplied with proper con- veniencies for the reception of food and water. FELLING, of timber, the cutting of trees close by the root, for the purpose of building : the proper season for this purpose, is about the end of April. FELT-GRAIN: when a piece of timber is cloven or split towards the centre of the tree, or trans- versely to the annular rings or plates, that po— sition of splitting is called the felt-grain,- and the transverse position, or rather that which is in the direction of the annular plates, is called the quarter-grain. FELTING, the splitting of timber by the felt- gram. FENCE (from the Latin defencz'o, to defend) any sort of construction for the purpose of enclosing land; as a bank of earth, a ditch, hedge, wall, railing, paling, Ste. FENCE, the guard of a plane which obliges it to work to a certain horizontal breadth from the ar— ris: all moulding planes, except hollows, rounds, and snipes’ bills, have fixed fences, as well as fixed stops; but in fillisters and plows the fences are moveable. FETCHIN G THE PUMP, the act of pouring water into the upper part of a pump, to expel the air contained between the lower box, or piston, and the bottom of the pump. FIGURE (from the Latin figura, likeness) in a ge. neral sense, the terminating extremes, or surface of a body. No body can exist without figure, otherwise it would be infinite, and consequently all Space would be solid matter. FIGURE, in geometry, any plane surface comprea hended within a certain line or lines. FIN M- ——ri Figures are either rectilinear or mixed, according as the perimeter consists of right lines, or curved lines, or both. The superficial parts of a figure are called its sides, or faces, and the lowest side its base; if the fi- oure be a triangle, the angle opposite the base is called the vertex, and the height of the figure is the distance of the vertex from the base. FIGURE, in architecture and sculpture, representa- tions of things made of solid matter, as statues, Ste. thus we say, figures of brass, of marble, of stucco, of plaster, 8C0. Figures in architecture are said to be detached, when they stand singly, in opposition to those compositions called groups. FIGURE, in conics, the rectangle under the latus rectum and transversum, in the hyperbola and ellipsis. FIGU RE, in fortification, the interior polygon, which is either regular or irregular. It is called a re- gular figure, when the sides and angles are all equal. FIGURES are either CIRCUMSCRIBED or IN- SCRIBED, EQUAL, EgUILATERAL, SIMILAR, REGULAR, or IRREGULAR. See these words. FIGURE OF THE DIAMETER, a name given to the rectangle under a diameter and its perimeter, in the ellipsis and hyperbola. FILLET (from the French, filet, a band) a small member, consisting of two planes at right angles, used to separate two larger mouldings, or to form a cap or crowning to a moulding, or sometimes to terminate a member, or series of members. The fillet is one of the smallest members used in cornices, architraves, bases, pedestals, 8m. It is called by' the French, reglet, bande, and bandelette; by the Italians, lista or Zistel/a. FILLET, in carpentry or joinery, any small timber scantling, equal to, or less than battens: they are used for supporting the ends of boards, by nail- ing them to joists or quarters, Sac. as in sound- boarding, and in supporting the ends of shelves. FILLET GUTTER, see GUTTERING. FILLING-IN PIECES, in carpentry, short tim- bers, less than the full length, fitted against the hips of roofs, groins, braces of partitions, Sec. which interrupt the whole length. FINE-SET : when the iron of a plane has a very small, projection below the sole, so as to take a very thin broad shaving, it is said to befine—set. FINE STUFF, in plastering, see PLASI'ERING. FIR * i FINIAL (from the Latin, finio, to finish) in the pointed style of architecture, a termination to a building, or principal part, in the form of a flower; used in high pointed pediments, cano- pies, pinnacles, &c. in the form of a lily, trefoil, acorn, pomegranate, endive, 8tc. FINISHING, a term frequently applied to the ter~ mination of a building, as also to the interior, in the plaster-work, in giving the last coat; and very frequently to the joiner’s work, as in the ar- chitraves, bases, surbases, 8w. FINISHING, in plastering, see PLASTERING. FIR (from the Welsh, fgrr ) a species of timber much used in building. The native fir of this country is called Scottish fir, which is chiefly employed in out-houses, offices, &c. It is much inferior to the Baltic timber, which is used wherever durability is required. See TIMBER. FIR, Wrought, that which is planed upon the sides and edges. FIR, Wrought andframed, such as is both planed and framed. ' FIR, thought,framed, and rehated, is what its name Imports. FIR, Wrought,framed, rebated, and beaded, is what its name imports. FIR BOARDS, the same as deal boards. See DEAL. F1 R-FRAMED, is generally understood of rough timber framed, without undergoing the operation of the plane. FIR-IN-BOND, a name given to all timber built in a wall, as bond-timbers, lintcls, wall-plates, and templets. FIR-POLES, small trunks of fir-trees from ten to six- teen feet in length, used in rustic buildings and out-houses. FIR-No-LABOUR, rough timber employed in wall- ing, without framing or planing. 7 FIRE-STONE, is used in joinery, for rubbing away the ridges made by the cutting edge of the ’ plane. . ' FIRE—PROOF HOUSES, such as are built without the use of any combustible matter: for this pur« pose, vaulted or cast-iron floors and roofs should be employed in every apartment. Vaulting is well adapted to the lower story ofa building, but if used in the upper stories, the walling must be car- ried up very thick, in order to resist the thrust of the arches; and this extra substance not only darkens the apartments, but occasions an enor- mous expense. The builder is therefore obliged 13 2 FLA 4 m to have recourse to other modes of construction for common purposes. The most convenient sub- stitute is cast-iron joists, vaulted between with brick, or covered with cast-iron boards, flanged and keyed together. F IRMER, FORMER, FURMER, FISI—LPON D a reservoir of water, for breeding, feeding, and preserving fish. FIS'I UCA (Latin) in antiquity, an instrument of wood, used 111 driving piles. It had two handles, and being raised by pullies, fixed to the head of large beams, was let fall directly on the piles; sometimes it was wrought by hand only. FIXED AXIS, in geometry, the axis about which . a plane revolves in the formation of a solid. FIXED POINTS, in carpentry, the points at the an- gles of a piece of framing, 01 where any two pieces of timber meet each other in a truss. If a third piecejoin the meeting of the two, it may be pushed or drawn in the direction of its length, without giving any cross strain. Fixed points are of the utmost use in shortening the bearings of the exterior timbers of the frame ;, neither is there any other method by which this can be so effectually done. When two sides of a frame are similar, any points in the length of the pieces may be supported by as many beams, extending between the opposite points: though this will keep the frame in equilibrio, it will not prevent it from being shaken by heavy winds, or lateral pressure. FLAGS, thin stones used 1n paving, hear one and a half to three inches thick, and of various lengths and breadths, according to the nature of the quarry. FLAKE WHITE, in painting, lead corroded by the, pressing of grapes, or a ceruse prepared by the acid of grapes. It is brought to England from Italy, and far surpasses, in the purity of its white- ness, and the certainty Of its standing, all the eeruses of white-lead made with us in common. It is used in Oil and varnish painting, for all pur- poses, where a very clean white is required. Flake white should be procured in lumps, as brought over, and. levigated by those that use it; as that which the colourmen sell ready prepared, is levigated and mixed up with starch, and often with white-lead, or even worse sophistications. FLANK (from the French,flanc) that part of a re- see TOOLS. FLI 1 ’—-—-_—_. *1 turn body which adjoins the front; as Hank-walls. In town houses, the flank-walls become party walls. FLANK ‘VALLS, in enginery, the same as the wing or return walls of a lock or bridge. F LAPS, folds or leaves attached to the shutters of a window, which are not sufficiently wide of themselves to cover the sash-frames, or to ex- clude the light. FLASHES, in enginery, a kind of sluices eIected upon navigable rivers, to raise the water upon any shoals therein, while the vessels or craft are passing. FLASHINGS, in plumbery, pieces of lead inserted in a wall for covering other pieces laid down for gutters, 8L0. FLAT CROWN, see CORONA. FLATTING, in house painting, a mode of painting in oil, without any gloss on the painted surface when finished. The paint is prepared with a mixture of oil of turpentine, which secures the colour; and when used in the finishing, leaves the paint quite dead, without gloss This is of great importance to those who are desirous to have their rooms continue white. Flatting is only used for inside work, and rarely for any but principal rooms. Nut oil is sometimes used for the purpose, but not often, on account of its high price. As useful aflatting as any is such as is ground In poppy oil. It IS pleasant In working, and leaxcs a beautiful white for some years; but it is rather expensive. FLEMISH BOND, see BRICKLAYING. FLEMIsu BRICKS, in bi Icklay In” strong bricks, of a yellowish colour, used in paving; their dimen~ sions are about 61‘? inches long, 2% broad, and 1% thick , 79. set upon their widest sides, or 100 011 edge, will pave a yard square, allowing a quarter of an inch for the joints. FLEXURE, 01 I‘LEXION (from the Latin) the op. position of curvature at a given point, where a straight line becomes a tangent, having the curve on both sides of it, one portion of the curve being concave, and that on the other side of the point of contact, convex. FLIGHT, in staircasing, a series of steps, whose treads are parallel, and terminate against a straight wall. FLIGHT, Leading, . ' ‘ .‘ FLIGHT: Retl‘,,,?;,g, } SCC STAIRLAbIr‘iLs FLO '5 FLO / -_————— = FLIGHT, is also used in London for a whole stair, between two adjoining floors. FLOAT, in plastering, see PLASTERING. FLOAT-BOARDS, the boards fixed to undershot _’ —* never exceed seven inches in width, nor be less than an inch in thickness. Floors are nailed either at both edges, or at one edge; the longitudinal joints, or those in the water-wheels, to receive the impulse of the stream. FLOAT-STONE, among bricklayers, LAYERs FLOATED LATH AND PLASTER, set fair for paper, see PLASTERIN G. V FLOATED, RENDERED, and SET, in plastering, see PLASTERING. FLOATING, in plastering, see PLASTERING. see BRICK- i FLOATING Burners, see BRIDGE. FLOATING RULES, in plastering, see PLASTERING. FLOATING SCREEDs, in plastering, see PLAS- TERING. FLOOD—GATE, a gate or sluice, that may be opened or shut at pleasure, to give passage to, or retain the water of a river liable to be swoln by floods. Flood-gates are necessary in many situations; as upon rivers where the water is retained for the service of mills, canals, navigations, docks, Ste. FLOOR (from the Saxon) the lowest horizontal side of an apartment, for walking, or for perform- ing different operations upon. Floors are of various kinds, according to the ma- terials of which they are constructed. Those made of brick and stone, are called pavements; I those Of earth are called cart/zen flows; those Of y plaster, lime floors; and those of timber are: called timberfloors. FLOOR, in carpentry, includes not only the boaiding for walking upon, but all the timber-work for its support. Boarded floors should never be laid till the building is properly covered in, nor indeed till the windows are glazed, and the plaster dry. laying of such floors, the boards ought to be rough-planed, and set out to season, a twelve- month at least, before they are used; that the na- tural sap may be thoroughly expelled, and thereby ; prevent the shrinking, which too frequently takes place on account of the use ofunseasoned timber. The best timber for flooring is yellow deal, well- seasoned. The quality of this material is such, that when laid, it will be easily kept of a good colour; whereas if white timber be used, it be- comes black in a very short time. . Narrow boards are called battens, which should Previous to the : direction of the fibres, are either square, ploughed and tongued, or rebated and lapped upon each other. Ploughed and tongued, and rebated joints may be used where the apartment is required to be air-tight, and where the stuff is suspected to be not sufficiently‘seasoned. The heading—joints are either square or ploughed and tongued. In square longitudinaljointed floors, it is’ necessary to nail the boards on both edges: but where the boards are dowelled, ploughed and tongued, or rebated, one edge only may be nailed, as the grooving and tonguing, or lapping, is sufficient to keep the other edge. down. Battens used in flooring are of three kinds, and are denominated best, second best, and common. The best battens are those that are free from knots, shakes, sap, and cross-grained fibres; the second best are free from shakes and sap, but in which small knots are suffered to pass. The common kind are such as remain after taking away the best and second best. The best floors are dowelled and nailed only at the outer edge, through which the nails are made to pass obliquely into the joists, Without piercing the upper su1tace of the boards, so that when laid no nails appea1; the heading joints of such floors are most commonly giooved and tongued. Some workmen dowel the battens over thejoists, but it makes firmer work to fix the dowels over the inter-joists. The gauge should be run from the under surface of the boards, which should be straightened on purpose. In the most common kind of flooring, the boards are folded together in the followingmanner: sup- posing one board already laid, and fastened, a fourth, fifth, sixth, or other board, is also laid and fastened, so as to admit of two, three, four, five, or more boards, between the two, but which can only be inserted by force, as the capacity of the opening must be something less than the aggregate breadths ofthe boards, in order that the joints may be close when they are all brought down to their places; for this purpose a board may be thrown across the several boards to be laid, which may be forced down by two or more menjumping upon it: this done, all the interme- diate boards are to be nailed down, and the opera- EL FLO tion is to be repeated till the whole is complete. This manner of flooring is called a folded floor. In folded floors, less than four boards are seldom laid together. N o attention is paid to the heading joints, and sometimes three or four joints meet in one continued line, equal in length to the ag- gregate of the breadths of the boards. In dowelled floors, the distances to which the dow- els are set, are from six to eight inches, generally one over each joist, and one over each interjoist; and, as has been already observed, the heading- joints of this kind of floor are generally ploughed “and tongued ; and no heading-joint of two boards ought to be so disposed as to meet the heading— joint of any other two boards, and thereby form a straight line equal to the breadth of the two boards. In common floors, the boards are always guaged from the upper side, then rebated from the lower side to the guage lines, and the intermediate part adzed down, in order to bring them to an uniform thickness. In doing this, great care should be taken not to make them too thin, which is fre- quently the case, and then they must be raised with chips, which present a very unstable resis- tance to a pressure upon the floor. Flooring is measured by throwing the contents into square feet, and dividing them by 100, which is called a square of flooring ; the number of hun- dreds contained in the superficial contents in feet are squares, and the remainder feet. The method of measuring floors, is by squares of ten feet on each side; the dimensions being multi- plied together, cut off two figures from the right of the product, and those towards the left give the number of squares, and the two on the right are feet. EXAMPLE.—-Suppose the length ofa floor 28 feet, and the breadth 24. The product gives six squares, seventy-two feet. When a naked floor is squared, and the contents found, nothing is deducted for the chimney, be- cause the extra thickness of the trimmers will make up for that deficiency. FLO FLOOR also denotes any portion of a building upon the same level: as basement floor, ground floor, one-pair floor, two-pair floor, 8L0. but when there is no sunk» story, the ground floor becomes the basement; the expressions one-pair floor, two- pair floor, 8tc. imply the floor above the first flight of stairs above ground, the floor above the second flight of stairs above ground, 8tc. The principalfioor of every building is that which contains the principal rooms. In the country they are generally on the ground floor; but in town, on the one-pair-of—stairs floor. ’ FLOOR, in carpentry, the timbers which support the boarding, called also naked flooring. See CAR- CASE FLOORING, and NAKED FLOORING. FLOOR JOISTs, or FLOORING‘JOISTS, such joists as support the boarding in a single floor; but where the floor censists of binding and bridging joists, the bridgings are never called floor joists. FLOORS 0F EARTH, or EARTHEN FLOORS, are commonly made of loam, and sometimes, espe- cially to malt‘on, of lime, brook—sand, and gun- dust, or anvil-dust from the forge; the Whole being well wrought and blended together with blood. The siftings of limestone have also been found exceedingly useful when formed into floors in this way. Ox blood and fine clay tempered together, so as to be perfectly blended, for some time before they are laid; and when done they should be repeatedly beaten down, and made perfectly smooth and straight. Earthen floors for plain country habitations are made as follows: take two-thirds lime and one Of coal-ashes, well sifted, with a small quantity of loam clay: mix the whole together, and temper it well with water, making it up into a heap: let it lie a week or ten days, and then temper it again. After this heap it up for three or four days, and repeat the tempering very high, till it becomes smooth, yielding, tough, and gluey. The ground being levelled, lay the floor with this ma- terial about two and half or three inches thick, smoothing it with a trowel: the hotter the season the better; and when it is thoroughly dried, it will make the best floor for houses, especially malt-houses. But should it be required to make the floor look better, take lime made of rag— stones, well tempered with whites of eggs, and cover the floor about half an inch thick with it, before the under flooring is quite dry. If this FLU - A‘s-uni be well-done, and thoroughly dried, it will appear when rubbed with a little oil, as transparent as metal or glass. In elegant houses, floors of this nature are made of stucco, or plaster of Paris, beaten and sifted, and mixed with other ingre- dients. W ell wrought coarse plaster makes ex- cellent safe upper floors for cottages, out-houses, 81c. when spread upon good strong laths or reeds. FLOR’ID STYLE, in pointed architecture, that beautiful style which was practised in England during the reigns of Henry VII. and Henry VIII. Its general external character consists of large arched windows, with very obtuse angles at the summit, and with numerous ramifications, con- sisting of light cuspidated mullions, filled with a variety of polyfoils. The buttresses, instead of having always rectangular horizontal sections, frequently have those of polygons, as in Henry VII.’s chapel, and are crowned with cupolas. The walls are loaded with niches, pinnacles, and croc- kets, terminating in open mullion-work, forming aparapet, or kind of balustrade, finished with finials or spiracles. The walls are decorated in- teriorly with panelling, moulded string-courses, niches, canopies, and other kinds of tracery, vaulted over with fan-groins. See ARCHITEC- TURE. FLUE, the long tube of a chimney, from the fire- place to the top of the shaft. See CHIMNEY. Flues in hot-houses and vineries, frequently make several turns on the floor, and then ascend to the wall with several horizontal turnings. In the construction of a stack of chimneys, no- thing can be more necessary than a drawing to shew the turnings of the flues, which will often prevent mistakes, and save the apartments from being incommoded with smoak. FLUSH, a term among workmen, signifying a con-- tinuity of surface in two bodies joined together. Thus in joinery, the style, rails, and munnions are generally made flush; that is, the wood of one piece on one side of the joint does not re. cede from that on the other. FLUSH, in masonry or bricklaying, signifies the ap- titude of two brittle bodies to splinter at the joints, when the stones or bricks come in contact when joined together in a wall. FLUSH AND BEAD, see BEAD AND FLUSH. FLUTES, or FLUTINGS, prismatic cavities de- pressed within the surface of a piece of architec- FLU w ture at regular distances, generally of a circular or elliptic section, meeting each other in an arris; or meeting the surface in an arris, and leaving a portion of the surface between every two cavities of an equal breadth; or diminishing in a regular progression; according as the surface is plane or curved, or applied to a prismatic or tapering body. 'Whenaportion of the surface is left between every two flutes, that portion is called a fillet. When the flutes are parallel, or diminish accord- ing to any law, the fillets are also parallel, or di- minish in the same degree. ‘ The proportion of each fillet to a flute is from a third to a fifth of the breadth of the flute. That species of fluting, in which the flutes meet each other without the intervention of fillets, is gene- rally applied to the Doric order; and that with fillets to the shafts of the Ionic and Corinthian orders. The flutes most frequently terminate in a spherical or spheroidal form, particularly in those which have fillets. In the Ionic order of the temple of Minerva Polias, at Athens, the upper ends of the fillets 'of the shafts of the co- lumns terminate with astragals, projecting from the surface of the fillet: the astragals may begin at a small distance from the top of the shaft, ascend upwards, and bind round the top of the flute. In the Corinthian order of the monument of Lysicrates, at Athens, the upper ends of the fillets break into leaves in a most beautiful man- ner. In the Doric examples of the temple of Theseus, and ofthe temple of Minerva, at Athens, and of the portico of Philip king of Macedon, in the island of Delos, the upper ends of the flutes terminate upon the superficies of a cone, immediately under the annulets, in a tangent to the bottom of the curve of the echinus of the capital. The same kind of termination takes place in the temple oprollo, at Cora, in Italy; but in this example, the conic termination of the flutes is not under the abacus, but at a small dis- tance down the shaft, leaving a small part quite a plain cylinder, and thus forming the hypotro- chelean or neck of the capital. In other ancient examples of the Dorie order, the flutes terminate upon a plane surface perpendicular to the axis of the columns, or parallel to the horizon, as in the Propylea at Athens. Palladio, and other Italian authors, have terminated the flutes of the shafts of their designs of Doric columns in the seg— FOL 8 FON w ments of spheres tauged by the surfaces of the fluung In the temple of Bacchus, at Teos, in Ionia, the lowe1 ext1emities of the flutes descend into the scape of the column. The Greeks never applied fluting to any member of the Dorie order, except the shaft, and this was their general practice. Fluting was used by the Romans almost in every plane, and in every cylindrical surface. See a very fine specimen in the corona of the cornice of the temple of Jupiter Stator, at Rome. FLYERS, a series of steps, whose treads are all parallel. FLYING BRIDGE, see BRIDGE. FLYING BUTTRESSES, in pointed architecture, arches rising from the exterior walls up to those of the nave of an ailed fabric, on each side of the edifice, for counteracting the lateral pressure of a gloined or vaulted r.Doof The eontrivance of flying buttresses is due to the a1chitects of the middle ages, and shews thei1 skill in the application of mechanics to the science of architecture. FOCUS (Latin) in geometry, and in the conic sec- tions, a point on the concave side of a curve, to which the rays are reflected from all points of such Curve. FOCUS, Of an ellipsis, hyperbola, or parabola, is particularly defined under the heads of ELLI PTIC CURVE, HYPERBOLIC CURVE, and PARABOLIC CURVE. FODDER, FUDDER, o1 FOTHER (Saxon) a ce1— tain quantity, p1op01tioued by weight. The weight of the fodde1 vaIies, in different counties, from 19% cwt. to 24 cwt. Among the plumbers in London, the fodder is 19% cwt. but at the Custom House 20 cwt. of lIle. FOLDED FLOOR, see FLOOR. FOLDING DOORS, such as are made in two parts, hung on opposite jambs, and having their vertical edge rebated, so that when shut, the rebates may lap on each other. To conceal the meeting as much as possible, a bead is most fre- quently run at the joint on each side of the doors. FOLDING JOINT, ajoint made like a rule—joint, or the joint of a hinge. FOLDS, or FLAPs, of shutters, those parts that are hinged to the shutters, and concealed behind when the shutters are in the boxings, so as to v cover the breadth of the window when the shut- ters and flaps are folded out in the breadth of the aperture. Folds are necessary when the walls are so thin as not to admit of shutters of sufficient breadth, when put together, to cover the opening. FOLIAGE, in a1chitecture, an a1tificial arrange- ment of leaves, fruit, 86c. See ORNAMENTS. FONT (from the Latin fans) the vessel used in churches to hold the water consecrated for the purposes of baptism. See BAPTISMAL FONT. FONTANA, DOMINIC, a distinguished architect, bow in 1543, at a village on the lake of Como. Having acquired the elements of geometry, he went to Rome, where his elder brother John was a student in architecture. Here he applied him- self most diligently to the study of the works of antiquity, and at length was employed by Car- dinal Montalto, afterwards Pope Sextus V. Mon- talto had already begun to display the magnifi- cence of his character, by unde1taking the con- struction of the grand chapel of the Mangel, 1n the chu1ch of St. Maria Maggiore. The pope, G1eg01y XIII. jealous of the munifieeuce of his cardinal, took from him the means of his designs, and thus put a stop to the works. Fontana, with a spirit worthy of a great man, went 011 with the building at his own expense, which so gratified the cardinal, that when he was raised to the pontifical chair, he appointed Fontaua to be his architect. The chapel and palace were finished in a splendid style; but this was a small part of the designs projected by Sextus. Besides completing the dome of St. Peter’s, he resolved to contribute to its grandeur, by conveying to the front of its piazza the obelisk, of a single piece of Egyptian granite, which had formerly decorated the Circus of Nero. This design had been contemplated by some of the predecessors of Sextus, but none had ac- tually attempted it. Sextus summoned archis tects and engineers from all parts, to consult upon the best means of effecting his purpose; Fontana’s plan obtained the preference, and he was able to execute what he had advanced in theory. This was regarded as the most splendid exploit of the age; and rewards and honours the most magnificent were bestowed on Fontana and his heirs. He was afterwards employed in raising other obelisks, and in the embellish-a ment of the principal streets of Home. He built the Vatican library, and had begun to make F00 F00 WM considerable additions to that place; but they were interrupted by the death of Sextus. One of Fontana’s great works was the conducting of water to Rome, the distance of fifteen miles, in an aqueduct supported on arcades. The suc- cessor of Sextus, Clement VIII. was prejudiced against the papal architect, and dismissed him; but his reputation caused him to be engaged by the Viceroy of Naples as architect to the king. He accordingly removed to Naples, in 1592, where he executed many works of consequence. His last efforts were directed to a new harbour at Naples, which he did not live to complete. He died at Naples in 1607, in his sixty-fourth year.———Gen. Bing. FOOT (Saxon) a measure, either lineal, superficial, or solid. The lineal or long foot is supposed to be the length of the foot of a man, and consists of twelve equal parts called inches; an inch being equal to three barley corns. Thus the English standard foot (31 EdW. I.) is : 12 lineal English inches, :: 36 barley-corns,: 16 digits, : 4 palms, = 3 hands, = 5; nails, = 1s} spans, = 1.5151 Gunter’s links, = .938306 feet of France, 2 .3047 metres of France. Geometricians divide the foot into 10 digits, and the digit into 10 lines, 8L0. ‘ The French divide their foot, as we do, into 12 inches; and the inch into 12 lines. See MEA- SURES. ' The foot square is the same measure, both in length and breadth, containing 144 square or su- perficial inches = 2.295684 square links; and the glazier’s foot in Scotland is : 64 square Scottish inches. The cubic, or solid Foot, is the same measure in all the three dimensions, containing 1728 cubic inches English : 6.128 ale gallons '= 3.478309 cubic links : .0283 cubic metres or steres of France. The foot is of dilierent lengths in difi'erent coun- tries. The Paris royal foot exceeds the English by nine lines and a half; the ancient Roman foot of the Capitol consisted of four palms, equal to eleven inches and seven-tenths English; the Rhinland, or Leyden foot, by which the northern nations go, is to the Roman foot as 950 to 1000. The portions of the principal feet of several na- tions, compared with the English and French, are here subjoined. The English foot being divided into one thousand VOL. 11. ll parts, or into twelve lines, the other feet will be as follow : Th. Pts. Ft. Inch. Li. London - - Foot 1000 Q 12 0 Paris foot, the royal, by Greaves - - 1068 _1 0 97 Paris foot, by Dr. Ber- nard - - - 1066 l 0 1 Paris foot, by Graham from the measure of half the toise of the Chatelet, the toise containing six Paris feet - - - ' 1065.41§- 0 O 0 By Monnier, from the same data - - 1065.351 0 O 0 From both these it may be fixed at - - 1065.4 1 O 9.4 Amsterdam — Foot 942 0 1 l 3 Antwerp - - ——- 946 0 11 2 Dort - - ——- 1184 1 2 2 Rhinland,or Leyden— 1033 1 O 4 Lorrain — — —- 958 O 1 1 4 Mechlin - - —- 919 0 1 1 0 Middleburgh - — 991 O 11 9 Strasburgh - -— 920 0 1 1 0 Bremen - - —- 964 0 1 1 6 Cologne - - —— 954 0 1 1 4 Frankfort on the ' Mayn - - — 948 O 11 4- Spanish - - —- 1001 0 1 1 0 Toledo - - -— 899 O 10 7 Roman - - —— 967 0 1 1 6 Bononia ‘- - -— 1204 1 2 4 Mantua - —- 1569 1 6 8 Venice — - —— 1162 l 1 Q Dantzic - —- 944 0 11 3 Copenhagen - —— 965 0 1 l 6 Prague - - —— \ 1026 1 0 3 Riga - - -— 1831 1 9 9 Turin - - — 1062 1 0 7 The Greek - —- 1007 1 0 1 Old Roman - —- 970 0 0 0 Roman foot, from the monument of Cossu- tius in Rome, by Greaves - _ - From the monument of Statilius, by the same Of Villalpandus, de- duced from the con- gius of Vespasian - c 967 O 00 972 0 00 996 0 00 FOO W Mr. Rapier, who has industriously collected a va- riety of authorities relating to the measure of'the old Roman foot, determines the mean to be nearly 968 thousandth parts of the London foot. And by an examination of the ancient Roman build- ings in Desgodetz’s Edi/ices Antiques de Rome, Paris, 1682, he concludes that the Roman foot, be- fore the reign of Titus exceeded 970 parts in 1000 of the London foot; and in the reigns of Severus and Diocletian fell short of 965. Phil. Trans. Vol. Ll. Art. 69, p. 774, &c. The Paris foot being supposed to contain 1440 parts, the rest will be as follow: Paris - - Foot 1440 Rhinland - - -- 1391 Roman - - —- 1320 London - - -— 1350 Swedish - - -— 39.0 Danish - - -— 1403 Venetian — - -—— 1.540%~ Constantinopoli tan —- 31620 Bononian - —- 168272; Strasburgh - -—- “282% Nuremburgh - —~ 134% Dantzic - - -— 1721—3. Halle — - —— 1320 In Scotland, this measure of length, though con- sisting of twelve inches, exceeds the English foot, so that 185 of the former is equal to 186 Of the latter. Accordingly the Scottish foot : 12 Scottish inches : 12-33- English inches, according to some, and 191—192? English inches, according to others. The glazier’s foot in Scotland : 8 Scottish inches. For a farther account of the foot, ancient and modern,and its proportions in different countries, see MEASURE. ,FOOT-BANK, or FOOT-STEP, in fortification, see BANQUETTE. FOOT OF THE EYE DIRECTOR, in perspective, that point in the directing line which is made by a vertical plane passing through the eye and the centre of the picture. FOOT OF A VERTICAL LINE, in- perspective, that ’ point in the intersecting line, which is made by a vertical plane passing through the eye and the centre of the picture. FOOT IRONS, in enginery, pieces of iron plate, used by navigators or canal diggers, to tie upon 10 FOR $225 that part of the sole of their shoes with which they strike the top of their spade or grafting tool, in digging hard soil. FOOT PACE, in hand-railing, a flat space in some stairs, always situated between the starting, or first step, and the landing. See STAiRCASlNG. FOOTING-BEAM, a term used in Cumberland, Westmoreland, Somersetshire, and perhaps in other counties, for the tie-beam of a roof. FOOTINGs, in bricklaying and masonry, projecting courses of stone, without the naked of each face of a superincumbent wall, used as a base to the wall, in order to prevent it from sinking and rocking by heavy winds. FOOTING DORMANT, the tie-beam ofarOOf; the term is used in Westmoreland. FORCE (from the Latin, fortis, strong) in philoso- phy, the cause Of motion in a body, when it be- gins to move, or when it changes its direction from the course in which it was previously mov- ing. While a body remains in the same state, whether of rest or of uniform and rectilinear mo- tion, the cause of its so remaining is in the nature Of the body, which principle has received the name of inertia. Mechanical force is of two kinds : that of a body at rest, by which it presses on whatever supports it, and that of a body in motion, by which it is impelled towards a certain point. The former is called by the names of pressure, tension, force, vis mortua, 8m. the latter is known by the appellation Of moving force, or was viva- To. the first of these are referred centry’ugal and cem- trz’petal forces ; because, though they also reside in the ois viva, they are homogeneous to weights, pressures, or tensions of any kind. For want of a true knowledge of the nature of force, we are accustomed to consider its measure by velocity, upon the supposition that under precisely similar circumstances, the velocity is equal to the force ;. an hypothesis highly probable, though not easily demonstrable. Velocity itself is a compound idea, derived from a certain relation between time employed and space described. Thus, if two bodies be supposed to move uniformly upon two different lines, the distances which they describe upon their respective lines in any given time, may be measured and represented by some standard measure, from which we acquire an idea of their relative velocity or force; and con- sidering velocity as an abstract number, it is said FOR to be equal to the space divided by the time; and thus we are led to consider velocity, or the space described in a given time, as the measure of force. , Force may also be expressed byother functions of velocity; for it may be proportional to the square or cube of the velocity; and La Place has very ingeniously proved that the difference between the proportionality of force to velocity, if any really exists, must be extremely small; whence he argues it is highly improbable that any does exist. If there were any material variation in this law, the relative motions of bodies on the surface of the earth would be sensibly affected by the motion of the earth; in other words, the effect of a given force would vary considerably, according as its direction coincided with, or was Opposed to that of the earth’s motion. The ef. fects of the same apparent forces would likewise vary in different seasons of the year; the velocity of the earth being less by about one-thirtieth in summer than it is in winter. But as no such varia- tion is discernible, we may justly conclude the proportion between force and velocity to be as 1 to l ; that is, there is no difference. To illustrate this, suppose two bodies moving upon one straight line with equal velocities; by impelling one of them with a force which increases its ori- ginal force, its relative velocity to the other body remains the same as if both had been primitively - in a quiescent state. The space described by the body, in consequence of its original force, and of that which has been added to it, becomes equal to the sum of what each of them would have caused it to have been described in the same time; therefore the force is proportional to the velocity. . This law, and that of inertia above alluded to, may be considered as derivedfrom observation and experiment: they are simple and natural, and are sufficient to serve as a basis for the whole science of mechanics. Early in the last century, awarm controversy arose relative to the measure of force, which was .carried on with considerable acrimony, though it now appears that the question was rather about words than facts. Sir Isaac Newton had defined the measure of force to ‘be “ the mass of a body multiplied into its velocity ;” which definition was not only convenient for the philo- sophical investigation. in whichvhe was engaged; 11 W FOR W FORCES, Composition cf but it was really mathematically just. But in another point of View, in which the effects of force may be said, without any impropriety, to depend on the massmultiplied into the square of the velocity, this product has been called the wt viva, and was considered by Bernouilli and Leibnitz as the true and universal measure of force, in opposition to Sir Isaac’s definition; though it now appears that they were led into an error, by not duly considering all the circumstances of the question at issue. The measure adopted by them, the 122's viva, however, merits attention, as in all cases of practical machinery it is frequently the most accurate, and always the most useful; at the same time it implies no contradiction to the Newtonian definition. But the force thus mea— sured ought to be distinguished by some appro- priate name, 1;. g. the vis mechanica, the New- tonian measure being applied to the vis matrix, .as suggested by Mr. VVollaston in the Bakerian Lecture for 1805. FORCE, Direction of, the straight line which it tends to make a body describe. If two forces be con- ceived to act on a material point, it is evident that if they both act in the same direction, they will mutually increase each other’s effect; but if they act in opposite directions, the point will move only in consequence of their difference, and it’ would remain at rest if the forces were equal. If the directions of the two forces make an angle with each other, the resulting force will take a mean direction ; and it can be demonstrated geo— metrically, that if, reckoning from the point of intersection of the two directions of the forces, we take on these directions straight lines to re- present them, and then form a parallelogram with such lines, its diagonal will represent their result- ing force, both as to its direction and magnitude. The resulting force thus determined, which like- wise represents the velocity of the moving point, may therefore be substituted as a force equivalent to the two component forces; .and reciprocally, for any force whatever, we may substitute any two forces, which according to this rule would compose it. Hence we see that any force what- ever may be decomposed into any, two forces, parallel to two axes situated in the same plane, and perpendicular to each other. To effect this, it is only necessary to draw from the first extre- mity of the line representing the force, two other C 2 FOR W lines parallel to the axis, and to form with such lines a rectangle, whose diagonal will be the force required to be decomposed. The two sides of this rectangle, or parallelogram, will represent the forces into which the given force may be decomposed, parallel to such axis. If the force be inclined to a plane in position, a line in its direction may be taken to represent it, having one of its extremities on the surface of the plane, and the perpendicular falling from the other ex- tremity will be the primitive force decomposed in the direction perpendicular to the plane. The straight line, which in the plane joins the other extremity of the line representing the force with the perpendicular (or the orthographic projection of the line of the plane) will represent the primi- tive force decomposed, parallel to the plane. This second partial force may itself be decomposed into two others, parallel to two axes in the same plane, perpendicular to each other. Thus we see that every force may be decomposed into three others, parallel to three axes perpendicular to each other; which axes are termed rectangular co-ordinates. Hence we have a very simple mode of obtaining the resulting force of any number of forces sup- posed to act on a material point; which was first adopted by Maclaurin, and has been followed by La Grange, in the Méchanique Analytique, and by La Place, in the Méckam'que Céleste. By de- composing each of these forces into three others, parallel to the given axes in position, and perpen— dicular to each other, we have all the forces pa— rallel to the same axis reduced to one single force, which latter will be equal to the sum of the forces acting in the same direction, minus the sum of those acting in a contrary direction: so that the point will be solicited by three forces perpendi- cular to each other. From the point of inter- section, or origin of the» co-ordinates, take three right lines to represent them in each of their di- rections, and on such lines form a rectangular parallelopipedon, and the diagonal of this solid will represent the quantity and direction of the resulting force of all the forces acting on the pomt. The principle of the composition of forces is of the most extensive utility in mechanics, and- is in itself sufficient for determining the law of equilibrium in every case. Thus, if we succes- sively compose all the forces, taking them by FOR two’s, and then take the result as a new force, we obtain one that is equivalent to all the rest, and which, in case of equilibrium, must equal 0, when the system under consideration has no fixed point; but if the conditions of the pro- blem insist on an immoveable point, the resulting force must necessarily pass through it. Though it is admitted by all writers on this sub- ject, that the most abstruse propositions may be deduced from a few simple principles, yet few are found who entirely agree in their. choice of such principles. The most advantageous, and indeed the most natural method, seems to be that wherein the relation between various forces in a state of equilibrum is first investigated, and then the consideration extended to a body in motion. If a body remain in equilibrium, at the same time that it is solicited by several forces, each force is supposed to produce only a tendency to motion, which is measured by the motion it would produce were it not checked by the power of the others: therefore, after expressing the effect of any one of the forces by unity, the relative effect of the others may likewise be expressed by lines or numbers. La Place merely assumes the two foregoing prin- ciples, and speaks of them as experimental facts; while Dr. Young does not scruple to declare them capable of demonstration. (See his Lectures.) But this difference of opinion is of little import- ance, since the principles themselves are univer- sally admitted. La Grange has founded the whole doctrine of the equilibrium of forces on the well-known principle of the lever, the composition of motion, and the principle of virtual velocity; each of which we shall here notice. The principle of the lever may be derived from the composition of forces, or even from much less complicated considerations. Archimedes, the earliest author on record, who at< tempted to demonstrate the property of the lever, assumes the equilibrium of equal weights at equal distances from the fulcrum, as a mechanical axiom; and he reduces to this simple and primi- tive case that of unequal weights, by supposing them, when commensurable, to be divided into equal parts, placed at equal distances on different points of the lever, which may thus be loaded with a number of small equal weights, at equal distances from the fulcrum. '& FOR » The principle of the straight and horizontal lever being admitted, the law of equilibrium in other machines may be deduced from it. Though it is not,without difficulty that the inclined plane is referred to this principle; the laws relative to which have been but lately known. Stevinus, mathematician to Prince Maurice of Nassau, first demonstrated the principle of the inclined plane by a very indirect, though curious mode of reasoning. He considers the case of a solid triangle resting on its horizontal base, whose sides then become two inclined planes: over these he supposes a chain to be thrown, consisting of small equal weights threaded together; the up. per part of such chain resting on the two inclined planes, and the lower ends hanging at liberty below the foot of the base. His reasoning is, that if the chain be not in equilibrio, it will begin to slide along the plane, and would continue so to do, the same cause still existing, for ever; thus producing a perpetual motion. But as this im- plies a contradiction, we must conclude the chain to be in equilibrio; in which case, as the efforts of all the weights applied to one side would be an exact counterpoise to those applied to the other, and the number of weights would be in the same ratio as the lengths of the planes; he concludes that the weights will be in equilibrio on the inclined planes when they are to each other as the lengths of the planes; but that when the plane is vertical, the power is equal to the weight; and that therefore, in every inclined plane, the power is to the weight as the height of the plane to its length. Virtual velocity is that which a body in equili- brium is disposed to receive whenever the equili- brium is disturbed; in other words, it is what a body actually receives in the first moment ofits motion. The principle of virtual velocity, in its most ge- neral form, is as follows: suppose a system in equilibrium composed of a number of points, drawn in any direction, by whatever forces, to be so put in motion, as that every point shall de- scribe an infinitely small space, indicative ofits virtual velocity; the sum of the forces being each multiplied by the space described by the point to which it is applied, in the direction ofthe force, will equal 0; the small spaces described in the direction of the forces being estimated as posi- tive, and those in a contrary direction as negative. 13 FOR _____— m 4"— Galileo, in his Treatise on Mechanical Science, and in his Dialogues, proposes this principle as a general property in the equilibrium of machines; he appears to have been the first writer on me- chanics, who was acquainted with it. His dis— ciple Torricelli was the author of another prin- ciple, which seems to be but a necessary conse- quence of Galileo’s. He supposes two weights to be so connected, that however placed, their centre of gravity shall neither rise nor fall; in every si— tuation, therefore, they will be in equilibrio. He contents himself with applying this principle to inclined planes; but it equally applies to all machines. Des Cartes deduced the equilibrium of different forces from a similar principle; but he presented it under another, and less general point of View, than Galileo had done; for he argues that to lift a given weight to a certain height, precisely the same force is requisite that would be sufficient to raise a heavier to a height proportionally less, or a lighter to a height proportionally greater; there— fore two unequal weights will be in equilibrio, when the perpendicular spaces described by them are reciprocally proportional to them. In the application of this principle, however, only the spaces described in the first instant of motion are to be considered; otherwise the accurate law of equilibrium will not be attained. Another principle, recurred to by some authors in the solution of problems relative to the equili- brium of forces, arises out of the foregoing, viz. When a system of heavy bodies is in equilibrio, the centre of gravity is the lowest possible. For the centre of gravity of a body is the lowest, when the differential of its descent is 0, as can be demonstrated from the principle ale maximus et minimus; that is, when the centre of gravity neither ascends nor descends by an infinitely small change in the position of the system. J. Bernouilli first perceived the great utility of generalising this principle of virtual velocity, and applied it to the solution of problems; in which he was followed by Varignon, who has de- voted the whole of the ninth section of his Nou- ve/le Méclzam'que to demonstrate its truth and exemplify its utility in various cases in statics. In the IlIémoz'res de Z’Académie for 1740, Mauper- tuis proposed another principle, originating in the same source, under the title of “ The Law of Repose 5” which was afterwards extended by ’“ FOR Euler, and explained in the Memoirs of the Berlin Academy for 1751: and the principle as- sumed by Mons. Courtivron, in the Mémoires (Ze Z’Académt'e for 1748-9, is of the same nature: viz. that of all the situations which a system of bodies can successively take, that wherein the system must be placed to remain in equilibrio, is that in which the vis viva is either a maximum or ami- nimum, because the m's viva is the sum of the re- pective masses composing the system, each mul- tiplied into the square of its velocity. Of all these methods, that of virtual velocity ap- pears to be most generally useful; indeed all the others are derived from it, and are serviceable in proportion as they approach nearer to it. La Grange has given practical examples of the analytical pro- cesses for determining general formulae or equa- tions for the equilibrium of any system; and La Place has demonstrated the principle on which the calculus is founded. In the foregoing observations, force is supposed to be the product of the mass of a material point, by the velocity it would receive if entirely free. By confining these considerations to the case of a single material point, the conditions of equili- brium will be found to be analogous to those above spoken of, but much simplified. The most elementary equation to express the state of equilibrium of a material point, actedon by any number of forces, is, that every force, multiplied by the element of its direction, equals 0: thus, suppose the point to change its position in an infinitely small degree in any direction; then, in thecase of equilibrium, if every force be multiplied by the elementary space ap— proached to, or receded from by the point, the force being estimated in its direction, the product will be 0. , Here the point is, supposed to be free; but if constrained to move on a curved surface,it will experience a reaction equal and contrary to the pressure which it exerts on such surface, but per- pendicular to it, or in the direction of the radius of the curve. This reaction may be considered as a new force, which, multiplied by the elements of its direction, must be added to the former equation. But if the variation of position, in- stead of being taken arbitrarily, be taken upon the curve, so as not to alter the conditions of the problem, the preceding equation will still hold good, because the elementary variation of the ra- 144 M FOR“ W» _ h“ dius is equal to O, as is evident from inspection. Again, if the magnitude of any force, or its in- tensity, multiplied by the distance of its direction from any fixed point, be denominated its moment, relatively to such point, it will be found that the sum of the moments of the producing forces is always equal to that of the resulting force; and in case of equilibrium, the sum of the moments of all the forces equals 0. If the forces acting on a point, or on a system of points, he not so proportioned as to maintain the system in equilibrium, a motion must necessarily take place, the laws of which may be deduced from an extension of the principles laid down for investigating the state of equilibrium; a method pursued by La Grange, and after him, by La. Place. The former combines the principle of virtual velocities with that of D’Alembert, which is very simple, and though long unobserved, may be considered as an axiom. It is as follows: If several bodies have a tendency to motion, in directions, and with velocities, which they are constrained to change in consequence of their reciprocal reaction; the motion so induced may be considered as composed of two others, one of which the bodies actually assume, and the other such, that had the bodies been only acted . upon by it, they would have remained in equili- brium. This theorem is not of itself sufficient to solve a problem, because it is always necessary to derive some condition relative to the equilibrium from other considerations; and the difliculty of deter- mining the forces and the laws Oftheir equilibrium, sometimes renders this applicationmore difficult, and the process more tedious, than if the solution were performed upon some principle more com- plex and more indirect. To ebviate this objec- tion, therefore, La Grange attempted to combine the principle of D’Alembert with that of virtual velocity; in which he was so successful, that he was enabled to deduce the general equations re- lating to the forces acting on a system of bodies. His description of the nature of this method is as follows: ' To form an. accurate conception of the mode in which these principles are applied, it is necessary to recur to the general principle of virtual velocity, viz. When a system of material points, solicited by any force, is in equilibrium, if the system re- ceive ever so small an alteration in its position, FOR ‘ 15 FOR every point will naturally and consequently de- scribe a small space; each of which spaces being multiplied by the sum of each force, according to the .direction of such force, must equal 0. Now supposing the system to be in motion, the motion that each point makes in an instant may be considered as composed of two, one of them ' being that which the point acquires in the follow- ing instant; consequently, rheother must be de- stroyed by the reciprocal action of the points or bodies upon each other, as well as of the moving forces by which they are solicited. There will therefore be an equilibrium between these forces and the pressures or resistances resulting from the motions lost by the bodies from one instant to another. Therefore, to extend to the motion of a system of bodies, the formulae ofits equilibrium, it is only necessary to add the terms due to the last-mentioned forces. . The decrement of the velocities, which every par- ticle has m the direction of three fixed rectangu— lar co—ordinates, represents the motions lost in rthose directions; and their increment represents such as are lost in the opposite directions. There- fore, the resulting pressures or throes of these motions destroyed will be generally expressed by the mass multiplied into the element of the ve- locity, divided by the element of the time; and their directions will be directly opposite to those of the velocities. , By these means the terms required may be ana— lytically expressed, and a general formula ob- tained for the motion ofa system of bodies, which will comprehend the solution of all the problems in dynamics; and a simple extension of it will give the necessary equations for each problem. One of the greatest advantages derived from this formula is, that it gives directly a number of general equations, wherein are included the prin- ciples or theorems, known under the appellations of conservation of the vis viva; conservation of the motion of the centre of gravity,- conservation of equal areas; and the principle (f the least action. Of these, the first, the conservation of the vis viva, was discovered by Huygens, though under a form somewhat different from that which we now give to it. As employed by him, it consisted in the equality between the ascent and descent of the centre of gravity of several weighty bodies, which descend together, and then ascend separately by the force they had respectively acquired. But by the known properties of the centre of gravity, the space it describes in any direction is expressed by the sum of the products of the mass of each body by the space such body has described in the same direction, divided by the sum of the masses. Galileo, on the other hand, has shewn in his pro- blems, that the vertical space described by a weighty body in its descent is proportional to the square of the velocity acquired, and by which it will reascend to its former elevation. The princi- ple of Huygens is therefore-reduced to this; that in the motion of a system of‘bodies, the sum of the masses by the squares of the velocities is con- stantly the same, whether the bodies descend conjointly, or whether they freely descend sepa- rately through the same vertical channel. This principle had been considered only as a simple theorem of mechanics, till J. Bernouilli adopted the distinction, established by Leibnitz, between such pressures as act without producing actual motion, and the living forces, as they were termed, which produced motion; as likewise the measure of these forces by the products of the masses by the squares of the velocities. Bernouilli saw nothing in this principle but a consequence of the theory. of the vis viva, and a general law of nature, in consequence of which, the sum of the vis viva of several bodies preserves itself the same, as long as they continue to act upon each other by simple pressures, and is always equal to the simple vis viva, resulting from the action of the forces by which the body is really moved. To this principle he gave the name of conservatio vivium vitamin, and successfully employed it in the solution of several problems that had not before been effected. From this same principle, his son, D. Bernouilli, deduced the law of the motion of fluids in vases, which he explains and renders very general in the Berlin ItIemoirs for 1748: before his time, it had been treated only in a vague and unsatisfactory manner. The advantage of this principle consists in its affording immediately an equation between the velocities of the bodies and the variable quantities which determine their position in space; so that when by the nature of the problem these variable quantities are reduced to one, the equation is of itself sufficient for its solution, as in the instance of the problem relating to the centre ofoscillation. In general, the conservation of the vis viva gives M FOR t _‘ afirst integral of the several differential equa- tions of each problem, which is often of great utility. The second principle above alluded to, conserva- tion of the motion ofthe centre ofgravz'ty, is given by Sir Isaac Newton in his Principia, as an ele- mentary proposition; where he demonstrates, that the state of repose or of motion of the centre of gravity of several bodies, is not altered by the reciprocal action of these bodies, in any man- ner whatever: so that the centre of gravity of bodies acting upon each other, either by means of cords or ofhlevers, or by thelaws of attraction, remains always in repose, or move uniformly in a direct line, unless disturbed by some exterior action or obstacle. This theorem has been extended by D’Alembert, who has demonstrated, that if every body in the system be solicited by a constant accelerating force, either acting in parallel lines, or directed towards a fixed point, but varying with the dis- tance, the centre of gravity will describe a simi— lar curve to what it would have done, had the bodies been free. And, it might be added, the motion of this centre will be the same as if all the forces of the bodies were applied to it, each in its ~ proper direction. This principle serves to determine the motion of the centre of gravity, independently of the re- spective motions of the bodies; and thus it will ever afford three finite equations between the co- ordinates of the bodies and the times; and these equations will be the integrals of the differential equations of the problem. Thethird principle, the conservation of equal areas, is more modern than the two former, and appears to have been separately discovered by Euler, D. Bernouilli, and D’Arcy, about the same period, though under different forms. Euler and Bernouilli describe the principle thus: In the motion of several bodies round a fixed centre, the sum of the products of the mass of each body by the velocity of rotation round the centre, and by its distance from the same centre, is always independent of any mutual action ex- erted .by the bodies upon each other, and pre- serves itself the same as long as there is no exte- rior action or obstacle. Such is the principle described by D. Bernouilli in the first volume of the Illemoires of the Berlin Academy, 1746; and by D’Alembert, the same year, in his Opuscula. F0 R t The Chevalier D’Arcy, also in the same year, sent his Memoir to the Academy of Paris, though it . was not printed till 1752, wherein he says, “ The sum of the products of the mass of each body by the areatraced by its radius vector about a fixed point, is always proportional to the times.” This principle is only a generalisation of Sir Isaac’s theorem of equality of areas described by centripetal forces: and to perceive its analogy, or rather its identity with that of Euler and Ber— nouilli, it is only requisite to recollect, that the velocity of rotation is expressed by the element of the circular are divided by that of the time; and that the first of these elements multiplied by the distance from the centre, gives the element of the area described about it; so that this latter principle is only the differential expression of that of the Chevalier, who afterwards gave the same principle in another form, which renders it more similar to the preceding, viz. The sum ofthe pro- ducts of the masses by the velocities, and by the perpendiculars drawn from the centre to the direc- tion of the forces, is always a constant quantity. Under this point of view, M. D’Arcy set up a kind of metaphysical principle, which he denomi- nates the conservation of act-ion, in opposition to, or rather as a substitute for the principle of the least action. But leaving these vague and arbitrary denomina- tions, which neither constitute the essence of the laws of nature, nor are able to raise the simple results of the known laws of mechanics to the rank of final causes, let us return to the principle in question, which takes place in every system of bodies acting on each other in any manner whatever, whether by means of cords, inflexible lines, attractions, Ste. and also solicited by forces directed to a centre, whether the system be en- tirely free, or constrained to move about it. The sum of the products of the masses by the areas de- scribed about this centre, and projected on any plane, is always proportional to the time : so that by referring these areas to three rectangular planes, we obtain three differential equations of the first order, between the time and the co—ordi- nates of the curves described by the bodies; and in these equations, the nature of the principle properly exists. The fourth principle, that of the least action, was so denominated by Maupertuis, and has since been rendered celebrated by the writings of seven FOR 17 ”H‘-w_..._—_ -_.._— ral illustrious authors. Analytically it is as fol- lows: In the motion of bodies acting upon each other, the sum of the products of the masses by the velocities, and by the spaces described, is a minimum. Maupertuis has published two Me- moirs on this principle; one in the Transactions oft/2e Academy of Sciences, for 1744; the other, in those of the Academy of Berlin, 1746; wherein he deduces from it, the laws of reflection and re- fraction of light, and those of the shock ofbodies. It appears, however, that these applications are not only too partial for establishing the truth of a general principle, but they are in themselves too vague and arbitrary; so that the conse- quences attempted to be deduced become uncer- tain: this principle, therefore, deserves not to be classed with the three foregoing. There is, how- ever, one point of view, in which it may be con~ sidered as more general and exact, and which alone merits the attention of geometricians. Euler first suggested the idea at the close of his Treatise on Isoprimetrical Problems, published at Lausanne, in 1744, wherein he shews that in trajectories described by central forces, the integral of the ve- locity multiplied by the element of the curve is constantly either a maximum or a minimum; but he knew of this property only as pertaining to in- sulated bodies. La Grange extended it to the motion ofa system of bodies acting on each other, and demonstrated a new general principle, biz. That the sum of the products of the masses by the integrals of the velocities multiplied by the elements of the spaces described, is always a lnaXlanln 01' a mmlmum. From a combination of this latter principle with that of the conservation of the vis viva, many dif- ficult problems in dynamics may be solved; as exemplified by La Grange in the .Memoirs (ft/1e Academy quurz'n, Vol. ll. La Place, in the JlIéchanique Céleste, treats the doctrine of dynamics much in the same manner as La Grange, but he carries his investigations much farther. He agrees with that writer in. adopting the principle of D’Alembert, and in re— solving every motion ,into two; that which the particle had in the preceding instant, and that which would have maintained it in equilibrio: but he differs from him in not admitting the prin- ciple of virtual velocity to be assumed as a fun- damental axiom; which he demonstrates by a regular train of inductions. 1:'-OL. II. FOR \ After having established nearly the same formulae, or differential equations, and deduced all the gene- ral principles in the mannerjust described, he in- troduces others in the nature of corollaries, many of which merit peculiar consideration. From the principle of the conservation of areas, it follows, that in the motion ofa system of bodies solicited only by their mutual attraction and by forces directed to the origin of the co-ordinates, there exists a plane passing through such origin, which possesses the following remarkable pro- perties: 1. That the sum of the areas traced on the plane by the projections of the radii vectores of the bodies, and multiplied by their respective masses, will be the greatest possible. 2. That such sum is also equal 0 upon all the planes perpendicular to it. As the principle of the vis viva, and that of areas, subsist relatively to the centre of gravity, even though the latter be supposed to have a rectilinear uniform motion, it follows, that a plane may be determined as passing through this moveable origin, on which the sum of the areas, described by the projections of the radii veetores, and mul- tiplied respectively by their masses, may be the greatest possible. This plane being parallel to the one passing through the fixed origin, satisfies the same conditions; and another plane passing through the centre of gravity, and determined according to the foregoing conditions, will re- main parallel to itselfduring the motion of the system; a circumstance of considerable utility and importance. To this we may add, that any plane parallel to the last-mentioned, and passing through any of the bodies, partakes of analagous properties. La Place next examines how far these results would be changed, if other relations subsisted between the force and the velocity. Force, he observes, may be expressed in a great variety of ways relatively to the veloity, besides that of the simple law of proportionality, without im- plying any mathematical contradiction. Sup- pose the force to be some other function of the velocity (analytically expressed by F=

, b C W ,"'1:;’\\\ ' ‘ ,uH 8c / \, ' \\\\\\\ [m/enfizi (WEN. \\\\\\\\\\§§\\\\\\\\\ J KI], \ V T \ \ \ X \\ \\\\\\\ :2 W .......................... \\\\§:\\§\\\ ‘\ F2211. I," \\ A R B 1 ( D [)n/ml {71’/j1’1'(~/m/.,.un. Landon,Dzb/idhe'd[378.1’1'vllvlsmz.Jhlb’m‘fie’ld "Eu-dourSurat/(5'12‘ Eugm'nwifly.AWE i; HAN 71 M 1 . lines, drawn by a thin piece of wood bent upon that side; the portion of the cylinder thus form- ed will represent the part of the rail intended to be made. The business of hand-railing is to find the moulds for cutting a rail out of planks. Though hand-railing is only treated of here, as connected with cylindrical well-holes; it is equally applicable to rails erected upon any seat whatever. The mould, which applies to the two faces of the plank, regulated by a line drawn on its edge, so as to be vertical when the plank is elevated to .. its natural position, is called the face-mould; or sometimes the racking-mould. A parallel mould, applied and bent to the side of the rail—piece, for the purpose of drawing the back and lower surface (which are to be so formed that every level straight line, directed to the axis of the well-hole, from every point of the side of the rail formed by the edges of the falling-mould, shall coincide with the surface) is called afalling- mould. When the upper surface of the plank is not at right angles to a vertical plane passing through the chord of the plan, in order to cut the corresponding portion of the rail out of the least thickness of wood, the plank is said to be sprung. A right-angled triangular board, made to the rise and tread of a step, is called the pitch-board. In a stair-case, where there are both winders and flyers, two pitch-boards will be concerned, of different treads, but of the same heights, as the height of the steps must be equal. The bevel by which the edge of the plank is re- duced from the right angle, when the plank is sprung, in order to apply the face-mould, is called the spring oft/re plank; and the edge or narrow side thus reduced, is called the sprung edge. The bevel by which the face-mould is regulated to each side of the plank, is called the pitch. The formation of the upper and lower surface of a rail is called the falling oft/1e rail. The upper surface of the rail is called the back. . The first thing in the practice is to spring the plank, then to cut away the superfluous wood, as directed by the draughts formed by the face- mould. This may be cut so very exactly with a saw, by an experienced hand, as to require no HAN l farther reduction; and when set in its place, the surface on both sides will be vertical in all parts, and in a surface perpendicular to the plan. In order to form the back and lower surface, the falling-mould is applied to one side, which is ge- ‘nerally the convex side, in such a manner, that the upper edge of the falling-mould at one end may coincide with the face of the plank, the same in the middle, and to leave so much wood at the other end to be taken away, as not to reduce the plank on the concave side. The piece of wood. to be thus formed into the wreath or twist, being agreeable to three given heights. This descrip- tion is general, in order to comprehend the following construction of the moulds them- selves, which, when explained, we shall then enter into a more particular detail of mar application. T 0 construct the falling and face moulds of a rail to a level landing, supposing the plane of the plank to rest upon the middle point qf the section, which separates the upper and lower circular parts, and to rest upon the line parallel to, and in the middle ofthe straight part, so as to have the grain if the- wood parallel. _ Plate 1. Figure 1.-——The falling-mould of the hand—rail: BC the extension of the semicircular part; B A and C D the treads of the adjoining flyers. To find the extension of the semicircular part, from the middle point, I, of B C, draw I K L per- pendicular to B C; divide the radius I K into- four equal parts, and repeat one of these parts from: K to L seven times; draw the diameter M N pa- rallel to B C; join L M and L N, and prOduce each of these lines to B and C; then BC is the rec- tification of the semicircumference M I- N. Draw B T and D H perpendicular to A D; make B E. equal to the height of a step; I O on the straight line I L, one step and a half; C F equal to the height of two steps; and D H equal-to the height- of three steps; join A E and H F, and through 0 draw P Q parallel to B C; produce A E and H F to meet P Q at P and Q; then cut off the angles at P and Q by equal touching curves, one at each; then A E O F is the middle of the fall- ingmould; and as the rail is generally made two inches deep, draw two parallel lines each an inch distant from this central line, and S U 8: will be the upper edge of the falling-mould, and 5‘ Y J the lower edge... HAN ' "" O I Tojind t/eeface—mould (y'tlze hand—rail. Figure Q.—-—-At any convenient place lay down the half plan, a bcdefa, of the handsrail; a 1) cf be— ing the straight part of the rail, and c d ef the plan ofthe circular part; draw g c d parallel to af or I) c; bisect (I e at It, anddraw It i perpendicular to g (i; make lei equal to I U, Figure 1, and the angle 11 ii; equal to the angle G H F; let It repre- sent the middle point of the section between the two circular parts; and suppose it to represent the resting point in the middle of the section, which separates the straight and circular parts; make B ll, Figure 1, equal to c b orfa, Figure 2, and draw R S, Figure 1, perpendicular to A B, cut- ting the upper edge of the falling-mould at S; make h 7', Figure 2, equal to B T, Figure 1, and draw rs, Figure 2, parallel to g d, cutting i It at ‘6; make It m equal to r s, and join m n, which is the directing ordinate; from I: draw kl parallel to m n, and I: Z is the intersection of the plane of the plank; find the cointersection lt‘ t, as in the SECTIONS OF CYLINDERS, or as in the subse- quent part of this \Vork, under SOLID ANGLES. ' bfiud any point in the curve oft/1e fizce-mould.—- Draw u v a) parallel to k 1, cutting k d at u, and the concave side of the plan at v, and the convex side at a"); draw u .1? parallel to It i, cutting k i at 9;,- draw xy ,2 parallel to k 1‘; make :r y equal to u v, and x 2 equal to u It); then 3/ is a point in the concave side of the face-mould, and z is a point in the convex side. The pitch-bevel shewn by the dark lines, is found by drawing a vertical line to the pitch-line, and the angle formed by these lines is the pitch-bevel. In this manner as many points may be found as will be necessary to complete the concave and convex sides of the falling-'inould; or rule each system of lines at the same line, thus; take as many points in the convex side of the plan as will be found requisite; through all these points draw lines parallel to k l, to cut g d; from all the points of division in g d draw lines parallel to h i, cutting lrz'; through all the points ofdivision in It i draw lines parallel to k t; terminate each line from the point of intersection equal to the corresponding outer and inner ordinates of the plan, and through the points found by its concave side draw a line; also through the points found by the convex side of the plan draw another curve: then the corresponding points found for each ex- tremity of the plan will complete the face-mould. ‘2 TIA N It is evident that the parts 34, 5-6 of the face- mould corresponding to a (7, of on the plan, is a parallelogram, therefore if the point 6, where the concave side and the straight parts meet, and the point 5, where the convex and straight parts meet, are found, and joined by the line 5‘6; and if 5-4 and 6-3 be drawn parallel to l; i, and the point q, corresponding to 0, be found, by drawing 4—3 through q, the straight part of the face-mould will be completed. The line of separation 5-6 will be more cxactlv determined as follows: Through n draw 72 7 pa- rallel to it 2', cutting k 2' at 7; then find onlv one of the points 5 or 6, say 5; draw 5-7“; then 5-6, which is a part of 5-7, is the line of separation. This face-mould will answer for the upper, as well as the lower half. The angle 12-1 is the spring of the plank, and is found in the same manner as in solid angles, and having the intersection and cointersection, the face mould is found as in the sections ofa cylinder. The face-mould might have been found as in Figure 3, by taking the heights from a line drawn over the face-mould parallel to A I), Figure l, and laying the plan upwards, as in Figure 3, then proceeding with the operation downwards, as di— rected in Figure 9. upwards. Or, if the drawing is inverted, the line V H, Figure 1, will become the base of the heights, and every thing else will be in the same position as in Figure 2. In the application of the moulds, imagine the plank set up to the pitch, and in the same way spring the edge from the under side for the lower piece, and from the upper side for the upper piece. To apply the moulds to the plank, now supposed to be sprung 0r beveled, take the pitch and draw the vertical line, the stock of the bevel being ap- plied to the acute edge of the plank, upwards or downwards, as the case may require: then draw a line equal to the distance of 3-6 from I; 2', ,upon each plane of the plank parallel to the side; then the point 8 being kept to the end of the vertical line, and the side 3-6 upon the parallel line, draw round all the edges of the mould; turn the mould to the other side, apply the point 8 to the other end of the vertical line, and the part 3-6 upon the line drawn parallel to the face, and draw round all the edges as before; then cut away the super- fluous stuff. The sides of the piece intended to form the twist must be perfectly cylindrical, an! , ..m\\\\\\\\\\\ . - l — - ‘\ ~\\\\\\\\\\\\\\\\\\\\\\ ’ \ \ \ , . KQ®WW§§fl \\\~\\\\\\‘ - x Fly, 2_M01I 41 \\ 1144.1. ------ \ u .... [711/5anny h’ldl’ll Z 7 Pub d b 'P1H" 7 f 3 ”117220 I )0. f 1’!” (’Iltit I l' I 4 . . l x . -- Z, k3}? 11 (f I ,’ It [50,2 / ”Will . , r I En glut/I'd {71 ' (‘mmsmmq ,-‘ g ‘9‘. ‘ ‘ . K. 95...:sz , 2+ «“53 , . x;\¢>n ' w; J ,- //////.,,h..wfl_w,// 74‘4""' \ HAND RAILING /////,///////1 HUMMHHHH ////// / . z 3/ 23/7 if”, a”? V13 . ‘ ‘tr. II [mulon . htblllrhtd by J‘ Barrie/«I. Maniamr . I Invented Sc men by P. M'dwbow. HAN '7 W all the parts so formed, that a straight line or edge may apply to any point, at the same time that it coincides with the surface, and is parallel to the vertical line drawn on the edge of the plank. The falling-mould is thus applied: Drawaline upon the ends of the solid piece, at right angles to the vertical sides, from zero at each end, next to the upper side; then apply the upper edge of the face-mould next to the top of the plank, and each end to the corresponding end of the piece, bending it so that all parts may be in contact with the stuff; then draw a line round all the edges, and it will shew the superfluous wood to be cut off. To construct the face-mould of a hand-rail to a stair upon. a level landing, in two parts, round a semicircular newel; so that when the two pieces are united orjixed in their places, the grain or fibres of the trend will mitre at thejoint. Plate ll.———Let Figure 1 be the rail stretched out, as in the preceding example: draw the chord of the rail, ilr, Figure 2, No. l; bisect the end it: u at a, and the other end in) at c; drawj z I) C per- pendicular to the chord k i, cutting the concave and convex sides atz and C ; make z 6 equal to to, and E C, Figure 1, equal to u) C, Figure 2, No. 1, extended: draw C D, Figure l, perpendicular to A E, cutting the upper edge of the falling- mould at D, and the lower edge at H. In Figure 2, No. I, draw a d perpendicular to k i, and c e parallel to a d; make a d equal to A B, Figure 1; 1-, c, Figure Q, No. :1, equal to E F, Figure l ; and of, Figure ‘2, No. 1, equal to C D, Figure 1; join a c and dc, Figure ‘2, No. 1; drawfg parallel to a c, cutting d e in g; draw g t parallel to e 6, cutting a r in t,- join t I); draw cg parallel to t1), cutting the convex side of the plan at 2/; produce 3/ c to cut the chord .k. i at ‘2; draw 2 h parallel to c e; make 2 h equal to ce; draw It K parallel to a d,- make I; K equal to a (I; join h K; produce h K and i I: to meet each other in I; draw [m paral- lel to H): from any point, 172, in lm, draw m 3 perpendicular to l i; produce i l to 3), cutting m 3 at :3; through 3 draw 4 n perpendicular to h l,- produce h l to 4; make 3 0 on pl equal to 3 4; join 0 m; make 4n equal to o m, and join n l: then draw ordinates on the plan parallel to lm, to cut both sides of it, and also the chord It i; from the intersections in It i, draw lines parallel to e e, to cut h l; from the points of section in h l, draw lines parallel to la; make the lines thus drawn i 0L. 1t. HAN parallel to l 12, equal to the corresponding lines on the plan; and a curve drawn through these respect-ivepoints will give the face-mould. In drawing ordinates upon the plan, care should be taken that an ordinate be drawn through the points upon each side of the plan at the line of separation of the straight and circular parts, and also through each extremity of the ends; or, by finding M N, the line of separation, and the point K, the point L will be found by drawing K L pa- rallel to N M, and M L parallel to N K; and thus the portion M N K L, corresponding to '0 x k u on the plan, will be obtained. The anglep o m gives the spring-bevel, Figure 2, No. ‘3; and the angle s r 9 gives the pitch-bevel, Figure 2, No. 2. The face—mould is applied to the plank by laying the points P and K close to the edge that is sprung ; then drawing the pitch- bevel, No. 2, from either point P or K ; for it is not necessary to draw them from both, as the corresponding point will be found upon the other side of the plank; then proceed with the remain- ing parts as before directed. To spring the plank for a level landing through two given points, so as to parallel the grain. Plate [IL—Let No. 3 be the falling-mould, as before: draw any line, CA, for the base of the heights of the face-mould; then C D is the lower height, Where the two wreathed pieces meet, and A B is the upper height, making allowance for the squaring of the joint. Lay down the plan A h C, No. 1; draw C n parallel to A h; draw AB perpendicular to Air; make A B equal to A B, No. 3, and the angle A B E, No. 1, equal to the angle V \V S, No. 3; produce A k to E; draw C D parallel to A B; make C D equal to C D, No. 3, and the angle C D F equal to the angle A B E, that is, equal to the angle V W S, No. 3: produce it C to F; join F E; in F E take any point, E, and draw El pe‘rpendimi- lar to F C, meeting it in I; from I draw I K perpendicular to F6, cutting it in L; make l ll equal toI L, and join H ll; make L K equal to H E, and join 1“ K; then 1“ E is the director of the ordinates of the base, and F K that of the face-mould. Proceed with the rest as in Plate 1. Figure I. No: Q shews the other mould; but: it must be oh- served, that one mould is suflieient for both wreaths. Plate IV. shews the falling and face moulds of a L HAN HAN rail with winders. As to the method of laying down the moulds from three given heights, the principle is the same as described in Plate I. for a level landing. It therefore only remains to speak of the manner of forming the but—joints. Draw a line at right angles to the sides of the falling-mould, through the middle of the vertical line, where otherwise would have been the splice joint; from the end of this line draw another at the upper edge, and also one from the under edge, perpendicular to the base line; then the middle height being taken as usual, the remote line is the height of the face—mould. Thus, H I, No. l, is the height of h 2', No. ‘2; K L, No. l, the height of l: l, No. 2; and M N, No. 1, the height of m 72, No. 2; the remaining part of the construction is as usual.——-No. 3 is the upper face-mould, taken from inverted heights: or the falling-mould may be considered as in— verted. The same letters are put upon both constructions, to shew the similar parts. Here ,are eight winders, all drawn to a scale, to shew the proportion of the parts in practice. This handurail requires two ' moulds, on ac- count of the middle of the falling-mould be- ing much higher than the bypothenuse of the winders. Plate V. shews the falling and face moulds for a rail constructed as in Plate IV. The only differ- ence is, that in this Plate the middle of the falling- mould is the hypothenuse of the wreath. This situation of the falling-moulds will cause both the face-moulds to be identical: that is, their figures will be equal and similar, so that consi— derable time will be saved in the preparation. This position, and the identification of the moulds, may always be adopted when the distance between the opposite parts of the string is more than ten inches. The mode of making the height of the rail in the middle of the winders the same as that of the flyers, is practised by several cele- brated staircase hands, though it is nothing more than a mere matter of opinion, and may be adopted or not, at the option of the architect, or of the workman, if left to him. It is worthy of notice, that the springing of the plank is of the utmost consequence in the saving of stuff, where the well-hole is wide; but where it is narrow, very little will be gained by it. To draw the scroll of a hand-rail, and to find the mould for executing the twist. Plate VI. Figure I, No. 1, represents the plan. of the rail. The scroll is drawn by centres, in the following manner: Make a circle in the centre, 3% inches in diameter; divide the diameter into- three equal parts, one of which subdivide into six equal parts; set one part from the centre up- wards, draw a line from the end of that part, at right angles, towards the left hand, and limit this perpendicular to two parts; from the end of the last perpendicular draw a. third downward, limit- ing it to three equal parts; proceed in this man- ner till six perpendiculars have been drawn, each differing in length by one from the preceding, and the form of a spiral fret will be obtained. The points ofconcourse of every tWo lines will give the centres, which are six in number, besides the centre of the circle, and are numbered in order from such centre: draw a straight line downward from the first centre, by continuing the line al- ready drawn till it cuts the circle: continue the second perpendicular to the right hand, and the third upwards to the left hand; these will form the limiting lines for the four arcs, which will complete one revolution. Continue the lines in the same order for the next revolution, or for the portion of it required. Begin with the centre next to that of the circle for the first centre, and describe a quarter are from the point of contact of the circle to the next limiting line; then around the second centre, with the distance to the intersection of the preceding are, on the pre- ceding limiting line, describe another are; pro- ceed in this manner till the whole spiral is com- pleted. Set the breadth of the rail from o to a, and describe another spiral by the same centres, by turning the arcs the contrary way, till the last are of the spiral cuts the first; which will com- plete the scroll of the rail; then the addition of a part of the straight of the rail will complete the whole. The outer spiral consists of one revolution and a half, and the inner of only about halfa revo- lution, which also makes the scroll itself appear only halfa revolution; but if more is required, every additional centre will add a quarter of a re- volution to the scroll. To find theflzce—mouldfor the shank of the scroll. Figure 1, No. 1. Lay the base of the pitch-board upon the outside of the shank of the scroll, with the acute angle turned to the outside, or largest convexity ; draw a line parallel to the base of the W W \\\\\\\\ / . l l ; 1 ; . ’« ( wt 7 ’41 JZ) 0’7 Q [3L2] Ia? allzfllll (7 71,72 2:7147'Wt’d (5 #777 I ) I 71,} ed @1 AM u. t HAND RAILING \\Wm\\w\ \ \\ \NWKWMW\ HAN 7 pitch—board, to touch the convex side of the scroll next to the straight part; let this line out the outside of the rail at 6: between 0 and 6 take any number of intermediate points, 1, 2, 3, 4, 5, and draw lines perpendicular to the base of the pitch—board, to cut the hypothenuse of the said pitch-board; from the points of section draw lines at right angles to the hypothenuse ; let the perpendiculars parallel to the base line of the pitch-board be continued downwards, to cut the concave side of the shank; and let one of the perpendiculars be drawn from the concave, and another from the convex side of the rail, where it is intersected by the line parallel to the base line; make all the lines at right angles to the hypothe- nuse equal to the respective ordinates of the shank taken from both concave and convex sides of it; then curves being traced, and the straight parts joined to the angular points will be the face- mould. ,hfind thefalling—mould. Divide the distance between 0 and 6, Figure 1, No. 1, into six equal parts, and run the chord on the convex side as far as the rail is required to fall; upon any convenient line, A D, No. 2, run the chord of the part from 0 to 13; place the angular point, C, of the pitch-board at 4; with the base A C, upon A D, tange the angle B C I) made by the hypothenuse of the pitch-board and the line A D, with a curve to touch at B and D, as shewn at No. 3 ; then draw another curvilinear parallel, containing the depth of the rail between the two curves; and the falling-mould, No. 2, will be completed as far as the rail has a descent, which ends at 13. The block of the scroll, which is the remaining part after the shank is taken away, is wrought out of a solid piere of wood, the height of the perpendicular upon 0. The shank is squared in the same manner as shewn in Plate 11. No. 4. The falling-mould for the concave side of the rail is exhibited here, in order to shew, that if the ramp and the curve of the scroll do not begin together, and if the rail be made abso- lutely square, that is, having all its plumb sec- tions, rectangles, and the convex side made agreeable to its falling-mould, with an easy curve, it will be impossible to form the back with a regular curve on the concave side, and a hump will always be formed. Therefore, in reducing the bump to an agreeable curve, the HAN W rail will be thrown out of the square; but the degree by which it deflects from the truth is so small as not to be perceived. The inside of the falling-mould is formed by taking the stretch out of a b, b c, c d, 8L0. of the corresponding parts 01, 1 Q, Q. 3, 8L0. in No. l, and applying them from a to b, from b to c, from c to d, See. No. 4; then drawing the perpendicu- lars from the points a, b, c, 8m. and transferring thereto the corresponding perpendiculars insists ing upon 0, 1, 2, See. No. Q, and then tracing the curves. According to the principles of hand- railing, a vertical or plumb section of the rail at right angles to the cylindric sides, or tending to the axis of the cylinder,islevcl on the back; there— fore, as the concave and convex sides ofthe plan of the scroll are concentric circles, the are on the con- cave side, so far as relates to the same quadrant, will be divided equally, as well as the outside; and therefore drawing lines to the centres from the points of sectiongon the convex side will divide each quadrant equally, and the lines thus radiat- ing will be perpendicular to the curve on both sides of the plan; all the parts throughout the same quadrant will be equal on the concave side as well as on the convex side; and on the con- vex side the parts will be equal throughout all the quadrants; but on the concave side the parts of each succeeding quadrant, in turning towards the centre, will be quicker than those in the pre- ceding quadrant. In the part of the rail which is straight upon the plan, the sections at right angles to the sides divide each side into equal parts, and the parts on the one side equal to those of the other: hence the reason why the hump takes place at the junction of the ramp and twist. Ifa scroll is made agreeable to the form of the plan as struck round centres with compasses, it will always appear to the eye as if crippled at the separating section of the straight and twisted parts. To remedy this defect, the curve of the vertical sides, or that which relates to the plan, ought to be extended with an easy curve into the straight part. ' No. 5. An elevation of the shank of the scroll. The portion of the plan is taken from No. 1, and the heights which give the curves are taken from the falling-mould, No. 2; its use is to shew the thickness of stuff which is contained between two parallel lines; the lower line comes in con« L 9. tact with the projection at two points, the upper one comes in contact with the projection in one point only. To shew the method of forming the curtail of the first step. Plate VII. Figure 1, No. 1.——Draw the scroll as in the preceding Plate; set the balusters in the middle of the breadth, putting one at the begin- ning of every quarter; then the front of the balusters is in the plane of the face of the riser, and the opposite side in the plane of the string- board: set the projection of the nosing before the balnster on both sides, and draw two spiral lines parallel to the sides of the scroll, till the curves intersect each other, and they will then form the curtail end of the step, as required. F G H I K represent the convex side of the scroll; L M N O P, the convex side of the curtail; and A, B, C, D, E, the centre points of the ba- lusters. No. Q shews the profile of the curtail, the end of the second step, and part of the end of the third. . Figure 1, No.3, shews the centres for drawing the curtail, which are the same as for drawing the scroll. To describe a section of the trail, supposing it to be two inches deep, and two and a quarter inches broad, the usual dimensions. Figure 2.———Let A B C D be a section of the rail, as squared. On A B describe an equilateral tri- angle, A B g; from g, as a centre, describe an arc to touch A B, and to meetg A and g B: take the distance between the point of section in g A and the point A, and transfer it from the point of section to k, upon the same line g A; join D h; from k, with the distance between k and the end of the arc, describe another are, to meet D k; with the same distance describe a third are, of contrary curvature, and draw a vertical line to touch it; thus will one side of the section of the rail be formed. The counter part is formed by a similar operation. Figure 3 is the most simple form for the section. of a rail, being that ofa circle. To describe the Mitre-cap of a rail. Figure 4.—-—Describe a circle, a e I) d, to the in- tended size (the proportion here between the rail and the cap is as Q. to 3); draw the diameters a I) and e d at right angles; produce e d, and place the middle of the section of the rail upon ed; draw B Q to touch the section of the rail, and to cut the circle a e 6 din Q; draw the side P Q ‘of the mitre; draw A B to meet the points of con- tact, A and B, of the lines parallel to e d, which are tangents to the section. Then to find any point in the curve of the section of the mine- cap: let G be a point in the section of the rail; draw G k, meeting P Q in k; from the centre of the circle a e b d, describe an arc, kf, meeting a b in f; from the point of section,f, draw f g, perpendicular to a b; and make f g equal to F G. All other points are found in the same manner; or a series of lines may be drawn from any num- ber of assumed points in the section, and lines parallel to e d, drawn from them to cut P Q; arcs may then be described from each point of section to meet a b, and perpendiculars drawn from the points of section in a b; all these perpendiculars should be made equal to the respective ordinates of the section, and a curve drawn through their extremities will form the curve of the mitre-cap. HANGING, of doors, or shutters, the act of plac- ing them upon centres or hinges, for the conve- nience of opening and shutting. Sec IIINGIN G. HANGING STYLE, the style of a door or shutter, to which the hinge is fastened. The term is also applied to a narrow style fixed to thejamb, on which the door or shutter is some— times hung. In this case, the hanging style is used with the view of making the shutter or door revolve more than a right angle, in order to turn it into a given position; as to bring a door close to a partition, to keep it out of the way. HANGINGS, linings for rooms, made of arris, ta— pestry, or the like. HAN GS OVER, an expression used in speaking of a wall, when the top projects beyond the bottom. HARD BODIES, such bodies as are absolutely inflexible to any shock or collisiou whatever. This is the common meaning of the term: but Huygens, by hard bodies (corpora dura) meant what others call perfectly elastic bodies; for he thus expresses himself: “ Queecunque sit causa, corporibus duris, a mutuo contactu resiliendi cum se invicem impinguntur: ponimus, cum cor- pora duo inter se aequalia, aequali celeritate, ex adverso ac directe sibi mutuo occurrent, resilire utrumque eadem qua advenit celeritate.” H uyg. De flIotu Carper Percuss. H ypoth. 2. But this hy~ pothesis is consistent only with perfect elasticity, ,PLJTLIII . EASE) BAILEE a; . .553 V \\§/ / .............. w \\\\\ / \\ \x § \\\\\\ i? s \ X\ \ :35 __ 1911:11sz 11/ [y ./ 721901077. Londmtflzblz‘flzrd btyli1’zl-7urlmn 511/ lfufyz'rlz/ , flimitml' J/Iw/ 761/ M7 /I'I/ /’,\'/'1'/111/.~'vi7 , HAR 77 I'm and not with the common supposition of hard- ness or inflexibility, which produces no resilition. The laws of motion for hard bodies are the same as for soft bodies, and these two sorts of bodies might be comprised under the common name of mzelastic. Some who follow Leibnitz’s doctrine, concerning the measure of the moving force of bodies, deny the existence of hard or inflexible bodies. And it is so far true, that no experience ever taught us that there are any such. The hardest bodies to appearance do not preserve their figures in collision, such bodies being only elastic, yielding to the shock, and then restoring themselves. l\-'I. Bernouilli goes so far as to say, that hardness, in the vulgar sense, is absolutely impossible, be- ing contrary to the law of continuity. For sup- posing two such hard bodies of equal masses, and with equal velocities, to meet directly, they must either stop or return after the collision. The first —supposition is commonly admitted; but then it follows, that these bodies must instantaneously pass from motion to rest, without going through successive diminutions of their velocities till they stop: but this is thought to be contrary to the fundamental laws of nature. Hence this author rejects perfectly solid and inflexible atoms, which others think a consequence of the impene- trability of matter. ‘ HARD, in enginery, signifies a ford or passable place in a river, particularly in and near the Fens, where many of these formerly occurred, com- posed of gravel, probably brought thither for the purpose, which proved very detrimental to navi- gation in dry seasons, and obstructed and aug- mented the floods in wet ones, until they were removed. Frequent mention is made of these bards by Mr. Smeaton, and other writers on the navigation and drainage of those districts. HARD FINISHING, see PLASTERING. HARDENING OF TIMBER. The Venetians are famous for the soundness of their ships, which do not rot as those of other nations, but will endure much longer than others. Tachenius tells us, that the whole secret of this consists in the manner of their hardening the timber intend- ed for this service; and that this is done by sink- ing it in water while green, and leaving it there many years. This prevents the alkali, or that salt which furnishes the alkali in burning, from ex- haling afterwards; and by this means the timber HEA becomes almost as incorruptible as stone. It is evident that the exhaling of this salt, and the rotting of wood, have some very great connection with each other, since the more sound any piece of timber is, the more salt it proportionably yields; and the rotten wood is found on trial to contain no salt at all. ' HARMONICAL DIVISION, or PRopoaTto-N. is when, in a series of quantities, any three ad- joining terms being taken, the difference between the first and second is to the difference between the second and third as the first is to the third. The reciprocals of a series of numbers in arithme— tical progression are in harmonical proportion: thus the reciprocals }, %, 3-, a, 8:0. of 1, 2, 3, 4, Ste. are in harmonical proportion; also, the reci- procals %, §, %, ;~, Ste. of l, 3, 5, 7, 86c. are har- monicals. HARMONY, an agreement between all the parts- ofabuilding; the word is of similar import with SYMMETRY, which see. HARNESS ROOM, a small apartment for keep- ing the harness in, that it may be preserved from mouldiness. It should be perfectly dry, and placed as near the stable as possible. HATCH-“7AY, an aperture through the ceiling, to afford a passage to the roof. HATCHET (from the French hackette) a small axe, used by joiners for reducing the edges. of boards. HEAD (from the Saxon) an ornament of sculpture or carved work, frequently serving, as the key of an arch or platband. These heads usually represent some of the heathen deities, virtues, seasons. or ages, with their at- tributes. The heads of beasts are also used in suitable places; as a bullock’s or sheep’s head, for a shambles or market-house; a dog’s for a kennel ;' a deer’s or boar’s for a park or forest, or a horse’s for a stable. In the metopes for the friezes and other antique- Doric temples, we meet with representations of bullocks’ or rams’ head flayed, as a symbol of'the sacrifices offered there. HEAD, Jerkin, see JERKIN HEAD. HEADER, see HEADING COURSE. HEADING COURSE, in masonry, a course of stones in which their length is inserted in the thickness of the wall ; those with their length in the face of the wall are called stretchers. The same is also to be understood of brick-work. HEC HEADING JOINT, in joinery, the joint of two or more boards at right angles to the fibres; or, in hand-railing, at right angles to the back: this is done with a view to continue the length of the board when too short. The heading-joints in good work are always ploughed and tongued, as in flooring, dado, See. In dado, the heading- joints, besides being ploughed and tongued, are also glued. I‘]EAD~VVAY or A STAIR, the clear distance, measured perpendicular to the horizon, from the tread of any step, resting-place, or landing, to the ceiling immediately above, in one revo- lution, making allowance for the thickness of the steps. HEART-BOND, in masonry, the lapping of one stone over two others, which together make the breadth of the wall. This is practised when thorough-stones cannot be procured. See MA- SONRY. HEARTH, see CHIMNEY. HEATHER-ROOF, that kind of roof employed in building which is thatched over or covered with heather or heath, instead of some other ma- terial. It is recommended, as well adapted to buildings of the farm description, by the writer of the Survey of the County of Argyle, in Scot— land, on the principle that it does well with tim- ber of the ordinary sort, is capable of being pro- cured fora trifle, lasts nearly as long as slates, and gives less trouble in the repair. It is as- serted that a roof of this material, when well put on, will last one hundred years, provided the tim- ber continues good that length of time. And it is stated, that'formerly most of the churches in the above county were covered with this sort of roof; likewise, that, heather-roofs are frequently met with in the district of Cowal, and that there are a few of them in Kintyre. This sort of material may certainly be employed with advantage as a covering for small houses and other buildings, where other kinds of sub- stances cannot be procured, except at a great ex- pense; but at the same time it is very inferior to slate, and other similar matters, in forming the coverings of such erections. HECATOMPEDON (from imrov, a hundred, and wag, feet) a name given to the Parthenon, or Tem- ple of Minerva, at Athens. IIECATONSTYLON (horrors-UAW) in ancient ar- chitecture, a portico with a hundred columns. HEL This name was peculiar to the great portico of Pompey’s Theatre, at Rome. HECK, a rack. HEEL, in mouldings, the same as the sima-inversa. HEEL or A RAFTER, the foot of the rafter, as it is formed to rest upon the wall—plate. HEIGHT, the perpendicular distance of the most remote part of a body from the plane on which 1t rests. HELICOID PARABOLA, or the PARABOLIC SPIRAL, a curve arising upon a supposition of the axis of the common Apollonian parabola being bent round into the periphery of a circle. The helicoid parabola, therefore, is a line passing through the extremities of the ordinates, which converge towards the centre of the said circle. HELIOPOLIS, or THE CITY or THE SUN, in ancient geography, a city of Egypt, placed by geographers not far from Hellé, at some distance from the eastern point of the Delta. It was built, according to Strabo, on a long artificial mount of earth, so as to be out of the reach of the inunda- tion. This causeway, covered with rubbish, is still visible two leagues to the north-east of Grand Cairo, and three from the separation of the Nile. This city had a temple to the sun, where a particular place was set apart for the feeding of the sacred ox, which was there adored under the name of Mnevis, as he was at lVIemphis under that of Apis. There was also in this city another magnificent temple, in the ancient Egyptian taste, with avenues of sphinxes and superb obelisks, before the principal entry. These temples were fallen into decay under the reign of Augustus; as the city had been laid waste with fire and sword by the fury of Cambyses. Of the four obelisks built by Sochis in that town, two were removed to Rome; another has been destroyed by .the Arabs; and the last of them is still standing on its pedestal. It is composed of a block of The— baic stone, perfectly polished, and is, without. including its base, 68 feet high, and about 6.31,; feet wide on each aSpect. It is covered with hieroglyphics. This beautiful monument, and a sphinx of yellowish marble, overset in the mud, are the only remains of Heliopolis. HELIX, little scrolls in the Corinthian capital, called also urillze: they are sixteen in number, viz. two at every angle, and two in the middle of the abacus, branching out of the caulicoli or stalks which rise between the leaves. HEN W # HELMET, a warlike ornament, in imitation of the helmet worn by the cavaliers, both in war and in tournaments, as a cover and defence of the head; the helmet is known by divers other names, as the [read-piece, steel-cap, &c. The Germans call it lie/en or lzellcm; the Italians elmo; the French cusque, as did alsothe ancient English. The helmet covered the head and face, only leav- ing an aperture about the eyes, secured by bars, which served as a visor. HEM, the protuberant part of the Ionic capital, formed by spirals. HEMI, a word used in the composition of divers terms. It signifies the same with semi or demi, viz. half; being an abbreviature of fipwug, hemisys, which signifies the same. The Greeks retrenched the last syllable of the word parts, in the com- position of words; and, after their example, we have done so too, in most of the compounds bor- rowed from them. HEMICYCLE (Latin henzicyclz'um, compounded of 941.5004, half, and nvum, circle) a semicircle. This word is particularly applied, in architecture, to vaults in the cradle form; and arches, or sweeps of vaults, constituting a perfect semicircle. To construct an arch of hewn stone, they divide the hemicycle into so many voussoirs; taking care to make them an uneven number, that there be no joint in the middle, where the key-stone should be. HEM ICYCLIUM, a part of the orchestra in the ancient theatre. Scaliger, however, observes, it was no standing part of the orchestra; being only used in dramatic pieces, where some person was supposed to be arrived from sea, as in I’lautius‘s Rudens. IIEMISI’HERE (Latin hemispherium, compounded of -' 'ba'tg, half, and camp, sphere) in geometry, one half of a globe, or sphere, when divided into two by a plane passing through its centre. HEMISI’HEROIDAL, a body approaching to the figure of a hemisphere, but not exactly so; of this description are what may be termed elliptical domes, upon either axis. HEMITH lGLYPH, the half triglyph. HENDECAGON, ENDECAGON, or UNDECAGON (compounded of s . eleven, and 7mm, angle) in geometry, a figure which has eleven sides, and as many angles. If each side of this figure be 1, its area will be equal to 9.3656399 : ‘13 tangent 73773, radius being 1. 7f) HIN W 3 HEPTAGON (of Ema, septem, seven, and yam, angle) in geometry, :1 figureconsisting of seven sides and seven angles. If the sides and angles be all equal, it is called a regular Izeptagon. The area of a regular heptagon is equal to the square of one of its sides multiplied by 3.6339126. HEPTAGONAL, consisting of seven angles, and therefore also of seven sides. HERBUSUM, Murmur, a species of marble, much esteemed and used by the ancient architects and statuaries. It was of a beautiful green colour, but had always with it some cast of yellow. It was dug in the quarries of Taygetum, but was esteemed by the workmen the same in all re. spects, except colour, with the black marble dug at Teenarus in Lacaedemonia, and thence called Tainarian marble. HERMOGENES, the inventor of the eustyle in- tercolumniation; also of the octostyle pseudo— dipteros. He is mentioned by Vitruvius, Chap. II. Book III. HE\VN STONE, any stone when reduced to a given form by means of the mallet and chisel. HEXAEDRON, or HEXAHEDRON (formed of £5, six, and saga, seat) in geometry, one of the five regular bodies, popularly called a cube. See CUBE. The square of the side of a hexaedron is in a subtriple ratio to the square of the diameter of the circumscribed sphere. Hence, the side of the hexaedron is to the diameter of the sphere in which it is inscribed, as one to the 4/ 8: and consequently, it is incommensurable to it. HEXAGON (from £5, six, and 7mm, angle) a figure of six angles, and consequently of six sides. If the angles and sides are equal, the figure is called a regular hexagon. If the side of a hexagon be denoted by 3, its area will be 2.5980762 s. HEXASTYLE (from E5, six, and runes, column) a building with six columns in front. HING ES, metal ligaments, upon which doors, shut» ters, folds, lids, 8m. turn in the act of opening and shutting. There are many species of hinges, viz. butts, rising-hinges, pew-hinges, casement-hinges, cast- ing-hinges, chest-hinges, coach-hinges, desk- hinges, dovetail-hinges, esses, folding-hinges, garnets, weighty side, side-hinges with rising joints, side-hinges with squares, screw-hinges, scuttle-hinges, shutter-hinges, trunk-hinges, of HIN SO HIN various descriptions, hook-and-eye-hinges, and centre-pin-hinges. HINGING, a branch of joinery, which shews the art of hanging a board to the side of an aperture, so as to permit or exclude entrance at pleasure. The board which performs this office is called a closure. The placing of hinges depends entirely on the form of thejoint, and as the motion of the closure is angular, and performed round a fixed line as an axis, the hinge must be so fixed that the motion may not be interrupted: thus if thejoint contain the surfaces of two cylinders, the convex one in motion upon the edge of the closure, sliding upon the concave one at rest on the fixed body, the motion of the closure must be performed on the axis of the cylinder, which axis must be the centre of the hinges; in this case thejoint will be close, whether the aperture be shut or open. But if the joint be a plane surface, it must be considered upon what side of the aperture the motion is to be performed, as the hinge must be placed on the side of the closure where it revolves. The hinge is made in two parts, moveable in any angular direction, one upon the other. The knuckle of the hinge is a portion contained under a cylindric surface, and is common to both the moving part and the other part at rest; the cylinders are indented into each other, and made hollow to receive a concentric cylindric pin which passes through the hollow, and connects the mov- ing parts together. The axis of the Cylindrical pin is called the axis of the hinge. W hen two or more hinges are placed upon a closure, the axes of the hinges must be in the same straight line. The straight line in which the axes of the hinges are placed is called the line of hinges. The following are examples of the different cases. The principle of hanging doors, shutters, or flaps, with hinges. The centre of the hinge is generally put in the middle of the joint, as at A, Figure l ; but in many cases there is a necessity for throwing back the flap to a certain distance from the‘ joint; in order to effect this, suppose the flap, when folded back, were required to be at a certain distance, as A B in Figure 2, from the joint; divide A B in two equal parts at the point C, which will give the centre of the hinge ; the dotted lines B D E F, thew the position when folded back. Note—The centre of the hinge must be placed a small degree beyond the surface of the closure, otherwise it will not fall freely back on the jamb 0r partition. It must also be observed, that the centre of the hinge must be on that side that the rebate is on, otherwise it will not open without thejoint being constructed in a particular form, as will be after- wards shewn. Figure 3 shews the same thing opened to a right angle. To hang two flaps, so that when folded back, they shall be at a certain distance from each other. This is easily accomplished by means of hinges having knees projecting to half that distance, as appears from Figure 4; this sort of hinges is used in hanging the doors of pews, in order to clear the moulding of the coping. To make a rule joint for a window-shutter, or other folding flaps. Figure 5.—-—Let A be the place of the joint; draw A C, at right angles to the flap, shutter, or door; take C, in the line A C, for the centre of ’the hinge; and the plain part A B, as may be thought necessary; on C, with a radius, C B, describe the arc B D; then will A B l) he the true joint. Note.——-The knuckle of the hinge is always placed in the wood, because the farther it is inserted the more of the joint will be covered, when it is opened out to a right angle, as in Figure 6; but if the centre of the hinge were placed the least without the thickness of the wood, it would shew an open space, which would be a defect in work- manship. ' To form the joints of styles, to he hang together, when the knuckle of the hinge is placed on the contrary side of the rebate. Figure 7.—I.et C be the centre of the hinge, M I thejoint on-the same side of the hinge; K L the depth of the rebate in the middle of the thickness of the styles, perpendicular to K M, and L F the joint on the other side, parallel to K M; bisect K L at H,join H C; on H C- describe a semicircle, C I H, cutting K M at I; through the points 1 and H, draw I H G, cutting l" L at G; then will PG 1M be the true joint; but if the rebate were made in the form of MK L F, neither of the styles could move round thejoint or hinge. To form the edges or joint of door—styles, to be hung to each other, so that the (1001' may ___:..———: fi#+§:_ —_—: II II Zanzim, Mliriwd év 131555019011 42* Jflarfidd, Wmdauer-ett, 160.3. 1y 7. NH IIIII II III I I IIIIIIIII IIIIIII IIIII I I I II I IIIIIIIII I ‘ ’1III liymwd QVJ 121 jinn u. Enqrdwd iv 1‘. M 175.12. M 1 I 129. 11.2w 1. HINGING. x [omionj‘hélzir/lfll in; [311711120an X‘ J, [Sarfi'rlafl Witnlnm‘ Ina-1,181.1. 3. Fg. 111V." Dram: 5y 1? Nth/(210071.. HIN ‘open to a right angle, and shew a bead to correspond exactly to the knuckle if the hinge. Also the man- ner of constructing the hinges for the various forms of . joints, so as to be let in equally upon each side. Figure 8, No. l, shews the edge of a style, or it may in some cases be a jamb, on which a bead is constructed, exactly to the size of the knuckle of the hinge, and rebated backwards, equal to half . the thickness of the bead: the manner of con— structing the rebate will be shewn as follows: Through C, the centre of the bead, which must also be the centre of the hinge, draw C B D per- pendicular to EF; draw AG parallel to it, touch- ing the head at G , make G A equal to G C, the radius of the bead , join CA, make A B per pen- dicular to AC, cutting C D at B; then will GA B D be the joint required. No. Q, shews a part of the hanging style con- structed so as to receive the edge of No. 1. No. 3, shews the above hinged together with common butt—hinges. Note—It must be observed in this, and all the following examples of hinges, that the joints are not made to fit exactly close, as sufficient space for the paint must be allowed. Figure 9, No.1 and 2. The manner of construct- ing these being only a plain joint at right angles to the face of the style, no farther description is necessary. No. 3 shews No. l and 2 hinged together, and the particular construction of the hinge, so as to be‘seen as a part of the bead, and the strap of the hinge to be let equally into each style: this construction will admit of a bead of the same size exactly opposite to it. .I"igure 10, No. 1 and 2. The manner of con- : ructing the edges of styles to be hinged to- gether with common butts, tobe let equally into each style: the manner of constructing thisjoint is so plain, by the figure, that it would be useless to give any other description of it. No. 3, the two pieces hinged together. ' > .Methods of jointing styles together so as to prevent seeing through the joints, each side of the styles to finish with beads of the same size, exactly opposite to each other and fbr the strap of the hinges to be let equally into both parts or styles. Figure 11, ha. 1 and" a, the manner of construct- ing thejoint, before hinged together. No. 3 shews No. 1 and 2 hinged together with , common butts. VOL. 11. 8! HIN .. Figure 12, No. 1 and 2,. shews another method‘of constructing the joints, before hinged together. No. 8,'shews No. 1 and Q, hinged, and the parti~ cular form of the hinges for the joint. The. principle of concealing hinges, shewing the manner ofjmaking them, and offarming the joint of the hanging style, with the other style connected to it by the hinges, either for doors or windows. Figure 13, for a window: - X, inside bead of the sash-frame. Y, inside lining. Z, style of the shutter. 4 Let A be the intersection of the face oft-the. shutter, or door, with that of the inside lining of the sash- frame. A R, the face of the inside lining. Bisect the angle PAR by the right line A A; now the centre C being determined 1n A A at C, so that the knuckle of the hinge may beat a given distance from the face PA of the shutter; through C draw the line D D, at right angles to AA; then one side of the hinge must come to‘the line C D, the hinge being made as is shewn by the figure. To construct the jamb to be clear of the shutter.—- On C, as a centre, with a radius CA, describe an arc AM, and it will be the joint required. Note.-—-VVhen these sort of hinges are used in shutters, the strap of the hinge may be made longer on the inside lining, than that which'is connected with the shutter. Figure 14, is the manner of hanging a door on the same principle: the shadowed part must be cut out, so that the other strap of the hinge may revolve, the edge, CD, of the hinge, will come into the position of the line AA, when the window is shut in. Here the strap part of the hinge mav be of equal lengths. Figure 15, the common method of hanging shut- ters together, the hinge being let the whole of its thickness into the shutter, and not into the sash- frame. By this mode it is not so firmly hung, as when halt rs let into the shutter and half into the sash. frame, but the lining may be of thinner stufl‘. Note.~—-It is proper to notice, that .the centre of the hinge must be in the same plane with the face of the shutter, or beyond it, but not within the thickness. Figure 16, the method of hanging a door with centres. Let AD be the thickness of the door, ' M HIP W m HIP and bisect it in B; draw BC perpendicular to AB; make BC equal to BA, or B1); on C (the centre of the hinge) with a radius CA or C D, describe an arc, AED, which will give the true joint for the edge of the door to revolve in. HIP, in architecture, a piece of timber placed be— tween every two adjacent inclined sides of a hip—roof, for the purpose of fixing the jack rafters. For the manner of finding the length and backing of the hips, see HIP-ROOF. HIP-MOULD, a mould by which the back of the hip-rafter is formed : it ought to be so construct- ed as to apply to the side of the hip, otherwise there will be no guide for its application. HIP-ROOF, a roof whose ends rise immediately from the wall-plate, with the same inclination to the horizon as the other two sides of the roof have. The backing of a hip is the angle made on its upper edge, to range with the two sides or planes of the roof between which it is placed. Jack-rafters are those short rafters fixed to hips equidistantly disposed in the planes of the sides and ends of the roof, and parallel to the common rafters, to fill up the triangular spaces, each of which is contained by a hip-rafter, the adjoining common rafter, and the wall-plate, between them. The seat or base of the rafter is its ichnographic projection on the plane of the wall-head, or on any other horizontal plane. The principal angles concerned in hip-roofing are, the angle which a common rafter makes with its seat. on the plane of the wall-head; the vertical angle of the roof; the angle which a hip makes with the adjoining common rafter; the angles which a hip makes with the wall-plate on both sides of it; the angle which a hip-rafter makes with its seat; and the acute angle which a hip- rafter makes with a vertical line. The principal * lengths concerned are, the height of the roof; the length of the common rafters and their seats; the length of the hips and their seats; and, lastly, the length of the wall-plate contained between the lower end of a hip and the lower end of the adjacent common rafter. The sides and angles may he found by geometrical construction or trigonometrical calculation. It is evident, that if the hipped end of a roof be cut off by a'vertical plane parallel to the wall, through the upper extremity of the hips, it will form a rectangular pyramid, or one whose base isa rect- angle. The base of this pyramid is bounded by the wall-plate between the two hips on one side, and on the opposite side by the seat of the two adjoining common rafters; on the other two op- posite sides by that part of the wall-plate on each side contained by the lower end of the hip and the next common rafter adjoining. One of the sides is the isosceles triangle contained by the two— adjoining common rafters with their seat; the Opposite side is the hipped end of the roof, form- ing also an isosceles triangle ; the other two op- posite sides are the right-angled triangles con» tained by the two hips and the two adjoining rafters on the side of the roof. This rectangular pyramid may be divided into three triangular pyramids by the two vertical triangular planes, formed by the hip-rafters, their seats, and the common perpendicular from their vertex. Two of these pyramids, when the plan of the building is a rectangle, are equal and opposite. In each of these equal and opposite pyramids the base is a right-angled triangle, contained by the seat of the hipcrafter, the seat of the adjoining common rafter, and the part of the wall-plate be- tween the hip and the adjoining common rafter, One of the sides is a right-angled triangle con- tained by the adjoining common rafter, its seat, and perpendicular; a second side is a right- angled triangle contained by the common rafter, the hip-rafters, and the wall-plate, between them; and the remaining third side is the triangle con— tained by the hip rafter, its seat, and perpendi. cular. With regard to the remaining pyramid, its base is a right-angled triangle contained by the seats of the two hips and the walelate be- tween them, the right angle being that contained by the seats of the two hips; two of its sides are the triangular planes passing the hip-rafter, which are also common to the other two pyra- mids; its third side is the hipped end of the roof. Given the plan of a building, or theform of a wall-plate of a hip-roof, and the pitch of the rogt‘, to find the various lengths and angles concerned, whether the roof is square or bevel. EXAMPLE l..--To find the length of the rafters, the backing of the hips, and the shoulders of jack- rafters and purlins, geometrically. Plate 1. Figure 1.—Let A B C D be the plan. ' Draw E F parallel to the sides, A D and B C, in the middle of the distance between them. On D C, as a ‘ ‘ ‘({V,V~A,..§(pn~ _ In”. I i' , V _ V 2 ‘ / ‘ \ t . ,. 7‘ HIP ROOF F111; . 1. PLA TE A 1:111) . 1’. 1"‘WWW’V‘ [mum/ml II" 1’, Win/1410011 . K / N \ \\ wry-7"»; 'm/%;sr.y 4mm P / 'Q S [nth/4:11.,I‘IIIIILr/ml [5r If.\'n-/m/.v.m A" Burlir/J, ”tum/um- .)‘hw't, .1115!th 1. “5'13. D 1‘1"].111111'4'4] I!" IllnnxhvV- HIP diameter, describe the semicircleD F C; draw F D and F C, then the angle D F C is a right angle. Draw G F Hperpendicular to E F, cutting the sides A D and B C in G and H; from F E cut off F I equal to the height or pitch of the roof, andjoin G I; from F C out ofi'F K equal to F1, and join K D; then G I isthe length of a com- mon rafter, and D K that of the hip; for if the triangles G F l and D F K be turned round their seats, G F and D F, until their planes become :- perpendicular to the triangle G F D, the perpen- dicular F I will coincide with F K, and the point j I will coincide with the point K; the lines G I and l) K, representing the rafters, will then be in their true position. The same by calculalion. Gl’zG F1+F I1 (Euclid [.47). therefore G 1::(G P+F I‘)%the . length of the common rafter, D F": G F1 +G D‘, the square of the seat of the hip. D ngD F3+ _ F K9: G F’+G D2+F 1", therefore D K = 1 G 1.2+ G D94. F 19’” In the same manner the other hip-rafter C L is found, as also the hip-rafters A M and B N. Let it be required tofind the backing of the bip- rafter, whose seat is C F. Gewnetrically.——lmagine the triangle C FL to be raised upon its seat C F, until its plane be- comes perpendicular to the plane of the wall-plate A B C D, then there will be two right-angled solid angles; the three sides of the one are the plane angles of F C D, F C L, and the hypothe- nusal plane angle D C L. In each of these solid angles the two sides, containing the right angle, u‘z. the plane angles F C H, F C D, and the per- pendicular plane angle C F L, which is common to both, being given, to find the two opposite inclinations to the sides F C H and F C D, and the remaining third sides. Now the angles G D C and H C D are bisected by the seats F D and F C of the hip-rafters; for if E F is produced to meet D C in U, U will be the centre of the circle D FC; and U C, U F, U D, are equal to each other : and because U F is equal to U C, the angle CFU is equal to F C U; but C F U is equal to the alternate angle FC H; therefore the angle FCU is equal to F C H : that is, the angle U C H is bisected by the seat F C of the hip-rafter. In the same man- ner may be shewn that U D G is bisected by the seat D F of the other hip-rafter. From any point, 83 W HIP W O, in F C, draw 0 V perpendicular to L C, cut- ting it in P, and O W perpendicular to F C, cut- ting D C in W’; from O C cut 030 Q equal to O P. Join Q W, then 0 Q W will be the in- clination opposite the plane angle F C U, and this is the angle which the end of the roof makes with the vertical triangle contained by the hip rafter, its seat, and perpendicular. Produce W O to meet B C in X, and joinQ X, then W Q X is the inclination of the two planes of a side and end of the roof, whose intersections are B C and C D, on the plane of the wall-head. Now the angle \V Q X, which is double the angle WQ 0, is the backing of the hip. Make P V equal to Q \V, andjoin C V, then will P C V be the angle contained by the two sides L C, C D, or that of the hypothenusal plane angle contained by the intersection B C, and the hip—rafter L C. This angle may be otherwise found thus: Produce G H to R; make C R equal to C L, then the angle H C R is equal to P C V. Now the angle H C R, or PCV, is the angle which the purlins (when one of their faces is in the side of the roof) make with the hip-rafter L C; and the angle C -V P, or C R H, is the angle which ajack-rafter makes with the same hip: in the same manner may the backings of the other hips be found. The other bevelofthejack-rafters is the angle H I F. Tofind the other bevel for cutting the shoulder of the purlin, proceed thus: on F, as a centre, with the distance F G, describe the arc G Y; draw FY perpendicular to G I, Y Z parallel to EF, cut- ting F D in Z, and Z 8: parallel to G H, cutting A D in St. Join 8:, F, then G 8:. F is the angle which the other side of the shoulder makes with the length of the purlin. At the other end of this diagram is shewn the manner of finding the two bevels for cutting the shoulder of the purlin against the hip-rafter, when the side of the purlin is not in the plane of the side of the roof. To find the same things by calculation—The back~ ing of the hip-rafter and hypothenusal side is obtained as follows: it has been shewn that the three plane angles, and the three inclinations of solid angles, consisting of three plane angles, are found exactly as the sides and angles of spheric triangles, any three parts being given; the de~ grees of the plane angles being exactly the same as the sides of the spheric triangles, and theincli- nations the proper measures of the spheric angles: M 2 HIP 84: ' HIP M - therefore, if mo of the plane angles should be per- As the sine of the side F C L, 27° 2 9.65705 pendicular to each other, the spheric triangle re- . o — ‘ presenting this solid angle will have also two of 15 t? the tangentofthesgdeFCHfiZ = 10-10719 its sides perpendicular to each other.. Now in SO ‘5 radius, sme 0f 90 " ’ " ‘ = 10-00000 this, there are given the two sides containing 20 16;; gigglersight angle to find the hypothenuse and 9’ 65705 It is shewn, by writers on spherical trigonometry, T0 the tangent 0f the angle OPPO' =_10.45014. that in any right-angled spherical triangle, radius is to the cosine of either of the sides, as the co- sine of the other side to the cosine of the hypo- thenuse. Suppose the plane angle F C L to be 27°, and the angle F C H 52°, to find the hypo- thenuse and angles of a right-angled spherical triangle, one of whose legs is 27° and the other 52°, it will'therefore be As radius, sine of 90° - - - = 10.00000 Is to the cosine of F C L, 27° - = 9 94988 So is the cosine of F C H, 52° = 9.78934 19.73922 10.00000 To the cosine of the hypothe- nusal side 56° 441 ’- - l — 973922 This ascertains the angle which the jack-rafter makes with the hip. Since all the sides are now given, we shall have, by another well-known pro— perty of the sines of the sides being as the sines of the opposite angles, the following proportion : As the sineofthel1ypothenuse56° 44’ - 9.922927 Is to the sine of a right angle,or 90° = 10.00000 So is the sine ofthe side FC H, 59° 2 9.89653 19.89653 999297 To the sine of the opposite angle} = 9.97426 70 28 - - '- - - - - Therefore the backing is twice } : MOO 56' 7o°es-------- In finding the angle opposite the side F C II, it was not necessary that the liypothenusal side should have first been found. It might have been found independently thus: the sine of either of the sides about the right angle is to radius, as the tangent of the remaining side is to the tangent of the angle opposite to that side; therefore, site the side F C H, 70° 28’ - In the same manner may other bevels be found by trigonometrical calculations; but as such extreme exactness is not necessary, the geometrical con- structions ought to be well understood. EXAMPLE 2.—Thefigure, A B C D (Figure 2) of the wall-plate of a hip span-roof, and the height of the roof, being given; to find not only the back- ing (f the hips, the angles made upon the sides of the purlins by their longitudinal arrises, and the angles made upon the sides of the jack-rafters; the roof being equally inclined to the different sides of the building, except at the oblique end, A B. Figure 2.—Let the two sides, A B, A D, and D C of the wall-plate be at right angles to each other, and the end C B at oblique angles to A B and C D; draw the seat, E F, of the ridge in the middle of the breadth, parallel to A B and D C; make A G and D H equal to half the breadth of the building; join G H, which will be the seat of the common rafters adjoining the hips; make E I equal to the height of the roof; and draw IG and I H, which are the length of the com- mon rafters. Draw E D and E A, the seats of the hips; make E K equal to E I; and draw K A, which gives the length of each hip. Through any point, L, in the seat of the hip A E, draw M N perpendicular to A E, cutting the adjacent sides of the wall—plate at M and N; take the nearest distance from L to the rafter A K, and make L 0 equal to it; and draw 0 M and O N; and M O N is the backing of the hips, repre- sented by their seats A E and D E. This operation is the same as having the two legs of a right—angled solid angle to find the angle op~ posite to one of the legs; the angle M O N be- ing exactly the double of the angle so found; for the hip angle of the roof consists of two equal solid angles. Suppose the bevel end at C B to be inclined at a different angle to the other sides, and let F C and F B be the seats of the hips; draw F Q perpen- dicular to 1’ C, and F P perpendicular to 1313, H E P=R G (b 3?. PLATE 1/. F127. :3. G F121. .3. ; ['11)]. 4. “Vi/MIWL lulu/(.m/zA/zm/ All, 13 JL-mw x- ./.1:.u-,;;-u,mumpm- .wmr, he“. 1,.»15” ~"r‘~//'- HHE’ 3943313 ”- l't’lltfi/ ’11/ If -‘7/(‘fi0/J‘Ull . [um/NI [’u/lev/n-J 1m /’ \',j-I...l...... v. / 12....22; 1 m HIP' W 85 HIP then draw Q C and P B, which are the lengths of the hip-rafters. The backings, S U T and V W X, are found in the same manner as above, and may be described in the same words. From A, with the distance A K, describe an are cutting G H at J, and join AJ; then G J A will be the side bevel,which the jack-rafters make with the hips; and if a right angle be addedto GJ A, it will form an obtuse angle, which is that made by the upper arris of the side of a purlin placed in the inclined side of the roof with the hip—rafter. - Let a be the position of a purlin in the rafterH I; in G H take any point, b, and draw b 0 parallel to the inward direction of the purlin a; from b, with any distance, b c, describe an are, c (1, cut- ting G H at d; draw b e, cf, and dg, parallel to E F; the former two cutting E D at e and f; drawfg parallel to G H, and join eg; produce be to h; and h eg, or b e g, will be the angle re- quired, according to which side it is applied: this will be found synonymous to one of the legs; and the adjacent angle of a right-angled solid angle being given, to find the hypothenuse. In the same manner, if neither side of the purlin should be parallel to the inclined side of the roof, as at k in the rafter G I, the bevel or angle upon each side may be found, as shewn. Plate ll. Figure 3, shews half the angle of the backing of the hips, the length of the common and hip rafters, the bevel of the jack-rafters on their upper sides in an equal inclined roof, without lay- ing down or drawing any more than the necessary seats; and this is all that is necessary when each side of the roof is alike; A B being the wall-plate between the hip and the rafter which joins the top of the hip, A C the seat of the rafter which joins the top of the hip, B C that of the hip. A F the length of the rafter which joins/the hip, B E the length of the hips, C H G: half the backing, A D B the angle which the jack-rafters form with the upper sides of the hips, and, consequently, with the addition of a right angle, the side bevel of the purlin. . Figure 4 shews the same bevels, except that the side joint of the purlin is found by a different process, thus: From B, with the distance B A, describe an are at D; from G, with the distance A C, describe another are, cutting the former at D; join B D, and the angle G B D will be the 1' angle in the plane of the roof, made by the lower arris of the purlin and the joint against the hip- rafter. Besides the angles already mentioned, A F C figure 3, shews the angle formed by the upper side of therafter and the ridge-piece, and the angle B E C, the angle which the top side of the hips makes with a vertical or plumb-line, also, the angle FA C shews the form of the heel of the common rafters, and E B C that of the hips. Figure 5 is a diagram shewing the length of the parts and angles concerned in the roof, in the same manner as above; but the plan of the build- ing, or form of the wall-plate, is a quadrilateral, which has neither part of its opposite sides paral— lel ; the method of executing the roofin this case is to form a level on the top, from the top of the— hips at the narrow end to the other extremity, as otherwise the roof must either wind, or be. brought to a ridge forming a line inclined to the horizon; and either of the two last cases is very unsightly. But, that nothing should be wanting, the construction is given in the next figure. Plate Ill. Figure (i.—To lay out an irregular roof in ledgment, with all its beams bevel upon the plan, so that the ridge may be level when finished,- the plan and height of the roof being given. The lengths of the common and hip rafters are found as usual. From each side in the broadest end of the roof, through C and D, draw two lines parallel to the ridge-line; drawlines from the centres and ends of the beams, perpendicular to the ridge-line, and lay out the two sides of the roon and 3, by making ED at 3, equal to X N in 1, the length of the longest common rafter, and c a in 3 equal to u 8; at A, and so on with all the other rafters. Tofind the winding ofthis roof—Take 3/ 8;, half the base of the shortest rafter, and apply this to the base of the longest rafter from z to 1; then the distance from 1 to 2 shews the quantity of winding. ' To lay the sides in winding—Lay a straight beam along the top ends of the rafters at E, that is, from C to E, and lay another beam along the line A B, parallel to it, to take the ends ofthe hip rafters at M and L, and the beams to be made out of winding at first. Raise the beam that lies from A to B,‘at the point B, to the distance 1 2 above the level; which beam, being thus raised, will III? 88 W HIP elevate all the ends of the rafters gradually, the «same asthcy would be when in their places. Thesame is to be understood of the other side 3 D; the ends are laid down in the same manner as .making a triangle of any three dimensions. In this example the purlins are supposed to be framed into the sides of the rafters flush, so that 3 the lop of the purlins may be flush with the back of the rafters. The manner of framing the dragon beams andt‘diagonal ties, is shewn at the angles. Plate IV. Figure 7. shews the manner of framing a roof when the sides are square. The purlins are prepared to bridge over the rafters which are notched Out of the sides next to the back, in order to receive them. .HIPPIUM, in antiquity, that part of the hippo- drome which was beaten by the horses’ feet. HIPPODROME (from the Latin hippodromus, composed of tying, horse, and 350mg, course, of the verb Spa», curro, I nun) in antiquity, a list, or course, wherein chariot and horse-races were per- formed, and horses exercised. The Olympian hippodrome, or horse-course, was .a space of ground of 600 paces long, surrounded with a wall, near the city Elis, and on the banks .of the river Alpheus. It was uneven, and in some .degree irregular, on account of the situation; in one part was a hill of moderate height, and the circuit was adorned with temples, altars, and other embellishments. Pausanias has given us ,the following account of this hippodrome, or horse-course: “ As you pass out of the stadium, :by the seat of the Hellanodics, into the place appointed for the horse-races, you come to the barrier (meson) where the horses and chariots rendezvous before they enter into the course. This barrier, in its figure, resembles the prow of a ship, with the rostrum or beak turned towards the course. The other end, which joins on to the Lportico of Agaptus (so called from him who built it), is very broad. At the extremity of the ros-’ trum or beak, over a bar that runs across the en- trance (rm xuvovoc), is placed a figure of a dolphin in brass. (This dolphin is a symbol of Neptune, surnamed Hippian or Equestrian, for his having produced a horse by striking the earth with his trident, according to the fable; without the re- collection of this circumstance, the reader might be surprised. to meet with the figure of a dolphin in a horse-course.) On the two sides of the bar- ;rier, each of which is above 400 feet in length, — are built stands or lodges, as well for the riding- horses as the chariots, which are distributed by lot among the competitors in those races; and before all these lodges is stretched a cable, from one end to the other, to serve the purpose of a barrier. About the middle of the prow is erected an altar, built of unburnt brick, which, every Olympiad, is plastered over with fresh mortar; and upon the altar stands a brazen eagle, which spreads out its wings to a great length. This eagle, by means of a machine, which is put in motion by the president of the horse-races, is made to mount up at once to such a height in the air, as to become visible to all the spectators; and, at the same time, the brazen dolphin before- mentioned sinks to the ground. Upou that signal, the cables stretched before the lodges, on either side of the portion of Agaptus, are first let loose, and the horses there stationed move out and ad- vance till they come over against the lodges of those who drew the second lot, which are then likewise opened. The same order is observed by all the rest, and in this manner they proceed through the beak or rostrum; before which they are drawn up in one line, or front, ready to begin the race, and make trial of the skill of the cha- rioteers and fleetness of the horses. On that side of the course, which is formed by a terrace raised with earth, and which is the largest of the two sides, near to the passage that leads out of the course across the terrace, stands an altar, of a round figure, dedicated to Taraxippus, the terror of the horses, as his name imports. The other side of the course is formed, not by a terrace of earth, but a hill of moderate height, at the end of which is erected a temple, consecrated to Ceres Chamyne, whose priestess has the privilege of seeing the Olympic games.” There is a very famous hippodrome at Constanti— nople, which was begun by Alexander Severus, and finished by Constantine. This circus, called by the Turks Atmez’dan, is 400 paces long, and above 100 paces wide, 2'. e. geometrical paces of five feet each. \Vheeler says, it was in length about 550 ordinary paces, and in breadth about 120; or, allowing each pace to be five feet, 2750 feet long and 600 broad. At the entrance of the hippodrome there is a pyramidal obelisk of gra- nite, in one piece, about 50 feet high, terminat- ing in a point, and charged with hieroglyphics, erected on a pedestal of eight or ten feet above HI P ROOF PLATE 11/. I ‘VI’r/Iu/mn/I . Limb/1 . I’ll/Ilia'lml [IJ'Ji Nil-hula)" 1" J Iful'lir/‘l, ”I'm/our III-(rt . 11915;. [fly/awn] lgy ('. JrI/LrIru/Iy . HIP 87 HOO 2.1! W =54 W- the ground. The Greek and Latin inscriptions on its base shew that it Was erected by Theodo- sius; the machines that were employed to raise it were represented upon it in basso-relievo. The beauty of the hippodrome at Constantinople has been long since defaced by the rude hands of the Turkish conquerors; but, under the similar appellation of Atmeidan, it still serves as a place of exercise for their horses. Whether the Olym- pic hippodrome was so long or so wide as this of Constantinople, it is not now easy to determine; but it must evidently have been considerably longer than an ordinary stadium, in order to allow for the turnings of the chariots and horses round the pil- lars which served as metas or goals, without running against them, or against one another. The length of the course, or the distance between the two metas or goals, is not easily ascertained. It is probable, however, that the two pillars, viz. that from which the horses started, and that round which they turned, which divided the course into two equal lengths,were two stadia distant from each other; consequently, the whole length of the race, for a chariot drawn by full aged horses, consist- ing of 12 rounds, amounted to 48 stadia, or six Grecian miles; and that of the chariot drawn by colts consisted of eight rounds, or 32 stadia, or four Grecian miles; a Grecian mile, according to Arburthnot’s computation, being somewhat more than 800 paces, whereas an English mile is equal to l056. Pausanias informs us, that in the Olym- pic hippodrome, near that pillar called Nyssé, probably that which was erected at the lower end of the course, stood a brazen statue of Hippo- damia, holding in her hand a sacred fillet or dia- dem, prepared to bind the head of Pelops for his victory over (Enomaus; and it is probable that the whole space between the pillars was filled with statues or altars, as that in the hippodrome at Constantinople seems to have been. Here, however, stood the tripod, or table, on which were placed the olive-crowns and the branches of palm destined for the victors. Besides the hip- podromes at Olympia and Constantinople, there were courses of a similar kind at Carthage, Alex- andria in Egypt, and other places. We have some vestiges in England of the hippo- drome, in whichthe ancient inhabitants of this country performed their races. The most remark- able is that. near Stone-henge, which is a long. tract of ground, about 850 feet, or 200'druid cubits wide, and more than a mile and three- quarters, or 6000 druid cubits in length, enclosed quite round with a bank of earth, extending di- rectly east and west. The goal and career are at the east end. The goal is a high bank of earth, raised with a slope inwards, on which the judges are supposed to have sat. The meta: are two tumuli, or small barrows, at the west end‘ of’: the course. These hippodromes were called, in the language of the country, rhedagmt, the racerr r/tedagwr, and the carriage Theda, from the British, word rhedeg, to run. One of these hippodromes, about half a mile to theisouthward of Leicester, retains evident traces of the old name rhedagua, in the corrupted one oframlikes. There is another. of these, says Dr. Stukely, neiir Dorchester; an-- other on the banks of the river Lowther, near Penryth in Cumberland; and another in the val- ley just without the town of Royslon. HISTORICAL COLUMNS, see COLUMN. HOARDING (from the Saxon) an enclosure about a building, while erecting or under repair. HOLLOW (from hole) a concave mouldinggwhose‘ section is about the quadrant ofa circle. It is by: some writers called easement. HOLLOW NEWEL, an opening in the middle of a staircase. The term is used in contradistinction to solid nerve], into which the ends of the steps are built. In the hollow newel, or well-hole, the- steps are only supported at one end by the sur-- rounding wall of the staircase, the ends next the hollow being unsupported. HOLLOW WALL, a wall built in two thicknesses, leaving a cavity between, either for the purpose of saving materials, or to preserve an uniform. temperature in the apartments. rHOLLow QUOiNs, in enginery, piers of stone or large bricks, made behind each lock-gate of a canal, which arecformed into a hollow from top, to bottom, to receive the rounded head of the lock-gates: in some instances the hollow quoin is formed of one piece of oalr, cut to the proper. shape, and fixed vertically against the wall; and even cast iron has been used, on. some recent occasions,.for forming the hollow-quoin or hinge for the lock-gates of'large canals, or the entrance- basons to docks. HOMOLOGOUS (from 51.49;, similar, and Aoyog, rea- son) in geometry, the correspondent sides ofsimi-~ lar figures. HOOK PlNS, in carpentry, iron pins-made tapering HOT m -——-——_— towards one end, for the purpose of drawing the pieces of a frame together, as in floors, roofs, See. In joinery,‘ the pins which answer a similar pur- pose are called DRAW-BORE PINs. HOOKS (Saxon) bent pieces of iron, used to fasten bodies together, or to hang articles on, out of the way. They are of various kinds, some of iron and some of brass; as casement-hooks, chimney- hooks, which are made of both brass and iron; curtain-hooks, hooks for doors and gates, double line-hooks, tenter-hooks, armour-hooks, Ste. HORDING, see HOARDING. HORIZONTAL CORNICE, of a pediment, the level part under the two inclined eornices. HORIZONTAL LINE, in perspective, the vanishing line of planes parallel to the horizon. HORIZONTAL PLANE, a plane passing through the eye, parallel to the horizon, and producing the vanishing line of all level planes. HORIZONTAL PROJECTION, the projection made on a plane parallel to the horizon. This may be understood either perspectively or orthographi- callyd accOrding as the projecting rays are directed to agiven point, or are perpendicular to the horizon. HORN (Saxon) a name sometimes applied to the Ionic volute., : . HORSE PATH, in enginery, a name sometimes applied to the towing-path by the side of all canals, and by narrow navigable rivers, for the use of the towing or track horses. HORSE RUN, in enginery, a simple and useful mo— dern contrivance, for drawing up loaded wheel- barrows of soil from the deep-cuttings of canals, docks, &c. by the help of a horse which goes backwards and forwards, instead of round, as in a horse-gin. llORSING BLOCK, a square framebfstrong boards, used by navigators or canal diggers for elevating the ends of their wheeling planks. HOSTEL, or HOTEL, a French term, anciently signifying a house, but now more commonly used for the palaces or houses of the king, princes, dukes, and great lords. HOT-HOUSE, a house for raising and preserving fine fruits Of various kinds, as the fig, the peach, the cherry, the nectarine, the pine-apple, grapes, Ste. each of which requires something particular in the construction of the hot-house. Those which are intended for the peach, necta- rine, cherry, and fig, 8te. are in general, with great propriety, in cold situations, constructed 8 QC- H OT . ‘ r against walls, being‘made with glass on one side. Butin climates that are less seVere, such houses as are formed of glass on allthe sides, having the trees so planted as to... grow irregularly in the 'standard‘method, may bemore beneficial as well as more ornamental. V _ For thefforcing Of vines, they may be of any kind of form,‘either small or large,,according to the season at which the trees are to be brought into fruit. But a double-roofed house, with an inner roofing, is advised by some as the most proper for general crops, as well as the most cheap in its nature. Butin the general construction of these houses, a wall of eight or ten feet in height or more, is raised behind, with a low wall in front and both ends, on which is placed upright glass—work, four, five, or six feet, and a sloping glass roof, ex— tending from the top of the front to the back wall. Internal fines for fire-heat, in winter, are also contrived, and a capacious Oblong or square pitpin the bottom space, in which to have a con- stant bark-bed, to furnish a continual regular heat at all seasons; so as in the whole to warm the enclosed internal air always to a certain proper . high degree. Houses thus formed are mostly used in raising pines. Hot-houses are mostly ranged lengthwise, nearly east and west, that the glasses of the front and roof may have the full influence of the sun. This is the most convenient situation for common houses, either for pines or exotic plants. But some houses of this sort, instead of being placed, in this direction, have lately been ranged directly south and north, having a sloped roof to each side, like the roof of a house; also to the front or south end ; both sides and the south end front being of glass. These houses are made from ten or twelve to fifteen or twenty feet wide, the length at pleasure; and from ten to twelve feet high in the middle, both sides fully head height; being formed by a brick wall all round, raised only two or three feet on both sides, and south- end; but at the north end like the gable Of a house. Upon the top of the side and south end walling is erected the framing for the glass—work, which is sometimes formed two or three feet up- right, immediately on the top of the wall, having the sloped glass-work above; and sometimes wholly Ofa continued slope on both sides, imme- diately from the top of the side walls to that of M ‘ HOT L the middle ridge. They are furnished either with one or two bark-pits ; but if‘ of any considerable width, generally with two, ranging parallel, one under each slope of the top glass, separated by a two-foot path running along the middle of the house, and sometimes continued all round each pit, with flues ranged along against the inside walls; the whole terminating in an upright fun- nel, or chimney, at the north end of the building. There are other hot-houses which are formed en- tirely on the square, having a ten or twelve feet brick wall behind; that of the front, and both sides, only two or three feet high for the support of the glass-work, placed nearly upright almost the same height, and sloped above on both sides and front, which are wholly of glass. These are furnished within with bark-pits and fines, as in the other sorts. . In particular cases they are likewise made semi- circular, or entirely circular, being formed with a two or three feet brick wall supporting the glass- framing, which is continued quite round; having the bark-pit also circular, and Hues carried all round the inside of the walling, terminating in a chimney on the northern side of the house. How- ever, the first forms are probably the best for ge- neral purposes. ‘ Hot-houses on these plans are made of different dimensions, according to the size of the plants they are designed to contain; but for common purposes they should be only of a moderate height, not exceeding ten or twelve to fourteen feet behind, and five or six in front; some are, however, built much more lofty behind, to admit .of the taller—growing exotics placed toward the back part, to grow up accordingly in a lofty sta- ture; but the above are best adapted to the cul- ture of pines, and other moderate growing plants, as well as for forcing in; as very lofty houses re- quire a greater force of heat, and by the glasses being so high, the plants receive less benefit from the sun, and are apt to draw up too fast into long slender leaves and stems, as they naturally tend towards the glasses. Where the top glasses are at a moderate distance from the plants, they receive the benefit of the sun’s heat more fully, which is'essential in winter, and become more stalky at bottom, and assume a more robust and firm growth, particularly the pine-apple, and are thereby more capable of producing large fruit in the season. VOL. II. 89 HOT #— After having determined on the dimensions as to length and width, the foundations of the house should be set out accOrdingly of brick-work, al- lowing due width at the bottom to support the flues a foot wide, wholly on the brick basis, de— tached an inch or two from the main walls; then setting off the back or north wall, a brick and a half or two bricks thick, and the front and end walls nine inches, carrying up the back wall from ten to fourteen feet high; but those ofthe front and ends only from about two feet to a yard; taking care in carrying up the walls to allot a proper space for a door-way, at one or both ends, to- ' wards the back part; setting out also the furnace or fire—place of the fines in the bottom foundao tion, towards one end of the back wall behind, formed also of brick-work, made to communicate with the lowermost flue within. But when ‘of' great length, as forty feet or more, a fire-place at each end may be necessary; or, if more conve- nient, may have them in the back part of the end walls, or both in the middle way of the back wall; each communicating with a separate range of fines; in either case, forming them wholly on the outside of the walls, about twelve or fourteen inches wide in the clear, but more in lengthwise inward; the inner end terminating in a funnel to communicate internally with the fines, fixing an iron-barred grate at bottom to support the fuel; calculated for coal, wood, peat, turf, 8cc. An ash-hole should be made underneath. The mouth or fuel-door should be about ten or twelve inches square, having an iron frame and door fixed to shut with an iron latch, as close as possible. The whole furnace should be raised sixteen or eighteen inches in the clear, finishing the top archwise. Then continue carrying up the walls of the build- ing regularly, and on the inside erect the fines close along the walls. It is sometimes advantageous to have the fines a little detached from the walls, one, two, or three inches, that, by being thus distinct, the heat may arise from both sides, which will be an advantage in more effectually diffusing the whole heat in- ternally in the house; as, when they are attached close to the walls, a very considerable portion of the heat is ineffectually lost in the part of the ‘ wall behind. In contriving the fines, they should .be continued along the front and bothends, in . one range at least, in this order. But it is better if they are raised as high as the outward front N HOT 90 HOT 4- and end walls, in one or tWo ranges, one over the other. On the tops of these may be placed pots of many small plants, both of the exotic and - forcing kinds, with much convenience. Thus proceed in the construction of the fines, making them generally about a foot wide in the whole, including six or eight inches in the clear, formed with a brick-work ‘on edge; the first lower flue should communicate with the furnace or fire-place without, and be raised a little above it, to promote the draught of heat more freely, continuing~ it along above the internal level of the floor of the back alley or walk of the house the above width, and three bricks on edge deep, re- turning it in two or three ranges over one another, next the back wall, and in one or two along the ends and front wall, as the height may admit; each return. two bricks on edge deep, and tiled or bricked over. In the beginning of the first bottom fine a sliding iron regulator may be fixed, to use occasionally, in admitting more or less heat, being careful that the brick-work of each fine is closely jointed with the best sort of mor- tar for that purpose, and well pointed within, that no smoke may break out; having each re- turn closely covered with broad square paving tiles on the brick-work ;' covering the uppermost flues also with broad thick flat tiles, the whole width, all very closely laid, and joined in mortar. The uppermost, or last range of fines, should ter- minate in an upright vent or chimney, at one end of the back wall; and where there are two sepa- rate sets of lines, there should be a chimney at each end. An iron slider in the termination of the last flue next the chimney may also be pro- vided, to confine the heat more or less on parti- cular occasions, as may be found necessary. ‘But sometimes, in very wide houses, in erecting the fines, to make all possible advantage of the fire—heat, one or more spare fines, for occasional use, is continued round the bark-pit, carried up against the surrounding wall, but detached an inch or two, to form a vacancy for the heat to come up more beneficially, and that, by having vent, it may not dry the tan of the bark-bed too much; and in the beginning a sliding iron regu- lator may be fixed, either to admit or exclude the ‘ heat, as expedient; so that the smoke, by run- ning through a larger extent, may expend its heat wholly in the fines, before it be discharged at the chimney. Great care must likewise be taken that neither the fire-place nor flues be car- ried too near any of the wood-work of the build- ings. After this work is done, proceed to set out the cavity for the bark-pit, first allowing aspace next the fines for an alley or walk, eighteen inches or two feet all round, and then in the middle space form the pit for the bark-bed, six or seven feet wide, the length in proportion to that of_the house, and a yard or more deep; enclosing it by a surrounding wall. It may either be sunk at bottom a little in the ground, raising the rest above by means of the pararapet wall ; or, if there is danger of wet below, it should be raised mostly above the general surface. The surrounding wall should be nine inches, but a brick-wide wall is often made to do, especially for that part which forms the parapet above ground. It should be coped all round with a timber plate or kirb, framed and mortised together, which effectually secures the brick-work in its proper situation. The bottom of the pit should be levelled and well rammed, and, if paved with any coarse material, it is of advantage in preserving the bark. And the path or alley round the pit must be neatly paved with brick or stone, as may be most con- venient. The glass part, for enclosing the whole, should consist ofa close continued range of glass sashes all along the front, both ends and roof, quite up to the back wall ; each sash being a yard, or three feet six inches wide; and for the support of which, f‘ramings of timber must be erected in the brick walling, conformable to the width and length of the sashes, the whole being neatly fixed. And for the reception of the perpendicular glasses in the front and ends, a substantial timber plate must be placed along the top of the front and end walls, upon which should be erected uprights, at proper distances, framed to a plate or crown- piece above, of sufficient height to raise the whole front head high, both ends corresponding with the front and back; a plate of timber being also framed to the back wall above, to receive the sloping bars from the frame-work in front; proper grooves being formed in the front plates below and above, to receive the ends of the per- pendicular sashes, sliding close against the out- side of the uprights all the way along the front, or they may be contrived for only every other M HOT sash, to slide one on the side of the other, but the former is the better method. And from the top of the upright framing in front should be carried substantial cross-bars or bearers, sloping to the back wall, where they are framed at both ends to the wood—work or plates, at regu- lar distances, to receive and support the sloping glass sashes of the roof, when placed close to- gether upon the cross bars or rafters, and generally ranging in two or more tiers, sliding one over the other, of sufiicient length together to reach quite from the top of the upright framing in front, to the top of the back wall. The cross bars should be grooved lengthwise above, to carry 03' wet falling between the frames of the sloping lights: making the upper end of the tier of glasses shut close up to the plate in the wall behind, running under a proper coping of wood or lead, fixed along above close to the wall, and lapped down of due width to cover, and shoot 03‘ the wet suffi- ciently from the upper termination of the top sashes. Some wide houses have, exclusive of the main slope, sliding glass sashes, a shorter upper tier of glass fixed; the upper ends being secured under a coping as above, and the lower ends lap- ping over the top ends of the upper sliding tier, and this over that below in the same manner, to shoot the wet clear over each upper end or term i- nation; likewise, along the under outer edge of the top plate, or crown-piece in front, may be a small channel to receive the water from the slop- ing glass sashes, and convey it to one or both ends without running down upon the upright sashes, being careful that the top part behind be well framed and secured water—tight, and the top of the back wall finished a little higher than the glass, with a neat coping the whole length of the building. And the bars of wood which support the glasses should be neatly formed, and made neither very broad nor thick, to intercept the rays of the sun. Those however, at top, should be made strong enough to support the glasses without bending under them. In wide houses, uprights are ar- ranged within, at proper distances, to support the cross rafters more perfectly than could other- wise be the case. But in respect to the glass-work in the sloping sashes, the panes of glass should be laid in putty, with the ends lapping over each other about half an inch, the vacancies of which are, in some, 91 I HOT —‘__7 closed up at bottom with putty, others leave each lapping of the panes open, in order for the air to enter moderately, and that the rancid vapours arising from the fermentation of the bark-bed, Sic. within, may thereby be kept in constant mo— tion, without condensing much, and also that such as condense against the glasses may dis- charge themselves at those places, without drop- ping upon the plants. The upright sashes in front may either be glazed as above, or the panes laid in lead-work; being very careful to have the glazing well performed, and proof against any wet that may happen to beat against them. The doors should have the upper parts sashed and glazed, to correspond with the other glass-work of the house. ' And on the inside, the walls should be plastered, pargeted, and white-washed; and all the wood~ work, within and without, painted white in oil« colour. Some, however, have the back wall painted or coloured rather dark. Ranges of narrow shelves, for pots of small plants, may be erected where most convenient, some he— hind over the flues, a single range near the top glasses towards the back part, supported either by brackets suspended from the crossbars above, or by uprights erected on the parapet wall of the hark-pit. A range or two of narrow ones may also be placed occasionally along both ends above the fines, where there is a necessity for a very great number. In wide houses, where the cross bars or bearers of the sloping or top glass sashes appear to want support, some neat uprights, either of wood or iron, may be erected upon the bark-bed walling, at convenient distances, and high enough to reach the bearers above. This is a neat mode of afford- ing them support. And on the outside, behind, should be erected a. close shed, the whole length, or at leasta small covered shed over each fire—place, with a door to shut, for the convenience of attending the fires; but the former is much the best, as it will serve to defend the back of the house from the outward air, and to stow fuel for the general use of them, also for garden tools, and all garden utensils, when not in use, to preserve them from the weather; as well as to lay portions of earth in occasionally, i to have it dry, for particular purposes in winter and early spring, as in forcing frames, Ste. Sometimes hot-houses are furnished with top H 2 HOU 4. covers, to draw over the glass sashes occasionally, in time of severe frosts and storms; and some- times by slight sliding shutters, fitted to the width of the separate sashes; but these are incon- venient, and require considerable time and trouble in their application. At other times they are formed of painted' canvass, on long poles or rollers, fixed lengthwise along the tops of the houses, 'just above the upper ends of the top sashes, which, by means of lines and pulleys, are readily let down and rolled up, as there may be occa- sion. HOVEL (Saxon) a low building, with some part of the lower side open, to afford shelter to young animals during stormy weather. HOVELING, thegcarrying up of the sides of a ’chimney, that when the wind rushes over the mouth, the smoak may escape below the current, or against any one side of it. The working up of the sides is covered at the top with tiles or bricks in a pyramidal form, in order to get rid of ‘the inconvenience occasioned by adjoining build- ings being higher than the chimney, or by its . being in the eddy of any very lofty buildings, or ~ in the vicinity of high trees ; in which cases the covered side must be towards the building. HOUSE, a habitation, orabuilding constructed for sheltering a man’s person and goods from the in- clemencies of the weather, and the injuries ofill- disposed persons. Houses differ in magnitude, being of two or three, and four stories; in the materials of which they consist, as wood, brick, or stone; and in the purposes for which they are designed, as a manor-house, farm-house, cottage, 8L0. Ancient Rome consisted of 48,000 houses, all in- sulated or detached from each another. A pleasure-house, or country-house, is one built for occasional residence, and for the pleasure and benefit of retirement, air, 8w. This is the villa of the ancient Romans; and what in Spain and Portugal they call gut/eta; in Provence, cassz'no; in some other parts of France, closerz'e; in Italy, ”lg-Ila. The citizens of Paris have also their maisons de boutei/les, bottle-houses, to retire to, and entertain their friends; which in Latin might be called mic-w; the emperor Domitian having a house built for the like purpose, mentioned under this name by Martial. It is a thing principally to be aimed at, in the H 0U W- site or situation of a country-house, or seat, that it have wood and water near it. It is far better to have a house defended by trees than hills; for trees yield a cooling, refreshing, sweet, and healthy air and shade, during the heat of the summer, and very much break the cold winds and tempests from every point in the win- ter. The hills, according to their situation, de- fend only from certain winds; and, if they are on the north side of the house, as they defend from the cold air in the winter, so they also deprive you of the cool refreshing breezes, which are " commonly blown from thence in the summer. And if the hills are situate on the south side, they then prove also very inconvenient. A house should not be too low seated, since this precludes the convenience of cellars. If you can- not avoid building on low grounds, set the first floor above the ground the higher, to supply what you want to sink in your cellar in the ground; for in such low and moist grounds, it conduces much to the dryness and healthiness of the air to have cellars under the house, so that the floors be good and ceiled underneath. Houses built too high, in places obvious to the winds, and not well defended by hills or trees, require more ma- terials to build them, and more also of repara. tions to maintain them; and they are not so com- modious to the inhabitants as the lower built houses, which may be built at a much easier rate, and also as complete and beautiful as the other. In houses not above two stories with the ground» room, and not exceeding twenty feet to the wall~ plate, and upon a good foundation, the length of two bricks,.or eighteen inches for the heading course, will be sufficient for the groundwork of any common structure, and six or seven courses above the earth to a water-table, where the thick- ness of the walls is abated, or taken in, on either side the thickness of brick, namely, two inches and a quarter. For large and high houses, or buildings of three, four, or five stories, with the garrets, the walls of such edifices ought to be from the foundation to the first water-table three heading courses of brick, or twenty-eight inches at least; and at every story a water-table, or taking in on the in- side for the girders and joists to rest upon, laid into the middle, or one quarter of the wall at least, for the better bond. But as for the inner- most or partition wall, a half brick will be suiti- HOU ciently thick; and for the upper stories, nine in- ches, or a brick length, will sutfice. The general principles of the construction of edifi- ces and private houses will be found under the ar- ticle BUILDING. We shall under this head give adescription of the private houses of the ancients, from Vitruvius and Pliny, and conclude the article with a description of several buildings designed by, and executed under the Author’s inspection. Of the private and public Apartments of Houses, and of their Construction according to the d-ifi"erent Ranks of People; (from V etruvius ). “ These buildings being disposed to the proper aspects of the heavens, then the distribution of such places in private houses as are appropriated to the use of the master of the house, and those which are common for strangers, must be also considered: for into those that are thus appro- priated, no one can enter unless invited; such as the cubiculum, the triclinium, the bath, and others of similar use. The common are those which the people unasked may legally enter; such are the vestibulum, cavaedium, peristylium, and those that may answer the same purposes : but to persons of the common rank, the magnifi- cent vestibulum, tablinum, or atrium, are not necessary, because such persons pay their court to those who are courted by others. “ People who deal in the produce of the country must have stalls and shops in their vestibules, and cryptae, horreae, and apothecae, in their houses, which should be constructed in such a manner as may best preserve their goods, rather than be elegant. The houses of bankers and public of- fices should be more commodious and handsome, and made secure from robbers; those of advocates and the learned, elegant and spacious, for the reception of company; but those of the nobles, who bear the honours of magistracy, and decide the affairs of the citizens, should have a princely vestibulum, lofty atrium, and ample peristylium, with groves and extensive ambulatories, erected in a majestic style; besides libraries, piuacothe- cas, and basilicas, decorated in a manner similar to the magnificence of public buildings; for in these places, both public affairs, and private causes, are oftentimes determined. Houses there- fore being thus adapted to the various degrees of people, according to the rules of decor, explained in the first book, will not be liable to censure, and will be convenient and suitable to all pur- 93 HOU poses. These rules also are applicable, not only to city houses, but likewise to those of the coun- try ; except that in those of the city the atrium is usually near the gate, Whereas in the country pseudo—urbana, the peristylium is the first, and then the atrium; havinga paved port'icus around, looking to the palestra and ambulatories. “ I have, as well as I have been able, briefly writ- ten the rules relative to city houses, as I propos- ed. I shall now treat of those in the country, how they may be made convenient, and in what man- ner they should be disposed. “ Of Country Houses, with the Description and use (ftheir several Parts. “In the first place the country should be examined with regard to its salubrity, as written in the first book concerning the founding of a city, for in like manner villas are to be established. Their magnitude must be according to the quantity of land and its produce. The courts and their size must be determined by the number of cattle and yokes of oxen to be there employed. In the warmest part of the court, the kitchen is to be situated,and adjoining thereto the ox-house, with the stalls turned toward the fire and the eastern sky; for the cattle seeing the light and fire, are thereby rendered smooth-coated ; even husband- men, although ignorant of the nature of aspects, think that cattle should look to no other part of the heavens than to that where the sun rises. The breadth of the ox-house should not be less than ten feet, nor more than fifteen; the length should be so much as to allow no less than seven- teen feet to each yoke. “ The bath also is to be adjoined to the kitchen, for thus the place of bathing will not be far from those of the husbandry occupations. The press-room should be near the kitchen, that it might be convenient for the olive business; and adjoining thereto the wine-cellar, having windows to the north; for, should they be toward any part which may be heated by the sun, the wine in that cellar would be disturbed by the heat, and become vapid. The oil-room is to be so situated as to have its light from the southern and hot. aspects; for oil ought not to be congealed, but be attenuated by a gentle heat. The dimen- sions of these rooms are to be regulated by the quantity of fruit, and the number of the vessels; which, if they be culleariae, should in the middle occupy four feet. Also, if the press be not IIOU worked by screws, but by levers, the press-room , should not be less than forty feet long, that thc pressers may have suflicient space: the breadth should not be less than sixteen feet, by which means there will be free room to turn, and to dispatch the work; but if there be two presses in the place, it ought to be twenty-four feet ~ broad. The sheep and goat houses should be so .large, that not less than four feet and a half, nor more than six feet, may be allowed to each animal. The granary should be elevated from the ground, and look to the north or cast, for thus the grain will not so soon be heated, but, being cooled by the air, will endure the longer: the other aspects generate worms and such vermin as usually de- stroy the grain. “ The stable, above all in the villa, should be built in the warmest place, and not look toward the fire, for if these cattle be stalled near the fire, they , become rough-coated : nor are those stalls unuse- ful which are placed out of the kitchen, in the _ open air, toward the east; for in the winter time, when the weather is serene, the beasts, being led thither in the morning, may be cleaned while they are taking their food. “ The barn, hay-room, meal-room, and mill, are placed without the villa, that it may be more secure from the danger of fire. » “ If the villa is to be built more elegantly, it must be constructed according to the symmetry of city houses, before described; but so as not to im- pede its use as a villa. “ Great care ought to be taken, that all buildings have suflicient light, which in villas is easily ob- tained; because there are no walls near to ob- struct it. But in the city, either the height of the party-walls, or the narrowness of the streets, may occasion obscurity. It may however be thus tried; on the side where the light is to be received, let a line be extended from the top of the wall that seems to cause the obscurity, to that place to which the light is required; and if, when looking up along that line, an ample space of the clear sky may be seen, the light to that place will not be obstructed; but if beams, lin- tels, or floors, interfere, the upper parts must be opened, and thus the light be admitted. The upper rooms are thus to be managed: on what- soever part of the heavens the prospect may lie, on that side the places of the windows are to be left, for thus the edifice will be best enlightened. 94. W lIOU As in tricliniums and such apartments, the light is highly necessary, so also is 'it in passages, ascents, and staircases, where people carrying burthens frequently meet each other. “ I have explained as well as l have been able the distributions of our buildings, that they may not be unknown to those who build; I shall now also briefly explain the distribution of houses, accord« ing to the custom of the Greeks, that they also may not be unknown. “ Of the Disposition ojthe Iiouses of tire Greeks. “ The Greeks use no atrium, nor do they build in our manner; but from the gate of entrance they make a passage of no great breadth: on one side of which is the stable, on the other, the porters’ rooms, and these are directly terminated by the inner gates. This place between the two gates is called by the Greeks t/1_1/7-orez'on. After that, in entering, is the peristylium, which peristylium has porticos on three sides. On that side which looks to the south, are two antae, at an ample distance from each other, supporting beams, and so much as is equal to the distance between the antae, wanting a third part, is given to the space inwardly; this place is called by some prostas, by others parastas. From this place, more inwardly, the great (eci are situated, in which the mistress of the family with the work- women reside. On the right and left of the prostas are cubiculae, of which one is called thalamus, and the other ampltithalamas; and in the surrounding porticos, the common tricliniums, cubiculums, and family rooms are erected. This part of the edifice is called gimeconitis. Adjoining to this is a larger house, having a more ample peristylium, in which are four porticos of equal height, or sometimes the one which looks towards the south, has higher columns: and this peristylium, which has one portico higher than the rest, is termed rho.- dian. In these houses they have elegant vestibu- lums, magnificent gates, and the porticos of the peristyliums are ornamented with stucco, plaster, and lacunariae, of inside work (wood). In the porticos which look to the north, are the Cyzicene triclinium, and pinaeothecte; to the east are the libraries, to the west the exedrte, and in those looking to the south are the square oeci, so large that they may easily contain four sets of dining couches, with the attendants, and a spacious place for the use of the games. In these oeci are made HOU I“ 95 HOU m I W the men’s diningcouches,forit isnot their custom for the mothers of families to lie down to dine. This peristylium and part of the house is called andronitides, because here the men only are invited without being accmnpanied by the women. “ On the right and left also, small. houses are erected, having proper gates, tricliniae, and con- venient cubiculze, that when strangers arrive, they may not enter the peristylium, but be re- ceived in this hospitalium; for when the Greeks were more refined and opulent, they prepared tricliniae, cubiculae, and provisions, for strangers ; the first day inviting them to dinner, afterwards sending them poultry, eggs, herbs, fruits, and other productions of the country ' Hence the pictures representing the sending of gifts to strangers, are by the painters called zenia. Mas- ters of families, therefore, while they abode in the hospitium, seemed not to be from home, hav- ing the full liberty of retirement in these hospi- taliums. Between the peristylium and hospita- lium are passages, which are called mesaula; because they are situated between two dale,- these are by us called andronas; but it is remark- able that the Greeks and Latins do not in this agree; for the Greeks give the name of andro- nas to the oecus where the men usually dine, and which the women do not enter. “ It is the same also with some other words, as systos, prothyrum, telamones, and others; for xystos is the Greek appellation of those broad porticos, in which the athlette exercise in winter time; whereas, we call the uncovered ambula- tories aystos; and which the Greeks callperidro- midas. The vestibula, which are before the gates, are by the Greeks called prot/zyra; whereas, we call protfiz/ra that which the Greeks call dzathyra. The statues of men bea1ing mutules or cornices we call tclamones, for what reason is not to be found in history; but the Greeks call them atlan- tas; Atlas being in history represented as sup- porting the world; for he was the first who, by his ingenuity and diligence, discovered and taught mankind the course of the sun and moon, the rising and setting of all the planets, and the revolutions ofthe heavens; for which benefit the painters and statuaries represented him bearing the whole earth; and the Atlantides, his children, which we call Vergilius, and the Greeks Pleiaa'es, are placed among the stars in the heavens. l have not, however, mentioned this in order to change the customary names or manner of dis- coursing, but only to explain them, that these things might not be unknown to the lovers of knowledge.” Extracts from Pliny’s Letters. Description of the villa at Laurentinum. “ You are surprised, it seems, that I am so fond of my Laurentinum or (if you like the appella- tion better) my Laurens: but you will cease to wonder, when I acquaint you with the beauty of the villa, the advantages of its situation, and the extensive prospect of the sea-coast. It is but seventeen miles distant from Rome; so that, having finished my affairs in town, I can pass my evenings here, without breaking in upon the busi~ ness of the day. There are two different roads to it: if you go by that of Laurentum, you must turn off at the fourteenth mile- stone , if by ()s- tia, at the eleventh. Both of them are, in some parts, sandy, which makes it somewhat heavy and tedious, if you travel in a carriage, but easy and pleasant to those who ride on horseback. The landscape, on all sides, is extremely diversified, the prOSpect, in some places, being confined by woods, in others, extending over large and beautiful meadows, where numberless flocks of sheep and herds of cattle, which the severity of the winter has driven from the mountains, fatten in the ver- nal warmth of this rich pasturage. lVIy villa is large enough to afford all desirable accommoda- tions, without being extensive. The porch before it is plain, but not mean, through which you enter into a portico in the form of the letter D, which includes a small but agreeable area. This affords a very commodious retreat in bad weather, not only as it is enclosed with windows, but par- ticularly as it is sheltered by an extraordinary projection of the roof. From the middle of this portico you pass into an inward court, extremely pleasant, and from thence into a handsome hall, which runs out towards the sea; so that when there is a south-west wind, it is gently washed with the waves, which spend themselves at the foot of it. On every side of this hall, there are either folding-doors, or windows equally large, by which means you have a view from the front. and the two sides, as it were, of three different seas: from the back part, you see the middle court, the portico, and the area; and, by another view, you look through the portico into the porch, from whence the prospect is terminated by the woods W HOU 9 . E I and mountains which are seen at a distance. On the left-hand of ,thishall, somewhat farther from the sea, lies a large drawing-room, and beyond that, a second of a smaller size, which has one window to the rising, and another to the setting sun: this has, likewise, a prospect of the sea, but being at a greater distance, is less incommoded by it. The angle which the projection of the hall forms with this drawing—room, retains and increases the warmth of the sun; and hither my family retreat in winter to perform their exer- ‘ cises: it is sheltered from all winds, except those which are generally attended with clouds, so that nothing can render this place useless, but what, at the same time, destroys the fair weather. Conti- guous to this, is a room forming the segment of a circle, the windows of which are so placed, as p to receive the sun the whole day: in the walls are contrived a sort of cases, which contain a collection of such authors whose works can never be read too often. From hence you pass ‘ into a bed-chamber through a passage, which, > being boarded and suspended, as it were, overa stove which runs underneath, tempers the heat which it receives and conveys to all parts of this room. The remainder of this side of the house is appropriated to the use of my slaves and freed- men: but most of the apartments, however, are neat enough to reCeive any of my friends. In the opposite wing, is a room ornamented in a very elegant taste; next to which lies another room, which, though large for a parlour, makes but a moderate dining-room; it is exceedingly warmed and enlightened, not only by the direct rays of the sun, but by their reflection from the sea. Beyond, is a bed-chamber, together with its anti-chamber, the height of which renders it cool in summer; as its being sheltered on all sides from the winds makes it warm in winter. To this apartment another of the same sort is joined by one common wall. From thence you enter into the grand and spacious cooling-room, belonging to the bath, from the opposite walls of which, two round basons project, sufficiently large to swim in. Contiguous to this is the per- fuming-room, then the sweating—room, and next to that, the furnace which conveys the heat to the baths: adjoining, are two other little bathing- rooms, fitted up in an elegant rather than costly manner: annexed to this, is a warm bath of ex- traordinary worlunanship, wherein one may swim, llOU and have a prospect, at the same time, of the sea. Not far from hence, stands the tennis court, which lies open to the warmth of the afternoon sun. From thence you ascend a sort of turret, contain~ ing two entire apartments below; as there are the same number above, besides a dining-room which commands a very extensive prospect of the sea, together with the beautiful villas that stand interspersed upon the coast. At the other end, is a second turret, in which is a room that receives the rising and setting sun. Behind this is a large repository, near to which is a gallery of curiosities, and underneath a spacious dining- room, where the roaring of the sea, even in a storm, is heard but faintly: it looks upon the garden and the gestatio, which surrounds the garden. The gestatio is encompassed with a box-tree hedge, and where that is decayed, with rosemary: for the box, in. those parts which are sheltered by the buildings, preserves its verdure perfectly well -, but where, by an open situation,it lies exposed to the spray of the sea, though at a great distance, it entirely withers. Between the garden and this gestatio runs a shady plantation of vines, the alley of which is so soft, that you may walk bare foot upon it without any injury. The garden is chiefly planted with fig and mulberry trees, to which this soil is as favourable, as it is averse from all others. In this place is a banqueting- room, which, though it stands remote from the sea, enjoys a prospect nothing inferior to that View: two apartments run round the back part of it, the windows whereof look upon the entrance of the villa, and into a very pleasant kitchen- garden. From hence an enclosed portieo ex- tends, which, by its great length, you might sup- pose erected for the use of the public. It has a range of windows on each side, but on that which looks towards the sea, they are double the number of those next the garden. When the weather is fair and serene, these are all thrown open; but if it blows, those on the side the wind sets are shut, while the others remain unclosed without any in- convenience. Before this portieo lies a terrace, perfumed with violets, and warmed by the reflec— tion of the sun from the portieo, which, as it re- tains the rays, so it keeps off the north-east wind; and it is as warm on this side as it is cool on the opposite: in the same manner it proves a defence against the south-west; and thus, in short, by means of its several sides, breaks the force of the Hod Afi— ! winds from what point soever they blow. These are some of its winter advantages: they are still more considerable in summer; for at that season it throws a shade upon the terrace during all the forenoon, as it defends the gestatio, and that part of the garden which lies contiguous to it, from the afternoon sun, and casts a greater or less shade, as the day either increases or decreases; but the portico itself is then coolest, when the sun is most scorching, that is, when its rays fall directly upon the roof. To these its benefits I must not forget to add, that, by setting open the windows, the western breezes have a free draught, and, by that means, the enclosed air is prevented from stagnating. On the upper end of the ter- race and portico stands a detached building in the garden, which I call my favourite; and in- deed it is particularly so, having erected it my- self. It contains a very warm winter-room, one side of which looks upon the terrace, the other has a View of the sea, and both lie exposed to the sun. Through the folding doors you see the opposite chamber, and from the window is a prospect of the enclosed portico. On that side next the sea, and opposite to the middle wall, stands a little elegant recess, which, by means of glass doors and a curtain, is either laid into the adjoining room, or separated from it. It con- tains a couch and two chairs. As you lie upon this couch, from the feet you have a prospect of the sea; if you look behind, you see the neigh- bouring villas; and from the head you have a view of the woods: these three views may be seen either distinctly from so many different windows in the room, or blended together in one confused prospect. Adjoining to this is a bed- chamber, which neither the voice of the servants, the murmuring of the sea, nor even the roaring of a tempest, can reach; not lightning nor the day itself can penetrate it, unless you open the windows. This profound tranquillity is occa— sioned by a passage, which separates the wall of this chamber from that of the garden; and thus, by means of that intervening space, every noise is precluded. Annexed to this is a small stove- room, which, by opening a little window, warms the bed-chamber to the degree of heat required. Beyond this lies a chamber and ante-chamber, which enjoys the sun, though obliquely indeed, from the time it rises, till the afternoon. When I retire to this garden-apartment, I fancy myself VOL. II. '97 HOU -—_————h———- a hundred miles from my own house, and take particular pleasure in it at the feast of the Satur- nalia, when, by the licence of that season of fes- tivity, every other part of my villa resonnds with the mirth of my domestics: thus I neither interrupt their diversions, nor they my studies. Among the pleasures and conveniencies of this situation, there is one disadvantage, and that is, the want of a running stream ; but this defect is, in a great measure, supplied by wells, or rather I should call them fountains, for they rise very near the surface. And, indeed, the quality of this coast is remarkable; for in what part soever you dig, you meet, upon the first turning up of the ground, with a spring of pure water, not in the least salt, though so near the sea. The neighbouring forests afford an abundant supply of fuel; as every other accommodation of life may be had from Ostia: to a moderate man, in- deed, even the next village (between which and my house there is only one villa) would furnish all common necessaries. In that little place there are no less than three public baths; which is a great conveniency, if it happen that-my friends come in unexpectedly, or make too short a stay to allow time for preparing my own. The whole coast is beautifully diversified by the con- tiguous or detached villas that are spread upon it, which, whether you view them from the sea or the shore, have the appearance of so many different cities. The strand is sometimes, after a long calm, perfectly smooth, though, in general, by the storms driving the waves upon it, it is rough and uneven. I cannot boast that our sea produces any very extraordinary fish; however, it supplies us with exceeding fine soals and prawns; but as to provisions of other kinds, my villa pretends to excel even inland countries, par- ticularly in milk; for hither the cattle come from the meadows in great numbers, in pursuit of shade and water. “ Tell me now, have I notjust cause to bestow my time and my affection upon this delightful retreat? Surely you are too fondly attached to the plea- sures of the town, if you do not feel an inclina— tion to take a view of this my favourite villa. I much wish, at least, you were so disposed, that to the many charms with which it abounds, it might have the very considerable addition of your company to recommend it. Farewel.” The following observations may tend to illustrate 0 , much considered in the disposition of the several HOU 98 . several of the obscure parts, in the foregoing » description of Pliny’s villa, at Laurentinum. Pliny had no estate round his. seat at Laurentinum; hislwhole possessions there being included (as ,he informs us, B. 4. Let. 6.)in the house and gardens. It was merely a winter villa, in which he used to spend some of the cold months, whenever his business admitted of his absence from Rome; and, for this reason it is, that we find warmth is so apartments, Src. And, indeed, he seems to have a principal view to its advantages as a winter house throughout the whole description of it. Scamozzi, in his Architect. Univers. lib. 3. 12. has given a plan and elevation of this villa. lVIons. Felibien has also annexed a plan to his transla- tion of this letter; as our own countryman, the ingenious Mr. Castel, has done in his Villas of the Ancients illustrated. But they differ extremely among themselves as to the disposition of the several parts of this building, and, perhaps, have rather pursued the idea of modern architecture, than that which is traced out in their original; at least, if the supposition advanced by one of the commentators upon this epistle be true; who contends, that the villas of the ancients were not one uniform pile of building contained under the same roof, but-that each apartment formed a distinct and separate member from the rest. The ruins of this villa are said to have been discovered some time about the year 1714, but whether any plan was ever taken of so valuable a remain of antiquity, or the reality of it ascertained, the translator has not been able to learn. The Roman magnificence seems to have particu- larly displayed itself in the article of their baths. Seneca, dating one of his epistles from a villa which once belonged to Scipio Africanus, takes occasion, from thence, to draw a parallel between the simplicity of the earlier ages, and the luxury of his own times in that instance. By the idea he gives of the latter, they were works of the highest splendour and expense. The walls were composed of Alexandrine marble, the veins whereof were so artfully managed, as to have the appearance of a regular picture: the edges of the basons were set round with a most valuable kind of stone, found in Thasius, one of the Greek islands, variegated with veins of different colours, interspersed with streaks of gold; the water was conveyed through silver pipes, and _ HOU fell, by several descents, in beautiful cascades. The floors were inlaid with precious gems, and an intermixture of statues and colonnades contributed to throw an air of elegance and grandeur upon the whole. Vide Sen. Ep. 86. “The custom of bathing in hot water was be- come so habitual to the Romans, in Pliny’s time, that they every day practised it before they lay down to eat; for which reason, in the city, the public baths were extremely numerous; in which Vitruvius gives us to understand, there were, for each sex, three rooms for bathing, one of cold water, one of warm, and one still warmer; and there were cells of three degrees of heat for sweating: to the fore-mentioned members, were added others for anointing and bodily exercises. The last thing they did before they entered into the dining-room was to bathe; what preceded their washing was their exercise in the spheris- terium, prior to which it was their custom to anoint themselves. As for their sweating-rooms, though they were, doubtless, in all their baths, we do not find them used but upon particular occasions.” Castel’s Villas of the Ancients, p.31. “The enclosed porticos in Pliny’s description differed no otherwise from our present galleries, than that they had pillars in them: the use of this room was for walking.” Castel’s Villas, p. 44. Mr. Castel observes, that though Pliny calls his house Villula; it appears that, after having described but part of it, yet, if every diaeta or entire apartment may be supposed to contain three rooms, he has taken notice of no less than forty-six, besides all which there remains near half the house undescribed, which was, as he says, allotted to the use of the servants; and it is very probable this part was made uniform with that he has already described. But it must be remembered, that diminutives in Latin do not always imply smallness of size, but are frequently used as words of endearment and approbation; and in this sense it seems most probable that Pliny here uses the word Villula. The following is Pliny’s description of his sum- mer villa in Tuscany, Book V. Letter VI. ad- dressed to Apollinaris. “ The kind concern you expressed when you heard of my design to pass the summer at my villa in Tuscany, and your obliging endeavours to dis- suade me from going to a place which you think unhealthy, are extremely pleasing to me. I con- A HOU 4 ECU 1—.— \ 4222M. fess, the atmosphere of that part of Tuscany, which lies towards the coast, is thick and un- wholesome: but my house is situated at a great distance from the sea, under one of the Apen- nine mountains, which, of all others, is most esteemed for the clearness of its air. But that you may be relieved from all apprehensions on my account, I will give you a description of the temperature of the climate, the situation of the country, and the beauty of my villa, which I am persuaded you will read with as much pleasure as I shall relate. The winters are severe and cold, so that myrtles, olives, and trees of that kind, which delight in constant warmth, will not flourish here: but it produces bay-trees in great perfection; yet, sometimes, though, indeed, not oftener than in the neighbourhood of Rome, they are killed by the severity of the seasons. The summers are exceedingly temperate, and con- tinually attended with refreshing breezes, which are seldom interrupted by high winds. If you were to come here, and see the numbers of old men, who have lived to be grandfathers and greatrgrandfathers, and hear the stories they can entertain you with of their ancestors, you would fancy yourself born in some former age. The disposition of the country is the most beautiful that can be imagined; figure to yourself an im- mense amphitheatre; but such as the hand of nature only could form. Before you lies a vast extended plain, bounded by a range of moun- tains, whose summits are covered with lofty and venerable woods, which supply variety of game: from thence, as the mountains decline, they are adorned with underwoods. Intermixed with these, are little hills of so strong and fat a soil, that it would be difficult to find a single stone upon them; their fertility is nothing inferior to the lowest grounds; and though their harvest, indeed, is somewhat later, their crops are as well matured. At the foot of these bills the eye is presented, wherever it turns, with one unbroken view of numberless vineyards, terminated by a border, as it were, of shrubs. From thence you have a prospect of the adjoining fields and mea- dows below. The soil of the former is so ex- tremely stiff, and, upon the first ploughing, turns up in such vast clods, that it is necessary to go over it nine several times, with the largest oxen and the strongest ploughs, before they can be thoroughly broken; whilst the enamelled mea- dows produce trefoil, and other kinds of herbage, as fine and tender as if it were butjust sprung up, being continually refreshed by never-failing rills. But though the country abounds with great plenty of water, there are no marshes; for, as it lies upon a rising ground, whatever water it receives without absorbing, runs off into the Tiber. This river, which winds through the mid-v dle of the meadows, is navigable only in the winter and spring, at which seasons it transports the produce of the lands to Rome; but its chan- nel is so extremely low in summer, that it scarcely deserves the name of a river; towards the autumn, however, it begins again to renew its claim to that title—You could not be more agreeably entertained, than by taking a view of the face of this country from the top of one of’ our neighbouring mountains: you would suppose that not a real, but some imaginary landscape, painted by the most exquisite pencil, lay before you: such an harmonious variety of beautiful objects meets the eye, which way soever it turns. My villa is so advantageously situated, that it commands a full view of all the country round; yet you approach it by so insensible a rise, that you find yourself upon an eminence, without per- ceiving you ascended. Behind, but at a great dis- tance, stands the Apennine mountains. In the calmest days we are refreshed by the winds that blow from thence, but so spent, as it were, by the long tract of land they travel over, that they are entirely divested of all their strength and vio- lence before they reach us. The exposition of the principal front of the house is full south, and seems to invite the afternoon sun in summer (but somewhat earlier in winter) into a spacious and well-proportioned portico, consisting of several members, particularly a porch built in the ancient manner. In the front of the portico isasort of ter- race, embellished with various figures, and bounded with a box hedge, from whence you descend ‘by an easy slope, adorned with the representation of divers animals, in box, answering alternately to each other, into a lawn overspread with the soft, I had almost said the liquid, acanthus: this is surrounded by a walk enclosed with tonsile evergreens, shaped into a variety of forms. Be- yond it is the gestatio, laid out in the form of a circus, ornamented in the middle with box cut in numberless different figures, together with a plan- tation of shrubs, prevented by the sheets from o 2* HOU 100 shooting up too high: the whole is fenced in with a wall covered by box, rising by different ranges to the top. On the outside of the wall lies a meadow that owes as many beauties to nature, as all I have been describing within does to art; at the end of which are several other meadows and fields interspersed with thickets. At the ex- tremity of this portico stands a grand dining- room, which opens upon one end of the terrace; as from the windows there is a very extensive prospect over the meadows up into the country, from whence you also have a view of the terrace, and such parts of the house which project for- ward, together with the woods enclosing the ad- jacent hippodrome. Opposite almost to the centre of the portico, stands. a square edifice, which encompasses a small area, shaded by four plane-trees, in the midst of which a fountain rises, from whence the water, running over the edges of a marble bason, gently refreshes the surrounding plane-trees, and the verdure under- neath them. This apartment consists of a bed- chamher, secured from every kind of noise, and which the light itself cannot penetrate; together with a common dining—room, which I use when I have none but intimate friends with me. A second portico looks upon this little area, and has the same prospect with the former I just now described. There is, besides, another room, which, being situated close to the nearest plane-tree, enjoys a constant shade and verdure: its sides are incrusted half‘way with carved marble; and from thence to the ceiling a foliage is painted with birds intermixed among the branches, which has an effect altogether as agreeable as that of the carving: at the basis a little fountain, playing through several small pipes into a vase, produces a most pleasing murmur. From a corner of this portico you enter into a very spacious chamber, opposite to the grand dining-room, which, from some of its windows, has a view of the terrace, and from others, of the meadow; as those in the front look upon a cascade, which entertains at once both the eye and the ear; for the water, dashing from a great height, foams over the marble bason that receives it below. This room is extremely warm in winter, being much ex- posed to the sun; and in a cloudy day, the heat of an adjoining stove very well supplies his ab- sence. From hence you pass through a spacious and pleasant undressing-room into the cold-bath- HOU ‘j room, in which'is a large gloomy bath: but if you are disposed to swim more at large, or in warmer water, in the middle of the area is a wide bason for that purpose, and near it a reservoir from whence you, may be supplied with cold Water to brace yourself again, if you should per— ceive you are too much relaxed by the warm. Contiguous to the cold-bath is another of a mo- derate degree of heat, which enjoys the kindly warmth of the sun, but not so intensely as that of the hot-bath, which projects farther. This last consists of three divisions, each of different de- grees of heat: the two former lie entirely open to the sun; the latter, though not so much exposed to its rays, receives an equal share of its light. Over the undressing-room is built the tennis-court, which, by means of particular circles, admits of different kinds of games. Not far from the baths, is the staircase leading to the enclosed portico, after you have first passed through three apart- ments: one of these looks upon the little area with the four plane-trees round it; the other has a sight of the meadows; and from the third you have a view of several vineyards: so that they have as many different prospects as expositions. At one end of the enclosed portico, and, indeed, taken off from it, is a chamber that looks upon the hippodrome, the vineyards, and the moun- tains; adjoining is a room which has a full ex- posure to the sun, especially in winter; and from whence runs an apartment that connects the hippodrome with the house: such is the form and aspect of the front. On the side, rises an en- closed summer-portico, which has not only a prospect of the vineyards, but seems almost con- tiguous to them. From the middle of this por- tico, you enter a dining-room, cooled by the salutary breezes from the Apennine valleys; from the windows in the back front, which are extremely large, there is a prOSpect of the vine- yards; as you have also another view of them from the folding-doors, through the summer- portico. Along that side of this dining—room, where there are no windows, runs a private stair- case for the greater conveniency of serving at entertainments: at the farther end is a chamber from whence the eye is pleased with a view of the vineyards, and (what is not less agreeable) of the portico. Underneath this room is an enclosed portico, somewhat resembling a grotto, which, enjoying in the midst of the summer heats, its S!“ HOU 101 HOU own natural coolness, neither admits nor wants the refreshment of external breezes. After you have passed both these porticos, at the end of ' the dining-room stands a third, which, as the day is more or less advanced, serves either for winter or summer use. It leads to two different apart- ments, one containing four chambers, the other three; each enjoying, by turns, both sun and shade. In the front of these agreeable buildings, lies a very spacious hippodrome, entirely open in the middle, by which means the eye, upon your first entrance, takes in its whole extent at one glance. It is encompassed on every side with plane-trees, covered with ivy, so that while their heads flourish with their own foliage, their bodies enjoy a borrowed verdure; and thus, the ivy twining round the trunk and branches, spreads from tree to tree, and connects them together. Between each plane-tree are planted box-trees, and behind these, bay-trees, which blend their shade with that of the planes. This plantation, forming a straight boundary on both sides of the hippodrome, bends at the farther end into a semi- circle, which being set round and sheltered with cypress-trees, varies the prospect, and casts a deeper gloom; while the inward circular walks (for there are several) enjoying an open exposure, are perfumed with roses, and correct, by a very pleasing contrast, the coolness of the shade with the warmth of the sun. Having passed through these several winding alleys,'you enter a straight Walk, which breaks out into a variety of others, divided by box hedges. In one place you have a little meadow; in another the box is cut into a thousand different forms; sometimes into letters, expressing the name of the master; sometimes that of the artificer; whilst here and there little obelisks rise intermixed alternately with fruit- trees: when, on a sudden, in the midst of this elegant regularity, you are surprised with an imi- tation of the negligent beauties of rural nature: in the centre of which lies a spot surrounded with a knot of dwarf plane-trees. Beyond these is a walk planted with the smooth and twining acan- thus, where the trees are also cut into a variety of names and shapes. At the upper end is an alcove of white marble, shaded with Vines, supported by four small Carystian pillars. From this bench the water, gushing through several little pipes, as if it were pressed out by the weight of the persons who repose themselves upon it, falls into a stone cistern underneath, from whence it is received into a finely polished marble bason, so artfully contrived, that it is always full without ever over- flowing. When I sup here, this bason serves for a table, the larger sort of dishes being placed round the margin, while the smaller ones swim about in the form oflittle vessels and water-fowl. Corresponding to this, is a fountain which is in- cessantly emptying and filling; for the water, which it throws up a great height, falling back into it, is, by means of two openings, returned as fast as it is received. Fronting the alcove (and which reflects as great an ornament to it, as it borrows from it) stands a summer-house of exquisite marble, the doors whereof project and open into a green enclosure ;. as from its upper and lower windows, the eye is presented with a variety of different verdures. Next to this is a. little private recess (which, though it seems dis- tinct, may be laid into the same room) furnished with a couch; and, notwithstanding it has win- dows on every side, yet it enjoys a very agreeable gloominess, by means of a spreading vine which climbs to the top, and entirely overshades .it. Here you may recline and fancy yourself in a wood; with this difference only, that you are not exposed to the weather. In this place a fountain also rises and instantly disappears: in different quarters are disposed several marble seats, which serve, no less than the summer-house, as so many reliefs after one is wearied with walking. Near each seat is a little fountain; and, throughout the whole hippodrome, several small rills run mur- muring along, wheresoever the hand of art thought proper to conduct them, watering here and there different spots of verdure, and, in their progress, refreshing the whole. “ And now,I should not have hazarded the im- putation of being too minute in this detail, if I had not proposed to lead you into every corner of my house and gardens. You will hardly, I imagine, think it a trouble to read the description of a place, which I am persuaded would please you were you to see it; especially as you have it in your power to stop, and, by throwing aside my letter, sit down as it were, and rest yourself as often as you think proper. I had, at the same time, a view to my own gratification: as I con- fess I have a very great affection for this villa, which was chiefly built or finished by myself. In a word (for wh y should I conceal from my friend H DU 1— my sentiments, whether right or wrong?) I look upon it as the first duty of every writer frequently to throw his eyes upon his title-page, and to con- sider well the subject he has proposed to himself; and he may be assured if he precisely pursues his plan, he cannot justly be thought tedious; where- 'as, on the contrary, if he suffers himself to wan- der from it, he will most certainly incur that cen- sure. Homer, you know, has employed many verses in the description of the arms of Achilles, as Virgil also has in those of lEneas; yet neither of them are prolix, because they each keep with- in the limits of their original design. Aratus, you see, is not deemed too circumstantial, though he traces and enumerates the minutest stars: for he does not go out of his way for that purpose, he only follows where his subject leads him. In the same manner (to compare small things with great) if endeavouring to give you an idea of my house, I have not deviated into any article foreign to the purpose, it is not my letter which describes, but my villa which is described, that is to be considered as large. But not to dwell any longer upon this digression, lest I should myself be con- demned by the maxim I have just laid down; I have now informed you why I prefer my Tuscan villa, to those which I possess at Tusculum, Tiber, 'and Preeneste. Besides the advantages already mentioned, I here enjoy a more profound retire- ment, as I am at a farther distance from the busi- ness of the town, and the interruption of trouble- some avocations. All is calm and composed; circumstances which contribute, no less than its clear air and unclouded sky, to that health of body and cheerfulness of mind which I particularly enjoy in this place; both which I preserve by the exercise of study and hunting. Indeed, there is no place which agrees better with all my family in general; I am sure, at least, I have not yet lost one (and I speak it with the sentiments I ought) of all those I brought with me hither: may the gods continue that happiness to me, and that honour to my Villa! Farewel.” This villa in Tuscany was Pliny’s principal seat, lying about one hundred and fifty miles from Rome, and in which he usually resided during the summer season. The reader will observe, there- fore, that he considers it in a very different man- ner from that of Laurentinum, (his winter villa) both with respect to the situation and the house itself. Cluver, in his geography, has placed this 102 HOU I villa a little above Tifernum Tiberium, now called Citta di Castello, where our author built a temple at his own expense. This has given room to imagine that, pOSSlbly there may be yet some remaining traces of this house to be discovered in Tuscany, near a town, which the Italians call Stiutignano, in the neighbourhood of Ponte di San Stefano, about ten miles north of an epis~ copal city now called Barge di San Sepulclzro. Amongst the Jews, Greeks, and Romans, houses were flat at top, so that persons might walk upon I 1 Axe them; and usually had stairs on the outside, by i which they might ascend and descend without coming into the house. Each house, in fact, was so laid out that it enclosed a quadrangular area or court. This court was exposed to the weather, and, being open to the sky, gave light to the house. This was the place where company was received, and for that purpose it was strewed with mats or carpets for their better accommodation. It was paved with marble or other materials, ac- cording to the owner’s ability, and provided with an umbrella of vellum to shelter them from the heat and inclemencies of the weather. This part of their houses, called by the Romans impla- uium, or cam radium, was provided with channels to carry off the water into the common sewers. The top of the house was level, and covered with a strong plaster, by way of terrace. Hither, especially amongst the Jews, it was customary to retire for meditation, private converse, devotion, or the enjoyment of the evening breezes. The following designs by the Author, and chiefly executed under his own superintendence, form a short series of designs, from the simple cottage to the complex decorated mansion. Plate lr~Plan and elevation of a house for a country baker at Taplow, Buckinghamshire.— Executed. Plate II.-—Plan and elevation of a cottage, de- signed for Mr. Buchanan, of Cruxton, near Glasgow, forming two separate dwellings—Exe- cuted. Plate III.—-Plan and elevation of a house, de- signed for Mr. Lowry, attorney, Carlisle. Plate lV.——Plan and elevation of a house, de- signed for Mr. Grey, jeweller, Glasgow—Exe- cuted. Plate V.—-Plan and elevation of ahouse, designed for Alexander Gordon, Esq—Executed. Plate VI.-—-—Plan of Castelton House, near Cari fl“ {7331‘} . 1’1“)”: 7, “WM-W” London B117 /17/1/// biz/71172711115101 X'lfi’zq‘flr/M [VIII-(011N222?! M’N. ling/nun? [11' [f fig/[‘2’ . P111772? [/1 HOUSE % V 1% / W M % // / / /fl y, , u up “.5“? :53 , 44M- M *r " - w «W J‘“ m; H 0 {T S E“ PLATE 11!. .w M \MH W‘hHV [III-[(716]? Dru Willa Rani/z /)[ll[/I(I [300/11 ‘ ’Y’.” ‘11/13x7’M/0W" [WU/4'”./'II['/11"/h'r/ [{1/ /{.\'1'z'/Iu/run .\" ./. Bani-r/J, [NIH/war J'Irr’flJfli4. /:"m/r.n’a/ [11/ ”flow/w. HOEISE. ”4””- :9 Front. Flank]. (r'mumi flan. (ha/fiber Flour. ‘ , 17,11 1’- NIWU’LWIL. lmulunl‘blzllklml 151/ 1? 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U 7 Vs. 4?”;42—4 E§§ET§E9 i I; :v ; 1'3 ,; , ;L_.__:L-,4L*.L__J;‘ ifiA~*——~———i Vm....mm_u - . . __..A_.. ‘ COFFEE 1600A! AT l’AIJ'L/z'Y. 'I// ///-.'////z'.'/, [um/1w, /'///!//'.a'//n/ /I’// /' .\'I}‘fi,u/own X‘ ./ ”(IMP/J “fin/MM J'IIW‘A/fl/g, /§'/1V4//‘¢“'l‘(//71/ [if/wad, \- PIA T]:' M". HOU 103 ‘- H 0U A lisle, the seat of Robert Mouncy, Esq. This design was made from a sketch by Thomas Telford, Esq. but the working drawings were made, and the Work was superintended, by the Author. Plate VIL—Elevation of the same. Plate VIII.-——-Corby Castle, near Carlisle, the seat of Henry Howard, Esq. The site of this house is delightfully situated upon the romantic banks of the river Eden—Executed. Plate IX.——Plan of the ground-floor of the same. This work is a considerable addition to an old house, of unknown date; the original parts of the building are shaded in light colour, and the additions in black. Plate X.——Front and rear elevations of a house, designed for Fulton Alexander, Esq. at Partick, near Glasgow. The Plate shews the original design, which only differs from that which was executed in having a circular turret in the centre, in order to conceal the chimneys, whereas the work was finished with a plane truncated roof, with chimney-shafts at the extremities and in the middle. Plate XI.——Plans of the same, as first intended. Plate XII.——Plans of the same, as executed. Plate XIII. — Plan and elevation of the offices, for Fulton Alexander, Esq. Plate XIV .—Elevation designed for a new house at Clifden, Buckinghamshire. For the Right Honourable the Countess of Orkney. Plate XV.—-Plan of the same. Plates XVI. XVII. XVIII. and XIX.——Design of the Coffee-house at Paisley, near Glasgow. The 0n€~pai1'-of-stairs floor being occupied for this purpose; the basement is used for cellaring, and the ground-floor contains a series of shops. Plate XVI.—-Plan. Plate XVII.—Elevation. Plate XVIII.——Longitudinal section. Plate XIX.—Transverse section. These designs have been selected from a very large collection by the Author; and though few in number,are sufficient to exemplify the different gradations from one class of building to another. The design for the additions to the college at Glasgow, which are now carried into execution, will be given under the article UNIVERSITY. Other works in which he has been employed will be noticed under ROOM and TOWN. There are four different rates into which the pro- portions of houses in town are divided or classed by the legislature. The first rate, or houses of the largest size, are such as exceed nine squares of building; those of- the second rate are from five to nine squares; those of the third from three and a half to five squares; and of the fourth, not exceeding three squares and a half. Their height is regulated in like manner, and the thickness of their walls and chimneys. With such restrictions the architect must often proceed under great dis- advantages, and must occasionally call forth the good quality of docility recommended by Vitru- vius. We cannot multiply rules for the different parts of a house; since these must be modified by a variety of circumstances, in which .the skill and judgment of the architect must direct: but we shall conclude this article with expressing a wish that contrivers of buildings would avail them- selves more of an important modern discovery in natural history, viz. the superior levity of infec- tious and unwholesome air. The upper sashes in most houses are too frequently immoveable; in consequence of which, no part of the foul air above the level of the lowest rail of the other sash’s greatest rise can escape by the window; and if it escapes by the doors, it is generally for Want ofa vent in the highest part of the roof, merely to accumulate in the upper story of the house, and add to the infection which the great quantities of old furniture usually stored up there are of themselves too apt to create. Thus the chief advantage to be expected from lofty rooms is in a measure lost; whereas, were the upper sashes contrived soas to draw down, all the air might be easily changed, and that almost insensi- bly, by letting them down an inch 01 two. Nay the uppe1 sash might he often let down entirely, with less danger or inconvenience from cold, than the lower thrown up the tenth part of an inch: though the doing of the former would be infi- nitely the most beneficial. It is perhaps on this principle that we are to account for the good health enjoyed by the poor who live crowded in damp cellars, and often with great numbers of rabbits, poultry, and even swine, about them. These cellars are open to the street, with doors reaching from the floor to the very ceiling, but never so close at bottom or at top as to prevent a free circulation of air; in consequence of which, that all—vivified fluid, as fast as it is spoiled by HOU 104. H 0U passing through the lungs of the inhabitants and their stock, or is infected by their insensible per— spiration, excrements, Ste. is driven out, and re- » placed by the fresh air. Blenheim HOUSE, the work of Sir John Vanburgh, is executed in a style which displays much bold- ness, diversity, and novelty of outline both in plan and elevation; the facade, however, has more the appearance of a triumphal monument than a private dwelling. In what regards the general outlines and disposition of the principal members, few architectural works have succeeded so well: but it is greatly deficient in the subor- dinate parts. ‘ .Holland HOUSE, and that of the Marquis of Salis- bury, present a specimen of the style which prevailed during the time of Elizabeth and James I. These houses contain large apartments and long galleries, heavy cornices, and ceilings in deep compartments. Holyrood HOUSE, the palace of the kings of Scot- land, is a very considerable edifice; but the period when it was begun is unknown. The north-west towers were erected by James V. The palace was burnt by the English, in the minority of Queen Diary, but speedily repaired. It then consisted of five separate courts. Some small alterations were, it is said, made by Inigo Jones, at the time he returned from Denmark with the queen of James I. Great part of this palace was burnt by Cromwell’s soldiers. The present edifice was designed by Sir William Bruce, a celebrated architect in the time of Charles II. and executed by Alexander Mylne, a mason, to whom a monument has been erected near the Old Abbey. It consists of one square, three sides of which have three stories, composed of the Doric, Ionic, and Corinthian orders. Round the interior of the square, there is an arcade. The west side, in which is the entrance, is only two stories high. Its external fagade is a mixed architecture, having a round castellated tower at each extremity. The entrance is ornamented by a fully enriched Roman Doric, with a whimsically shaped open pediment, over the centre of which there is a .cupola, with very small Corinthian columns, having its covering or roof in the shape of an imperial crown. Had the whole of the entrance front corresponded with the towers at the ex- tremities, it would have been expressive of strength and protection; as it is, we can hardly l wish them exchanged for features of Roman architecture. The external front eastward has a distinct order to each of its three stories; the entablature being continued along the whole front without a break, has a fine effect; the root is after the French fashion, very high and con- cave. Though the inside of the square, by the introduction of three orders, has the parts ren- dered minutely small, yet the outlines being free of unnecessary projections and recesses, and the two upper rows of windows being large and plain, the whole exhibits a correctness and simplicity not frequently met with. India House, possesses more chasteness of design than most public buildings of modern construe-- tion, particularly the north front, which has no break, except that made by a very fine portico, with six Ionic columns, occupying the whole height of the edifice. It is ornamented with an excellent sculpture, by Bacon. Mansion HOUSE of London, the residence and. court of the Lord Mayor, is a very grand pile of building. The portico is bold and striking, and and though some of its features are rather clumsy, yet as a whole it is grand and impressive, and reflects credit on its architect, the father of the present city architect, Mr. Dance. Somerset HOUSE, from the designs of Sir William Chambers, who also superintended the work, con- sists of a series of adjoining houses surrounding a square, forming one uniform design. Its situa- tion on the banks of the Thames is favourable for being viewed from'the middle of the river, or Westminster bridge. Towards the street, the front, which is on a line with the houses on each side of it, is seen to disadvantage. The inside of the square has all the advantages a similar space can afford. The whole design has not been completed, but the central part has; and we therefore see what must have been in- tended as the principal features of the composi- tion. In the river front, there is a fine terrace; but the extensive facade, which is elevated upon it, is deficient in majesty. The disproportioned height of the basement takes away from the effect of the order. In the dark recesses, the columns appear very diminutive. If the base-u ment had been only so high above the terrace, as to raise the order to be all seen from the middle of the river, the parts would have been more dis- tinct and impressive; and had the face of the HUN l un— building been plain, instead of being wholly cut into small rustics, there would have been more simplicity. The dome in the centre of the roof is much too small. The small extent of the street front renders the improper height of the basement more conspicuous; and the whole is rather crowded than grand. Within the square, which is 300 feet north and south, and 200 east and west, there is a tiresome repetition of rustic work: this edifice has many fine door-eases and windows, adorned with exquisite sculpture; but as a great design, it is deficient in the magnificence which a national structure of this description ought to possess. The interior of the building is ar- ranged with much care; and it has several fine staircases. The architect appears to have been careful and persevering, and endeavouring cor- rectly to follow what he conceived the true clas- sic style; but he was ignorant of, or despised Greek architecture, and seems to have been deficient in taste. HOUSE AND WINDOW TAX, a branch of the king’s extraordinary revenue. The clauses rela- tive to the house-tax are, I. That offices, yards, gardens, coach-houses, brew-houses, wood-houses, wash-houses, 5‘0. provided they all stand within the compass of one acre, belonging to the dwell- ing-house, must be valued with the dwelling- house, and be liable to the same duties. 9. Shops and warehouses are also liable, if attached to the dwelling-house; except those of warfingers. 3. No warehouse that is a distinct building is liable. 4. No house to be deemed occupied, when one person only is left in charge of it. 5. Where houses are let in tenements, the landlord must pay the duty. 6. Halls and offices that pay other taxes are liable to this. 7. Farm-houses used only for husbandry, under 10!. per annum, are not chargeable; nor houses for the reception of the poor, or if not occupied by the owner or rented by a tenant. 19 Geo. III. c. 15. HOUSING, the space excavated out of a body for the insertion of some part of the extremity of another, in order to fasten the two together: thus the string-board of a stair is most frequently ex- cavated, or notched-out for the reception of the steps. IIUE (from the Saxon) in painting, any degree of strength or vividness of colour, from its greatest or deepest, to its weakest teint. HUNDRED OF LIME, a denomination of mea- VOL. II. ] 05' HUT J x 4—. sure, in some places denoting 35, and in others 25 heaped bushels or bags. HUNDRED, Great, or Standard, : 1121b. avoirdu- poise = 4 quarters = 7 stone (of 1611).) = 14 cloves (8lb.) : 16 cloves (71b.) = 1792 ounces = 20,672 drachms avoirdupoise = .9333310ng cwt. (1201b) : 1031b. 2%02. Dutch, or Secttish weight. This is the legal hundred weight of the custom- house of London, and in all the southern parts of England. HUNDRED, Long, or Northern, =120lb.: ,— stones (141b,) : 12 rationes (lOlb.) : 1.0714Q86 great cwt. (1121b.) This weight is legalized on all or most of the canals and navigable rivers in the north of England and of the midland counties, by their acts for collecting tolls, Syc. HUNDRED is also used as a measure to express a certain quantity or number of things. Deal boards are sold at six score to the hundred, called the long fiundred. Pales and laths are counted at five score to the hundred if five feet long, and six score if three feet long. HUNG, Double, see DOUBLE HUNG. HURRIES, in enginery, is sometimes applied, at Newcastle and other places, to the strong stages of wood erected on the sides of navigable rivers and harbours, to which the railways are con- ducted from the coal pits; by which means the load is emptied at once by the help of a spout, from the railway waggons into the holds of ships. HUT (from the Saxon hutte) a small cottage or hovel. It is also used for the Soldiers’ lodges in the field, otherwise called barracks or caserns. HUT, in rural economy, a low sort of building, of the cottage kind, generally constructed of earthy materials, as strong loamy clay, Syc. A number of huts of this description have within these few years been built on the borders of the South Esk, in Scotland, which have a very neat and rural appearance, affording the idea at a distance of their being formed of a kind of brown brick- work. The materials employed consist of a sort of muddy clay, blended with the roots of aquatic plants, which are dug beyond the flood-mark of the river, in such sizes and shapes as are suitable for the intended purpose. The pieces, or peats, as they are called, are generally cut out in the form of bricks, but somewhat larger, being pre- pared in every respect in the manner of peat-fuel. It is useful in some cases to build huts with lime- mortar, but more commonly with clay only. P HYP M 106 HYP .- !‘1 r These huts are generally preferred by the cot- tagers to such as are built of stone, being warmer, and not much less durable. It seems not improbable but that a similar sort of material for building this kind of cottages may be met with in many situations where it has not yet been discovered, and be made use of in this way, as well as for various fences of the wall kind. HYPETHRAL TEMPLE, see article. HYPIETHRON, or I‘IYPIETHROS (from the Greek, open above) a temple with ten columns on the pronaos and posticus, in external appearance similar to the dipteral; but within it had a double tier of columns on each side, detached from the wall, and the middle area was open to the sky. The cell was approached from both front and rear. From the description given by Vitruvius, it ap- pears, that Rome did not afford any example of this species; and he points out the temple of Jupiter Olympus at Athens as one. HYPERBOLA (from Em; and 302m.) one of the conic sections, being that which is made by a plane cutting the opposite side of the cone produced above the vertex, or, by a plane which makes a greater angle with the base than the op- posite side of the cone makes. In this figure the squares of the ordinates are greater than, or exceed, the rectangles under the parameters and abscissas, whence the name hyperbola. A few useful properties (f the hyper-bola.—~1. The squares of the ordinates of any diameter are to each other, as the rectangles of their abscissas. 2. As the square of any diameter is to the square of its conjugate, so is the rectangle of two ab- scissas to the square of their ordinate. 3. The distance between the centre and the focus, is equal to the distance between the extremities of the transverse and conjugate axes. 4. The difference of two lines drawn from the foci to meet in any point of the curve, is equal to the transverse axis. 5. All the parallelograms inscribed between the four conjugate hyperbolas, are equal to each other, and each is equal to the rectangle of the two axes. (i. The rectangles of the parts of two parallel lines, terminated by the curve, are to each other as the rectangles of the parts of any other two parallel lines, any where cutting the former. Or, the following the rectangles of the parts of two intersecting lines are as the squares of their parallel diameters, or squares of their parallel tangents. 7. All the parallelograms are equal which are formed between the asymptotes and curve, by lines parallel to the asymptotes.~ For other properties, see the articles CONE, and CONIC SECTION. HYPERBOLA, Acute, one whose asymptotes make an acute angle. HYPERBOLA, Ambigenal, that which has one of its infinite legs falling within an angle formed by the asymptotes, and the other falling without that angle. HYPERBOLA, Apollonian, the common hyperbola, as derived from the cone. See HYPERBOLA. HYPERBOLA, Deficient, a curve having only one asymptote, though two hyperbolic legs running out infinitely by the side of the asymptote, but contrary ways. HY PERBOLA, Equilateral, has its asymptotes equal to each other. HYPERBOLAS, Iryim'te, or HYPERBOLAS or THE HIGHER KINDS, are expressed or defined by general equations similar to that of the conic or common hyperbola, only having general ex- ponents, instead of the particular numeral ones, but so that the sum of those on one side of the question is equal to the sum of those on the other side. Such as aym+n : b x'“ (d + at)“, where .r and 3/ are the abscissa and ordinate to the axis or diameter of the curve; or arm y“ : a “‘+“, where the abscissax is taken on one asymptote, and the ordinate 3/ parallel to the other. HYPERBULIC CONOID, a solid formed by the revolution of an hyperbola about its axis: it is otherwise called H YPERBOLOID, which see. HYPERBOLIC CURVE, the same as the hyperbole. To draw a tangent to any point in the hyperbolic curve, draw a semi-diameter to the given point, and find its conjugate; then through the given point, draw a straight line, parallel to the con- jugate diameter; which line will be a tangent to the curve. To find the focus of the hyperbolic curve, take the distance between the extremities of the trans- verse and conjugate axes, and apply it from the centre upon the axis, and the remote extremity of the distance gives the focus. HYPERBOLIC CYLINDROID, a solid formed by the revolution of an hyperbola about its conjugate HYP 107 M axis, or line through the centre perpendicular to the transverse axis. HYPERBOLOID, a conoid formed by the revolu-. tion of an hyperbola about its axis. It is other- wise called an hypirboh‘c conoid. To find the solidity of an hyperboloid, or the frus- tum of an hyperboloid.——To the areas of the two HYP - - - ._ .— ends, add fourtimes the area of the middle section parallel thereto, and multiply the sum by one— sixth part of the axis or height, and the product is the solidity. In the complete hyperboloid, the area Of the end at the apex being nothing, the rule will be similar to what is laid down under the article C0N01D. An hyperboloid is to a paraboloid of the same base and altitude as t + 33—3: is to t + x. Let t = the transverse c = the conjugate } axes of the generating hyperbola. x = the abcissa or altitude of the solid. y = the ordinate or radius of the base. p: 3.1416. Thenyg =c x———-—-— mil-we andpy x=pc xx—————- xt+x ,by the property of the solid; , the fluxion of the solid; py x=pc x x%—:———- :7x,thefluentof the solid; 1 but becausey2 = c1 xt 2 1 . . 3/ Therefore, substltutmg t x +4.2 half the area of the base multiplied into the altitude, x , we obtain c2 for c in the fluentp c x x——- .7]: {2. t .1: +111 % +_%_r p y“ w t + a .r _ ——-we obtain x -t—+—x—- —t————t.:_3:, for the solidity of the solid. 1’ .y But the parabolo-idal area is half the area of the base multiplied into the altitude; that is, 2 a2; pyzx t+—§-x ’ py‘x 2 t+x . 2 no W HYPOCAUSTUM (from Zara, under, and mum, to burn) among the Greeks and Romans, a subter- raneous place, in which was a furnace for heating the baths. Another kind of hypocaustum was a sort of kiln to heat their winter parlours. HYPOGIEUM (from 3m, under, and 7),, the earth) in ancient architecture, a name given to all parts of a building that were underground. HYPOPODIUM (from {la-o, under, and 71%;, foot) 3 piece of furniture in the ancient baths, on which the feet rested. I t + % x ; t + x; and hence the proposition is manifest. HYPOSCENIUM (from {1120, under, and a-xma‘y, a scene) a partition under the logium appointed for the music. HYPOTRACHELIUM (from 37», under, and 796420?- Nov, the neck) the lower part of the Tuscan and Doric capitals, comprehended between the astragal at the top of the shaft, and the fillet or annulets under the ovolo. This description applies only to the Roman Doric; for the Grecian, instead of an astragal, had from one to three horizontal. grooves circumscribing the column. ,. ICE I CE-HOUSE, a repository for the preservation of ice during the summer months. The aspect of an ice-house ought to be towards the south-east, on account of the advantage of the morning sun in expelling the damp air, which is far more prejudicial to it than warmth. The best soil on which such a house can be erected is a chalk-hi1], or declivity, as it will conduct the waste water, without the aid of. any artificial drain; but where such land cannot be procured, a loose stony earth, or gravelly soil on a descent, is preferable to any other. For the construction of an ice-house, a spot should be selected at a convenient distance from the dwelling-house. A cavity is then to be dug in the form of an inverted cone, the bottom being concave, so as to form a reservoir for the recep- tion of waste water. Should the soil render it necessary to construct a drain, it will be advisable to extend it to a considerable length, or, at least, so far as to Open at the side of the hill or decli- vity, or into a well. An air-trap should likewise be formed in the drain, by sinking the latter so much lower in that opening as it is high, and by fixing a partition from the top, for the depth of an inch or two into the water of the drain, by which means the air will be completely excluded from the well. A sufficient number of brick- piers must now be formed in the sides of the ice- l‘iouse, for the support of a cart-wheel, which should be laid with its convex side upwards, for the purpose of receiving the ice; and which ought to be covered with hurdles and straw, to afford a drain for the melted ice. The sides and dome of the cone should be about nine inches thick, the former being constructed of brick-work, without mortar, and with the bricks placed at right angles to the face of the work. The vacant space behind ought to be filled with gravel, or loose stones, in order that the water oozing through the sides may the more easily be conducted into the well. The doors of the ice- liouse should likewise be made to shut closely; and bundles of straw put before them, more effec- tually to exclude the air. IMP The ice' to be put in should be collected during the frost, broken into small pieces, and rammed down hard in strata of not more than afoot, in order to make it one complete body; the care in putting it in, and well ramming it, tends much to its preservation. In a season when ice is not to be had in suflicient quantities, snow may be substituted. ICHNOGRAPHY (from ixm, footstep, and 7pa¢w, to describe) an orthographical projection of an object on a horizontal plane, or the description of an object on a plane representing the horizon, by straight lines from all points of the object per— pendicular to the plane. This term is used only in reference to a projection of the same nature with another, on which it is made perpendicular to the former, by lines from all points of the ob- ject falling perpendicular to such plane, and con— sequently parallel to that of the ichnography. ICOSAHEDRON (from the Greek, sixoa‘aed‘par) in geometry, a regular solid, consisting of twenty triangular pyramids, whose vertices meet in the centre of a sphere, supposed to circumscribe it, and therefore have their height and bases equal; wherefore the solidity of one of those pyramids multiplied by twenty, the number of bases, gives the solid content of the icosahedron. To form or make the icosahedron.—Describe upon a card paper, or some other such like substance, twenty equilateral triangles; cut it out by the extreme edges, and cut all the other lines half through, then fold the sides up by these edges half out through, and the solid will be formed. The linear edge or side of the icosahedron being A, then will the surface be 5 A’ ,x 3 = 8.6602540A9, 7+3¢5 2 and the solidity :%A3«/ = 2.1816950A3. IMAGE (from the Latin, imago) the sceuographic or perspective representation of an object. See PERSPECTIVE. IMAGERY, painted or carved work. lMBOlV (from bars) to arch over, to vault. lMBOlVMENT, an arch, or vault. [MPAGES (Latin) in ancient joinery, is supposed INC 109 IND to mean the rails of'a door, as appears from: Vitruvius, Book IV. Chap. VI. “The doors are so framed that the cardinal scapi may be the twelfth part of the whole height of the aperture. Out of twelve parts between the two scapi, the tympans have three parts. The impages are so distributed, that the height being divided into five parts, two superior and three inferior are dis- posed. Upon the middle, the middle impages are placed; of the rest some are framed at top, and some at bottom ; the breadth of the impage is a third part of the tympan ; the cymatium is a sixth part of the impage; the breadth of the scapi is the half of the impage; the replum is the half and a sixth part of the impage.” IMPETUS (Latin) the span of a building, roof, or arch. » IMPOST (French) the upper part of a pier or pillar, which sustains an arch ; or the collection of mouldings under an arch, forming a cornice of small projection as a finishing to the pier. IN BAND JAM B-STONE, a stone laid in the jamb of an aperture for the purpose of bond: its length being inserted in the thickness of the wall, and shewing only its end in the face of it. INCERTAIN WALL, see WALL. INCH (ince, Saxon, uncia, Latin) a measure of length, supposed equal to three grains of barley laid end to end; the twelfth part of a foot. INCLINATION (from the Latin) 3. word frequent- ly used by mathematicians to signify the mutual approach of a line and a plane, or of two planes, to each other, so as to constitute an angle. In this sense we speak of the inclination of the me- ridians, the inclination of the sun’s rays, 4%. The inclination ofa line :to a plane is measured on a second plane, by supposing the second to pass along .or through a line perpendicular to the first, and forming an intersection with it: then the angle comprehended on the second plane, between the line and the intersection, is called the inclination of the line to the plane. The inclination of one plane to another, is mea- sured on a third plane drawn perpendicular to the common intersection of the two first, till it inter- sect them : then the angle contained between the lines of section is the inclination (ft/re planes. INCLINED PLAN E, in mechanics, :1 plane form- ing an oblique angle with the horizon, or placed at a given angle to another: so that when an in- .clined plane is spoken of absolutely, another is always to be understood,-whi-ch is the primitive or first plane, from which the inclined plane rises. When a force, in a given direction, supports a weight upon an inclined plane, such force is to the weight as the sine of the inclination of the plane is to the sine of the angle made by the line in which the force acts with the line perpendicular to the plane. Given, the heights Qf any three points in an inclined plane, and their seats in position upon the primitive plane, to determine the inclination of the planes.— Join the seat of the greatest height to that of the least height, and take the least height from the other two: then say, As the greatest difference is to the least difference, so is the whole length of the line joining the two seats to the portion of it between the seat of the least height and that of the greatest; join the intermediate point to the seat of the mean height by a straight line, which call A B; draw a straight line, C D, perpendicu- lar to A B; through the seats of the greatest and least heights draw two lines, C E and D F, par- rallel to AB; make CE equal to the greatest height, and D F equal to the least; join EF, and produce CD and EF to meet in G; then the angle C G E is the inclination of the planes. INC RUSTATION (French) an adherent covering. This term is frequently applied to plaster, or other tenacious materials employed in building. IN DEFINITE (From the Latin indefinitus, not limited) is sometimes used to express something that has but. one extreme; as a line drawn from any given point, while the other extremity is extended infinitely,or to any given distance, with- ‘out affecting its use. INDENTED (from the Latin in, and dens, a tooth) in architecture, toothed together. INDIAN ARCHITECTURE, the style which was practised by the inhabitants of lndia. Al- though what relates to India was anciently but very imperfectly known to the western world, yet such is the change in human affairs, and the eagerness with which every matter relating to India has of late been investigated, that we are now furnished with accounts fully as ample as those relating to Egypt or Persia. In the fol- lowing brief relations we shall be guided by some excellent papers, by Sir William Jones and others, in the Asiatic Researches; Robertson’s Disgui— sitions respecting Ancient India; the learned and laborious work of Maurice on Indian Antiquities,- IND 110 r 4m and several other authorities quoted for particular descriptions. In India, the cities and palaces were on a scale ‘ with itsgreat wealth and population. They were generally indebted for their origin to the favour of powerful princes, and successively became the centre of the riches and tralfic of the East. In the historical poem, called the Illa/zabbarit (or History of the Great War) translated by Abul Fazel, the secretary or minister of the great Akbar, it is said, that Oude, the capital of a pro- vince of that name, to the north-east of Bengal, was the first regular imperial city of Hindoostan, and that it was built in the reign of~Krishen, one of the most ancient rajahs. The Ayeen Akbery (Vol. II. p. 4]) represents Oude to have anciently been 148 coss (or about 259 miles) in length, and 36 coss (or about 53 miles) in breadth; but this bears mor-e resemblance to a province than a city. “This city,” says Sir W. Jones, “extended, if we may believe the Brahmins, over a line of ten yojans (or 40 miles). It is supposed to have been the birth—place of Rama.” According to the Mahabbarit, Oude continued the imperial city 1500 years, until about the year 1000 before the Christian aera, when a prince of the dynasty of the Surajas,who boasted their descent from the sun, erected Canouge upon the banks of the Ganges, and made the circumference of its walls 50 coss, or' about 87 miles. Strabo, from NIe- gasthenes, who had seen Canouge, says it was situated at the confluence of another stream with the Ganges; that its form was quadrangular, the length 80 stadia, breadth 1.5, or taking the mean stadium 'of the ancients, about 8 miles by 1%; that it had wooden fortifications, with turrets for archers to shoot from, and was surrounded by a vast ditch.———Strabo, Lib. XV. p. 667. Arrian calls it the greatest city amongst the Indians; he says that it was situated at the junction of the Eran- naboa with the Ganges: he gives the same di- mensions as Strabo; and says, that there were 570 towers on the walls, and 65 gates. Diodorus Siculus, Lib. XVII. p. 678, says, that when Alex- ander passed the Hyphasis, he was informed, that on the banks of the Ganges, he would meet the most formidable sovereign of India, called Xam- branes, king of the Gangarides, at the head of 20,000 horse, 200,000 foot, 2000 war chariots, and 4000 fighting elephants. The llIaIIabbm-z't states, that Sinkol, a native of Canouge, brought IND " -—‘ into the field, against Afl‘rasiah, king of Persia, 4000 elephants, 100,000 horse, and 400,000 foot. But that after Delu had founded Delhi, and es- tablished his court there, Canouge declined, and was involved in civil discord;——still we learn. from the same authority, that Sinsarchand, or Sandrocottus, the successor of Porus, restored Canouge to its ancient splendour; and that here, about the year 300 before Christ, he entertained the ambassadors from Seleucus, the successor of Alexander, and that Megasthenes was amongst the number. In the beginning of the fifth century, ' Ramd’eo Rhator (or the Mahratta) entered Canouge in triumph, and reigned there 54 years. The last king under whom this city may be considered as the metropolis of a great empire, was Maldeo, who, about the beginning of the sixth century, added Delhi to his dominions. At this time, Canonge was said to contain 30,000 shops, in which areca was sold. Although not the metropolis, it long after continued of great con- sequence. About the year ]000, when Sultan Mahmed invested it, it is represented as a city which, in strength, had no equal. It became an appendage to the empire established by M ahmed. —-Fe7'z's}ita, Vol. I. p. 27. Major Rennel is of opinion that Canouge and- Palibothra were the same. Others endeavour to prove the contrary ; and that both may have ex- isted at the same time capitals of the Prasii, as Delhi and Agra have done in later times. The precise period of the origin of Delhi is not correctly ascertained : According to the Ferishta, it was founded by Delu, who usurped the throne about 300 years before Christ. The Ayeen Akbery fixes it about the commencement of this era, and informs us, that twenty princes of the name of Bal, or Paul, followed in regular suc- cession for 437 years; that the last of its native princes was Pithonra, when it was conquered by the Mahomedan slave Cattub, named by Herbelot, Cathbaddin Ibek, who made Delhi the capital of the vast empire he established in Ilindoostan; and that each successive monarch of the Mahomedan dynasty adorned it with splendid edifices, appropriated to the purposes of religion and commerce. At the invasion of Timur Bee, it had arrived at the highest distinction for commerce and wealth, being then the centre of the traffic carried on between Persia, Arabia, and China. Timur entered it on the 4th ofJuly, 1399; IND‘ 111 IND ' r , I I'll-W" ' ' . and on the 13th of the same month, this celebrated city was destroyed. Sherifedden, the Persian his- torian, says, that old Delhi was celebrated for a mosque and palace, built by an ancient Indian king, in which were a thousand marble columns. Under the dynasty which succeeded Timur, it recovered its original splendour, and was again ornamented with mosques, baths, caravanseras, and sepulchres. The great Akbar, the glory of the Timur house, having fixed his residence at Agra, Delhi, of course, experienced a partial eclipse; but in 1647, according to Fraser, Ischaim Shah, the grandson of Akbar, restored Delhi under the‘name of Is- chaimbad, where he built a magnificent palace, formed extensive gardens, and constructed a throne in the shape ofa peacock, whose expanded tail was entirely composed of diamonds, and other precious stones. It continued the capital oinn- doostan till 1738, when it was sacked by Nadir; and afterwards repeatedly by Ahmed Abdallah, from 1756 to 1760, when it was totally destroyed. During the reign of Aurengzebe, it was said to contain two millions of inhabitants. Lahore is situated to the north~west of Delhi, on the banks of the Rauvee, the ancient Hydraotes : it appears to have been the Bucephalus of Alex- ander. Jeipal, the rajah of Lahore, during the incursions of Subuitagi, and his son 1AIahmud, de- fended his possessions with great bravery; and so great were his riches, that, when taken prisoner, around his neck alone was suspended sixteen strings of jewels, each of which was valued at .- 180,000 rupees, and the whole at c£320,000. Lahore continued to flourish under the sultan of ,1 Cosro, and was the imperial seat of Cuttub be- fore he removed it to Delhi; even afterwards it remained the general storehouse for the traffic of i Persia, Arabia, India, and China. It was re- stored by Homaion, who, amongst other magni- ficent buildings, erected a palace, which was com- pleted by Ischaim Geer, the son of Akbar. This palace, according to Mr. Finch, who visited it in 1609, had twelve gates, nine towards the land side and three towards the river. He says, the rarities were too numerous and glorious to be represented in a description; that the mahls, courts, galleries, and rooms of state, were almost endless ; and that, in the king’s lodgings, the walls and ceilings were overlaid with plates of gold. M. Bernier, who was in this city in the suite of Aurengzebe, speaks of this place as a high and magnificent building, but then hastening to ruin. Agra, the Agara of Ptolemy, situated in 27° 15’ north latitude, on the banks of the Jumna, We have already'observed, was raised to splendour by the great Acbar. He caused the earthen wall, by which the city had been enclosed by the Patan monarchs, to be taken away, and replaced by one of hewn stone, brought from the quarries of Fettipore. He collected the most skilful artificers from every part of his dominions; and the palace alone employed above 1000 workmen for twelve years. A The castle was built in the form of a cres- cent, upon the banks of the Jumna; and in a line with it were ranged the palaces of the princes and great rajahs, intersected with canals and beautiful gardens. Acbar also erected many caravanseras and mosques. He invited foreigners of all nae tions; he built them factories; and permitted to all the free use of their religion. It was soon crowded with Persian, Arabian, and Chinese mer- chants, besides those immediately from European settlements. But when Ischaim removed the im- perial insignia and treasures to Delhi, and made it the residence of his court, Agra sunk rapidly to decay. , These five imperial cities seem, with regard to extent, splendour, and wealth, to have exceeded the greatest cities of the western world ; and, be- sides these, many others were almost of equal magnificence; for Chundery is said to have con- tained 384 markets, and 360 earavanseras; and Ahmedabad was once so large as to require to be divided into 360 quarters—Maurice, Ind. Antiq. Vol.1. p. 118—124. These extensive and proud Cites were evidently the symbols of temporary policy and power, and have passed away; like so many splendid scenes on the great theatre of the East. But as the religion of India has been more permanent than their political relations, it is from the sacred edifices we are to trace most distinctly the cha- racters of Indian architecture, and be enabled to judge how far they have any affinity with those of other nations. Oftheirlarge temples (pagodas) we find accounts of five different forms. 1. Simple pyramids constructed of large stones, and diminished by regular recesses or steps, as at Deogur and Tanjore; the exterior rude, and the interior having only light from without by a small entrance door; illuminated by a profusion IND 112 IND of lamps, with the exception ofa chamber in the middle, which has only a single lamp. Aquetil says, that to him one of the mountains of Canara seemed hewn to a point by human art. 2. The second kind were formed by excavations in the sides of rocky mountains. Abul Fazul (fly/em Alrbery, Vol. II. p. 908) says, that, in the soobah of Cashmere, in the middle of the moun- tains, 12,000 recesses were cut out of the solid rock. From Captain VVilford’s paper on Caucasus, inserted in the sixth volume of the. Asiatic Re— searches, we learn that an extensive branch of the Caucasus was called by the Greeks Parapamis, obviously derived from Para Vami, the pure and excellent city of Vami, commonly called Bantiyan. It is situated on the road between Balkh and Cabul, and, like Thebes in Egypt, consists of vast numbers of apartments and recesses cut out of the rock; some of which, on account of their extraordinary dimensions, are supposed to be temples. There are also, at that place, two co- lossal statues, one of a man eighty ells high, and another of a woman fifty ells high, erect and ad- hering to the mountain from which they are cut. At Salsette, Elephanta, and Vellore or Ellora, the excavations were not only extensive, but were divided into separate apartments, with re- gular ranges ofsculptured pillars and entablatures, and the walls and ceilings covered with multi- tudes of figures of their genii, deutah, men, and women; and various animals, such as elephants, horses, lions, Ste. all of the most excellent work- manship. See Plates I. and II. 3. A third set was composed of square or oblong courts of vast extent. The circumference of the outward wall of that in the island of Seringham, adjacent to Trichinopoly, is said to extend nearly four miles. The whole edifice consists of seven square enclosures, the walls being 350 feet dis- tant from each other. In the innermost spacious vsquare are the chapels. In the middle of each side of each enclosure wall there is a gateway under a lofty tower: that in the outward wall, which faces the south, is ornamented with pillars of single stones, thirty-three feet long and five in diameter.——V0_yages de M. Somzerat, Tom. I. p. 217; and Robertson’s India, p. 268. Tavernier de- scribes the pagoda of Santidas, in the Guzerat, as consisting of three courts paved with marble, and surrounded with a portico supported by mar- ble columns: the inside of the roof and walls formed of mosaic work and agates, and all the portico covered with female figures cast in marble. Aurengzebe profaned this temple by killing acow within its precincts, and converting it into a Turkish mosque. At Chittambrum, on the coast of Coromandel, there is only one court, 1332 feet in one direction, and 936 in another, with an en- trance gateway under a pyramid 120 feet high, and the ornamental parts finished with great de- licacy—John Call, I’lzil. Trans. Vol. LXII. p. 354. Orme’s Hist. Vol. I. p. 178. 4. A fourth sort, as Benares pagoda, in the city of Casi, which from the earliest times was de- voted to Indian religion and science. The temple is in the form of a cross, with a cupola terminated by a pyramid in the centre, and having also a tower at each extremity of the cross. From the gate of the pagoda to the Ganges, there is a flight of steps.———Tavernier, Tom. IV. p. 149. Rouen edit. 5. A fifth are made in a circular form, as the celebrated pagoda ofJuggernaut, which Hamilton compares to an immense butt, set on end. Jug- gernaut, only another name of the god Mahadeo, who is represented by the vast bull whichjnts out of the eastern aspect of the building. It is the seat of the arch-brahmin of all India, and its sacred domains are said to afford pasturage for 20,000 cows. Besides these general terms, if our limits per- mitted us to trace those interesting structures through the various districts of this extensive country, many different arrangements might be described; but, for the present, we must be sa— tisfied with mentioning the pagoda of Bezoara, (or Buswara of Major Rennel) now a fort upon the Kistna river; it was not enclosed with walls, but erected upon 59. lofty columns with statues of Indian deities, standing between the columns. It was situated in the midst of an oblong court, round which there was a gallery raised on sixty» six pillars,likea cloister.—-Voy. des Ind. Tom. III. p. 226. Rouen Ed. 1713. Near this, on a hill ascended by one hundred and ninety-three steps, was another pagoda of a quadrangular form, ter- minated by a cupola. These temples were generally erected on the banks of the Ganges, Kistna, and other sacred rivers for ablation. Where there was no river, a tank or reservoir of a quadrangular form was construct— ed and lined with free-stone or marble, with steps descending into them. Crawford observed o W 1ND many 300 or 400 feet in breadth.—Crawford’s Sketches, Vol. I. p. 106. At the entrance of the principal pagodas, there is a portico supported by rows of lofty columns, and ascended, as in the case of Tripetty,by more than one hundred steps; under these porticos, and in the courts which generally enclose the buildings, multitudes attend at the rising of the sun, and having bathed and left their sandals at the border of the tank, impa- tiently await the unfolding of the gates by the ministering Brahmin.-——-T/«ez*enot. \Ve must reserve, until we come to treat of the detail of Indian Architecture, many particulars relative to those splendid edifices, which, with the plates accompanying them, will afford a more distinct view of the nature of their arrangements and appropriations; but it will be proper in this place to notice some leading circumstances re- specting the Indian sculptures, with a view to ascertain what affinity they had to those in Egypt. From the Ayeen Airbery, and Captain VVilson’s paper on Caucasus, we find, that in the Soubah of Cashmere, between Balkh and Cabul, in the numerous excavations, there are 700 places where the figure of a serpent is carved; and that near these excavations, there are sculptured in rock, on the side of the mountain, figures of 15, 50, and 80 ells high; that in the great temple of the sun, which was near Juggernaut, and Said, by the Ayeen Alt-(wry, to have consumed, in the expense of building, the whole revenue of the Orissa for twelve years; that in front of the gate, there was a pillar of black stone, of an octagon form, 50 cubits high; that at the eastern gate, there were two elephants, each with a man on his trunk; at the western gate were figures of horsemen, completely armed ; and at the northern gate two tigers, who had killed two elephants, and were sitting upon them. That in one ex- tensive apartment, there is a large dame con- structed of stone, upon which is carved the sun and stars, and round thema border of human figures. In the pagoda at Juggernaut, Hamilton describes the idol as a huge black stone, of a pyramidal form; and there was a bull, repre- senting the god Mahadeo, jutting from the wall of the eastern aspect. Tavernier observed a con- spicuous idol of black stone in the temple of Benares; and that the statue of Creeshna, in his celebrated temple of Mathura, was of black marble. In the great pagoda at Elephanta, the t- 0L. n. IND bust of the triple-headed deity measures 15 feet from the base to the top of the cap, the face is five feet long, and it is 20 feet across the shoulders. Along the sides of the cavern are co- lossal statues, to the number of forty or fifty, from 12 to 15 feet high; some have a sort of helmet of a pyramidal form ; others a crown with devices; others display bushy ringlets, some with curled, and others with flowing hair; many have four hands, some six; with sceptres, shields, weapons of war, and symbols of peace. At the west end of the pagoda, there is a great dark recess, 20 feet square, totally destitute of orna- ments, except the altar in the centre, and the gigantic figures which guard the several doors which lead into it. Niebuhr says these figures are eight in number; they are naked, and 13% feet high ; their heads, decorated like the other statues, have rich collars round their necks, and jewels of great size in their cars. In the before mentioned recess, the Lingam divinity is represented. The pagoda at Salsette exceeds that at Elephanta; the two colossal statues immediately before the entrance of the grand temple are 27 feet high; they have caps and ear-rings. There are here two hundred figures of idols; ninety of which are in and about the great pagoda. In the interior spaces which recede from the apartments, the Lingam is represented. Many of the sculptures in these grand temples have reference to the astronomical, as well as mythological notions prevalent in India. At Vellore, Eilore, or Ellora, (Plates 1. and II.) the sculptures, 8%. are still more extraordinary; and all are dedicated to the Liugam or Mahdeu. The height of the grand pyramid is here 90 feet ; the smaller ones 50 feet; the obelisks 38 feet. The elephants on each side of the court are larger than life; and there is an apartment for the bull Nundee. See Sir C. W. Mallet’s paper, Asiatic Researches, Vol. VI. p. 383. Sir W. Jones (.43. Res. Vol. I. p. 253) is of opinion, that the Eswara and Isi of the Hiudoos are the Osiris and Isis of Egypt. He says, that the word Misr, the native appellation of Egypt, is familiar in India; that Tirhoot was the country, asserted by a learned Brahmin to be that in which an Egyptian colony of priests have come from the Nile to the Gauges and Yamma (J umna.) And again, in his third annual discourse, the remains of architecture and sculpture in India, prove an 9 IND 114 early connection between this country and Africa; the pyramids of Egypt, the colossal statues of the Sphinx, and the Hermis Canis, which last bears a great resemblance to the Varahavatu, or the incarnation of Vishnu, indicate the style and mythology of the same indefatigable workmen, who formed the vast excavations of Canarah, the various temples and images of Buddah, and the idols which are continually dug up at Gaya. Kempfer asserts, that the great Indian saint, Buddha, was a priest of Memphis, and having fled to India, introduced the worship opris.-——Kemp- fer’s Hist. Japan. Vol. I. p. 38, ed. 1738. ,Athanasius Kircher is of opinion, that after Cambyses had murdered Apis, the most revered of the Egyptian deities, he committed wanton cruelties on the priests, and destroyed their mag- nificent temples, as related by Herodotus, and that the priests flying into the neighbouring coun- tries of Asia, there propagated the superstitions of Egypt. The lotus was anciently in Egypt, and is still in India, held sacred. Herodotus calls it the lily of the Nile. The Egyptian priests had a sacred language; so have the Brahmins. The Egyptians, according to Diodorus Siculus, were divided into five tribes, of which the first was sacerdotal; the Indians are separated into four tribes, besides an inferior one, named Buzzer Sunker. Father Loubere, who went ambassador from the king of France to the king of Siam, in 1687, thinks the superstition of Boodh no other than the Sommonacodom, or stone deity of the Siamese, originally from Egypt. He says, that their astronomers have fixed the death of Sommona— codom to the year BC. 545, and that it was then their first grand astronomical epocha commenced. Now, according to Usher, Cam byses invaded Egypt in 525 B.C. Loubere adds, that the Siamese priests live in convents, which consist of many cells ranged within a large enclosure; that in the middle of the enclosure stands the temple; that pyramids stand near to, and quite round the temple, all within four walls.—-See Loubere’s Hist. ofSiam, in Harris’s Coll. of Veg. Vol. II. p. 489.. Sir W. Jones thinks that the great statue of Narayen, or the Spirit of God, who at the begin- ning floated on the waters, as that statue is now to be seen in the great reservoir of Catmander, the capital of Nipaul, is the same as the Cneph of Egypt, under a different appellation; both statues IND a are made of blue marble—See Asiatic Researches, Vol. I. p. 261. Mr. Call has published a drawing of the signs of the zodiac, which he found in the ceiling of a choultry at Verdapettah, in the Madurah country, viz. Brahma, painted in pagodas, in the act of creation, floating over the watery abyss, reclining upon the expanded leaf of lotus; and Osiris is found in the same attitude, recumbent on the same plant, in the Egyptian monuments—Maurice, Vol. II. p. 394. In the Hindoostan edifices,althongh many parts of the general arrangement and principal features resemble those of Egypt, yet simplicity has been more departed from, and circular outlines similar to those of pagodas have been introduced. The most splendid of the Indian edifices being wholly, formed by excavation, may most properly be de— nominated sculptures; but even for this mode, abundance of originals exist in Egypt. The nu- merous sculptured tombs adjacent to the prin- cipal cities in the Thebai'd, are perfect examples, as far as regards excavations within the natural rock; and the gigantic colossal statues are equally so as to isolated forms. Detail of Indian Architecture—The city of Agra was built in the form of a crescent along the banks of the Jumna; its walls were constructed with stones of great size, hard, and of a reddish colour resembling jasper. It was four miles in extent, and consisted of three courts, with many stately porticoes, galleries, and turrets, all richly painted and gilt, and some overlaid with plates of gold. The first court was built round with arches, which afforded shade; the second was for the great omrahs and ministers of state, who had here their apartments for transacting public bu- siness; and the third court, within which was the seraglio, consisted entirely of state apartments of the emperor, hung round with the richest silks of Persia. Behind these were the royal gardens. In front of the palace, towards the river, a large area. was left for the exercise of the royal elephants, and for battles of the wild beasts; and in a square which separated the palace from the city, a nu- merous army lay constantly encamped. Man- desto, who visited Agra in 1638, then in the zenith of its glory, says, it was surrounded by a wall of freestone and a broad ditch, with a draw- bridge at each of its gates. He states, that at. the farther end of the third court, under a piazza, IND J IND were a row of silver pillars; that beyond this was the presence-chamber, with golden pillars; that within a balustrade was the royal throne of massy gold, almost incrusted with diamonds, pearls, and other precious stones; that above this throne was a gallery, where the Mogul appeared every day at a certain hour, to hear and redress the complaints of his subjects; and that no person but the king’s sons were admitted behind these golden pillars. He mentions also an apartment remarkable for its tower, which was covered with massy gold, and for the treasure it contained, having eight large vaults filled with gold, silver, and precious stones. Tavernier, who visited Agra near the end of the 17th century, and in the absence of the court had permission to examine the inside, describes a gallery, the ceiling of which was de- corated with branched-work of gold and azure, and the walls hung with rich tapestry. The gal- lery which fronted the river, the monarch had proposed to cover over with a sort of lattice- work of emeralds and rubies to represent grapes with their leaves, when they are green, and when they begin to grow red; but this design then re- mained imperfect, there being only three stocks of a vine in gold, with their leaves enamelled with emeralds, and rubies representing grapes; being a specimen of what was intended for the whole. \Ve have been thus minute in the description of the palace of Agra, because, having been built by one of the most enlightened princes of the East, it affords a perfect specimen of the scale upon which the monarchs of those extensive and rich countries acted. And it will be allowed, that the establishments of Akbar and his great rajahs, oc- cupying four miles along the banks of the J umna, and connected with a handsome and prosperous city, must have produced a picture sufliciently splendid and emblematic of the wealth and power of the prince who erected it. At Cuttek, or Cuttack, the capital of Orissa, there is a fine palace. It consists of nine distinct buildingsz—l. For elephants, camels, and horses; 2. For artillery, military stores, and quarters for the guards; 3. For porters and watchmen; 4. For artificers; 5. For kitchens ; 6. For the rajah’s public apartments; 7. For the transaction of private business; 8. Where the women reside; 9. The rajah’s sleeping apartments. The specimens here selected being the most noted, will, we trust, convey an idea of the nature of the Indian cities and palaces; and we shall therefore proceed to consider their sacred edi— fices. We have already stated, that these were of five different sorts; that is, 1. Pyramids; 2. Excava- tions; 3. Square or oblong courts; 4. In the form ofa cross; and, 5. Perfectly circular. ]. We are here at a loss to determine whether or not the construction of Indian pyramids preceded that of their excavations. To construct a pyramid of rude stones, is certainly a much simpler ope- ration than forming a cavern ornamented with sculpture; so that although it may be conceived that mankind might, for the purposes of worship. make use of the simple plain cavern, either na- tural or artificial, previous to the construction of buildings of great magnitude on the surface; yet it is not very probable that the splendid ex- cavations of Elephanta and Vellore, in which were rich sculptures, and even pyramids cut out of the solid rock, could have preceded a rude pyramid on the surface. But as the purposes to which the pyramids of Deogur and Tanjore are appro- priated partake very much of the nature of the cavern, their entrance-doors being very small, their interior being lighted by means of lamps, and the middle chamber by one lamp only; there is some reason for supposing, that in places where rocky eminences were not conveniently si~ tuated, or from motives now unknown, some change of ideas taking place, these pyramids might be constructed for purposes similar to the original cavern or grotto, in the same manner as the Egyptian pyramids are considered to have been done with regard to the tombs of the The- ba'id. The external faces of the pyramids of Deogur and Tan jore are very rude. 2. In regard to excavations, they are numerous and extensive. In some instances, they are very simple and plain; in others, highly ornamented with architectural forms and Seulptures. From Captain Wilson’s paper in the 6th vol. of the Asiatic Researches, we learn, that an extensive branch of the Caucasus was named by the Greeks, Parapamis, from Para Vami, the pure and excel- lent city of Vami, commonly called Bamaiya. It is situated on the road between Balkh and Cabul, where vast numbers of apartments are cut out of the rocks, some of them so large that they are supposed to have been temples. And Abul Fazel 9 0 d 1ND 116 IND says, that in the soubah ofCashmere, in the middle ofthemountains, 12,000 apartments were cut in the solid rock. At this place there were 700 places where the figure of a serpent was sculptured. Although neither the precise form nor dimen- sions are given, yet from the great number of excavations, and the place being noticed by the Greeks, it must, in former ages, have been of importance, at least for its sanctity; and its situ- ation between India and Persia renders it still an interesting subject of inquiry. In other parts of India, the excavated temples have fallen more frequently under the observation of well-informed scientific persons, who have, with laudable industry, furnished the public with exact representations, and full details respecting them. The three principal ones, and which our limits will only enable us to notice, are Elephanta, Salsette, and Vellore or'Ellora. Elephanta is situated near Bombay, in an island so named from the figure of an elephant being cut upon the rocks on the south shore. The grand temple is 120 feet square, and supported by four rows of pillars; along the side of the cavern are from forty to fifty colossal statues, from 12 to 15 feet high, of good symmetry, and, though not quite detached from the rock, boldly relieved; some have a helmet of pyramidal form, others a crown, decorated with jewels and de- vices, and others have only bushy ringlets of flowing hair; many of them have four hands, some six, holding sceptres, shields, symbols of justice and religion,warlike weapons and trophies of peace; some inspire horror,others have aspects of benignity. The face of the great bust is 5 feet long, and the breadth across the shoulders 90 feet. At the west end of this great pagoda is a dark recess, 20 feet square, totally destitute of orna- ment; the altar is in the centre, and there are two gigantic statues at each of the four doors by which it is entered. Niebuhr represents these statues as naked, 13% feet high, and the sculpture good; their heads are dressed like the other statues, and they have each rich collars round . their necks, and jewels in their ears. Hunter states, that, on entering Elephanta, there is a feerandah or piazza, which extends from east to west 60 feet, that its breadth is 16 feet, and that the body ofthe cavern is on every side surrounded by similar feerandahs.—Arck¢tologia, Vol. VII. p. 287. Canara, in the island of Salsette, which is also situated near Bombay, is represented by Linschotten, who visited it in 1759, as being like a town. He describes the front as hewn out of the rock, in four stories or galleries, in which there are 300 apartments: these apartments have generally an interior recess, or sanctuary, and a small tank for ablution. In these recesses, as at Elephanta, are representations ofthe Lingam deity. The grand pagoda is 40 feet high to the sofiit of the arch or dome; it is 84 feet long, and 4G broad. The portico has fine columns, decorated with bases and capitals: immediately before the entrance to the grand temple are two colossal statues, 27 feet high, which have. mitre caps and ear—rin gs. Thirty-five pillars, of an octagonal form, about 5 feet diameter, support the arched roofof the temple; their bases and capitals are composed of elephants, horses, and tigers, carved with great exactness. Round the walls, two rows of cavities are placed with great regularity, for receiving lamps. At the farther end is an altar ofa convex shape, 27 feet high, and 20 in diameter; round this are also recesses for lamps, and directly over it is a large concave dome cut out of the rock. Imme- diately about this grand pagoda, there are said to be 90 figures of idols, and not less than 600 within the precints of the excavations. Mr. Grose, who visited India in 1750, seems to be of opinion, that the labour required to con- struct Elephanta and Salsette, must have been equal to that of erecting the pyramids of Egypt; and though it is not mentioned which of the many pyramids he refers to, the remark suffi- ciently expresses his admiration of the greatness of these Indian works. He observes (p. 92) that the roof of Elephanta was flat; that of Salsette of an arch form, supported by rows of pillars, of _ great thickness, arranged with much regularity; that the walls are crowded with figures of men and women, engaged in various actions, in dif- ferent attitudes ; that along the cornice there are figures of elephants, horses, and lions, in bold relief; and above, as in a sky, genii and dewtah are seen floating in multitudes. But magnificent as the excavations at Elephanta and Salsette must appear, they are still surpassed by those near Vellore, Ellore, or Ellora, which is situated 18 miles from Aurungabad, capital of the province of Balagate, N. Lat. 19° 20', E. Long. 75° 30'. IND Sir C. Mallet, in a paper he transmitted to the president of the Asiatic Society, and published in the sixth volume of their Researches, gives a detailed account of sixteen of them. 1. Jugnath Subba. 10. Ramish \Vur. 0 Adnaut Subba. 1 l. Kylas, or Paradise. Indur Subba. 12. Bus Outar. 4-. Pursuram Subba. 13. Tee Tel. 5. Doomar Lyna. 6. Jun VVassa. ~- 0 s). 15. Biskurma, 01' Car- 7. Comar W ana. penter’s Hovel. 8. Ghana, or Oil Shop. 16. Dehr VVanar, or 9. N eclkunt Mahdew. Hallulcore’s quarters. Of these we must, of course, confine ourselves to such parts as are calculated to convey a general idea of their architecture; with this view, we have selected for engravings (see Plates 1. and II.) the ground-plan of Kylas, the entrance and sec- tion of Biskurma, the elegant entrance to the cave of J ugnath Subba, the temple of Indur Subba, and a singularly beautiful piece of sculpc ture at the door of Jun Wassa. We shall also give the description and dimensions of the Kylas and the Biskurma. Kylas, alias Paradise, (aspect, west.)—-This won— derful place is approached more handsomely than any of the foregoing, and exhibits a very fine front in an area cut through the rock. On the right-hand side of the entrance is a cistern of very fine water. On each side of the gateway there is a projection reaching to the first story, with much sculpture and handsome battlements, which, how- ever, have suffered much from the corroding hand of time. The gateway is very spacious and fine, furnished with apartments on each side that are now usually added to the dewries of the eastern palaces. Over the gate is a balcony, which seems intended for the Nobut Khanneh. On the out- side of the upper story of the gateway, are pillars that have much. the appearance of a Grecian order. The passage through the gateway below is richly adorned with sculpture, in which appear Bouannee Ushtbooza on the right, and Gunnes on the left. From the gateway you enter a vast area cut down through the solid rock of the mountain, to make room for an immense temple of the com- plex pyramidal form, whose wonderful structure, variety, profusion, and minuteness of ornament, are too. elaborate for description. This temple, which is excavated from the upper region. of the rock, and appears like a grand building, is con- 14. Bhurt Chutturghuu. 117' IND W. nected with the gateway by a bridge left out of the rock as the mass of the mountain was exca- vated. Beneath this bridge, at the end opposite the entrance, there is a figure of Bonannee sitting onalotus, and two elephants with their trunks joined, as though fighting, over her head. On each side of the passage under the bridge, is an elephant, marked (a) in the plan, one of which has lost its head, the other its trunk, and both are much shortened of their height by earth. There are likewise ranges of apartments on each side behind the elephants, of which those on the left are much the finest, being handsomely decorated with figures. Advanced in the area, beyond the elephants, are two obelisks (b) of a square form, handsomely graduated to the commencement of the capitals, which seem to have been crowned with ornaments, but they are not extant, though, from the remains of the left-hand one, I judge them to have been a single lion on each. To preserve some order, and thereby render easier the description of this great and complex work, we shall, after mentioning that on each side of the gateway within there is an abundance of sculpture, all damaged by time, proceed to describe the parts of the centre structure; and. then, returning to the right side, enumerate its. parts ;, when, taking the left hand, we shall terminate the whole in a description of the end of the area opposite to the gateway, and behind the grand temple, ex- emplifying the whole by references to the annexed plan. , Centre below—Passing through the gateway (1) below, you enter the area (2), and proceeding under a small bridge,pass a solid square mass (3), which supports the bull Nundee stationed above: the sides of this recess are profusely sculptured with pillars and figures of various forms. Having passed it, you come to the passage under another small bridge, beneath which. there is, on one side, a gigantic figure of the Rajah Bhoj, surrounded by a groupe of other figures, opposite to which is a gigantic figure of Guttordhuj, with his ten hands. At each end of this short passage com- mences the body of the grand temple (4), the excavation of which is in the upper story, that is here ascended by flights of steps on each side (5). Right and left liamlsirles qfthe temple below—The right-hand side is adorned with a very full and complex sculpture of the battle of Ram and IND Rouon, in which Huuomaun makes a very con- spicuous figu-re. Proceeding from this field of battle, the heads of elephants, lions, and some imaginary animals, are projected, as though sup- porting the temple, till you come to a projection (6), in the side of which, sunk in the rock, is a large groupe of figures, but much mutilated. This projection was connected with the apart- ments on the right-hand side of the area by a bridge (7), which has given way, and the ruins of it now fill up the sides of the area. It is said to be upwards of a hundred years since it fell. Passing the projection of the main body of the temple, it lessens for a few paces, then again pro- jects (8), and after a very small space on a line of the body of the temple, the length of this wonderful structure, if what is fabricated down- wards out of a solid mass can be so called, ter- minates in a smaller degree of projection than the former. The whole length is supported in the manner above mentioned, by figures of ele- phants, lions, 83‘s. projecting from the bases, to give, it should seem, the whole vast mass the ap- pearance ofmoveability by those mighty animals. The hindmost or eastern extremity of the temple is composed of three distinct temples, elaborate- ly adorned with sculpture, and supported, like the sides, by elephants, Ste. many of which are mutilated. The left-hand side (from the en— trance) difl'ers so little from the right, that it is unnecessary to be particular in mentioning any thing, except that opposite the description of the battle of Ram and Rouon, is that of Keyso Pando, in which the warriors consist of footmen, and others mounted on elephants, and cars drawn by horses, though none are mounted on horses. The principal weapon seems the bow, though maces and straight swords are discoverable. Centre above-The gateway consists of three centre rooms (9), and one on each side (9). From the centre rooms, crossing the bridge (10), the ascent is by seven steps (11) into a square room (12,) in which is the bull Nundee. This room has two doors and two windows. Opposite the windows are the obelisks (b) before mentioned. From the station of Nundee we cross over the second bridge (13), and ascend by three steps (14) into a handsome open portico (15), sup- ported by two pillars (above each of which, on the outside, is the figure of a lion, that, though mutilated, has the remains of great beauty; and 118 IND r 4' 1-» on the inside, two figures resembling sphinxes) towards the bridge, and two pilasters thatjoin it to the body of the temple, the grand apartments of which (16) are entered from the portico by four handsome steps and a door—way, on each side of which are gigantic figures. Advancing a few paces into the temple, which is supported by two rows of pillars, besides the walls that are deco- rated with pilasters, there is an intermission of one pillar on each side, leading to the right and left to an open portico (17), projecting from the body of the temple; from the right—hand one ofwhich, the bridge, already mentioned as broken, connected the main temple with the side apartments, to which there is now no visible access but by putting a ladder for the purpose; though I was told there is a hole in the mountain above that leads to it, which I had not time nor strength to explore. The access to the opposite is .by stairs from below. The recess (18) of the Lung (19) of Mahdew, to which there is an ascent of five steps, forms the termination of this the saloon, on each side of the door of which IS a profusion of sculpture. The whole of the ceiling has been chunamed and painted, great part of which is in good preservation. A door (9.0) on each side of this recess of the Ling of Mahdew leads to an open platform (21.), having on each side of the grand centre pyramid that is raised over the recess of the Ling, two other recesses (22), one on each side, formed also pyramidically, but containing no image. .Three other pyramidical recesses (23), having no images within them, terminate the platform, all of them elaborately ornamented with numerous figures of the Hindoo mythology. Many of the outer, as well as the inner parts of this grand temple are chu- named and painted. The people here attribute the smoky blackness of the painting within, to Au- rengzebe having caused the difi'erent apartments to be filled with straw and set on fire, which can be reconciled on no other ground than that he meant to efl‘ace Obscenities, as there are many in the sculptures. Upon the whole, this temple has the appearance of a magnificent fabric, the pyra- midal parts of which seem to be exactly in the same style as that of the modern Hindoo temples. Right-hand side (film mew—This side of the rock has a continuance of excavations, as marked in the Plan; but all those below, except the veranda, . [ND 119 W which I shall quit for the present, are of little note; and those above of three stories, called Lunka (24), which appear much more worthy of attention, are inaccessible but by a ladder, from . the fall of the bridge. We shall therefore pro- ‘ ceed to the Ltft-Iumd side of the area.—In this side there are excavations of some consideration below, from which we ascend to an upper story, called Par Lunka, by an indifferent staircase, into a fine temple (2.5); at the extremity of which is a recess, containing the Ling of Mahdew; and opposite thereto, near the entrance from the staircase, is the bull Nundee,with two large fine figures, rest- ing on maces, on each side of the recess, in. which he sits. The ceiling of this temple is I think lower than any of the foregoino. The whole of this temple is in fine preservation, strongly sup- ported by very massy pillars, and richly orna- mented with mythological figures, the sculpture of which is very fine. The ceiling, like the others, has the remains of painting visible, through the dusky appearance of smoke, with which it is ob- scured. Descending from Par Lunka, we pass through a considerable ensculptured excavation (26), to a veranda (27), which seems allotted to the personages of the Hindoo mythology (a kind of pantheon) in open compartments. These figures commence on the left hand with, 1. The Ling of Mahdew, surrounded by nine heads, and supported by Rouon. 2. Goura, Parwuttee, and beneath Rouon,writing. 3. Mahdew, Parwuttee, and beneath Nundee. 4. Ditto, ditto. 5. Vishnu. 6. Goura and Parwuttee. 7. A Bukta (votary) of Vishnu, with his legs chained. 8. Goura and Par- Wuttee. 9. Ditto. These representations of Goura and Parwuttee all differ from each other. 10. Ditto. 11. Vishnu and Luchmee. 12. Bal Budder, issuing from the Find, or Ling of Mah-x dew. Here ends the left-hand side, and com- mences the east extremity, or end of the area (28), in which the figures are continued, viz. 13. Goura and Parwuttee. 14. Behroo, with Govin Raj transfixed on his spear. 15. Dytasere on a chariot, drawing a bow. 16. Goura and Par- wuttee. 17. Kal Behroo. 18. Nursing Outar, issuing from the pillar. 19. KalBehroo. 20. Bal Behroo. 21. Vishnoo. 22. Govin. 23. Brimha. 24. Luchmcdass. 25. Mahmoud. 26. Nunain. 27. Behroo. 28. Govin. 29. Bal Behroo. 30. Govin Raj and Luchmee. 31. Kissundass. IND' Here ends the veranda of the eastern ex- tremity; and we now proceed with that on the right hand (29) having in our description of that side stopped at the commencement of this extraordinary veranda, for the purpose of preserving the enumeration of the figures un— interrupted, viz. 32. Mahdew. 33. Ittuldass. 34. Dhurm Raj embracing Uggar Kaum. 35. Nursing destroying Hurn Kushb. 36. Vishnu sleeping on Seys Naug, the kummul (lotus) issuing from his navel, and Brimha sitting on the flower. 37. Goverdhun. 38. Mahdew Bullee, with six hands. 39. Krishna sitting. on Guuoor. 40. Bharra Outar. 41. Krishna Chitterbooz trampling on Callea Naug. 42. Ballaju. 43.- Anna Pooma. It is to be observed, that almost all the principal figures are accompanied in their respective panels by others, explanatory of the character of that part of the history of the idol in which it is represented. Dimensions of the Kylas. Ft. In. Outer area,broad . . . . . . . .138 0 Ditto, deep- . . . . . . . . . . 88 0 Greatest height of the rock, through which the outer area is cut . . . . 47 0 Gateway, height . . . . . 14 0' Ditto, breadth, without the modern building . . .. . . . . . . . 14- 4 Passage of the gateway,having on each side rooms, 1.5 feet by 9 . . .. . . 42 0 Inner area or court, length from gateway to the opposite scarp . . . . . . 247 0 Ditto, breadth . . . .. . . . . . 150 0 Greatest height of the rock, out of which the court is excavated . . . . 100 0 Left Side of the Court, lower Story, viz. A small cave, in front two pillars, and a pilaster at each end, with three female figures buried up to the knees with rubbish, length. . . . . . . . .‘ 22 6 Ditto, breadth .. . . . . . . . . 8 0 Ditto, height . . . . . . . . . 9 8 Another excavation, in front five pillars, two pilasters, length . . . . . 57 9 Ditto, breadth, within the benches that are round this cave . . . . . . . 6 0 Ditto, height, at the end of this is a stair- case to the upper story . . . . . . 10 4 Interval unexcavated . . . . . . . 20 0 each is low er than the ceiling. IND 190 IND Another excavation, having two large no In. and 11 feet4 inches high. Right end Ft- 1"- plain square pillars, and two pilasters unfinished: length . . . . . 60 O in front,with a bench round the inside, Ditto, breadth . . . . . . . . . 17 O the rock projecting beyond the pillars, Ditt-o, height . . . . 13 0 length . . . . . . . . . . . 54 6 A small projecting room, 15 feet by 13, Ditto, breadth . . . . . . . . . 12 6 and 6 feet high, being choked with Ditto, height . . . . . . . . . 16 0 several finel scul tured figures. An Doorway, leading to a gallery, or veranda, excavation riilised 1% feet from the sur- 5 feet 11 inches high, by 2 feet 9 face of the court;length . . . 36 10 inches wide. Gallery containing figures. Ditto, depth . . . . . l4 9 Length from doorway to the extreme D1tto,he1 \ 0F 1'le TEMPLE OF FORTUZVE VIRIZIS AT ROM I 4/“ /, " V '4" ur in para :m by trim; mm. a. :4 - mismxm‘ S&¥*x-f’.~:€ -. \ [01111071, mama by fifViLleJ'aIl .é me-fidzl Wurduur gm. 2313. - “gm” by "75"”?- IONIC ORDER . . . Mimi FRUM THE THEATRE 0F MCELZUS AT ROME . 1 2 4 modular 29' ‘ L haw p.343 , \ ' .304 \ \ .30 '15 v» I “~- JJ“; - r2 3', 1; modular w J 2 7III/(III/IW (Ir //(/ [ml-Ar r >7,El > A‘ 2.1% :.. t J'MJ’ E . 4 JJ 5 V 5:. ) (a: , N “t ’ J” I L‘. \ _‘. ‘ ' ~ Jaw 1 , I " "H [{I/ ’1). .YI'I'lIn/a'n/z. Li’lll/Oll,’fil/l/l;)'/It’(i by I’. J'ir/Iulo'wl X'JBar/I'fl/a’ Minimu-.)‘.’Jfi//I’. [J'Il‘dl‘mw/ [{1/ 3.17017}. 180 139 IRO m I 3.: =3 white heat, iron appears as if covered with a kind of varnish, and in this state, if two pieces be ap- plied together, they will adhere, and may be per- iectly united by forging. Biitish cast 11 on is excellent for all kinds of cast- ings; our wrought iron also has of late been much improved in the manufacture, and is by many persons thought not inferior to the Swedish, which till lately had a decided preference; and is to be attributed to the use of charcoal in the pro— cess of smelting, which cannot be procured in sufficient quantity in England, where pit-coal has of necessity been substituted. The Navy Board and East-India Company, however, now contract for British iron only. See STEEL. IRON BRIDGE, a species of bridge, constructed, as its name implies, of iron, invented in England towards the close of the 18th century, and now preferred in many instances to similar structures of wood or stone. Under the article BRIDGE (page 133, 251:.) we have taken a general view of this kind of bridges; but having since re- ceived some valuable additional information, we here resume the subject, which is farther illus- trated by representations of the most consider- able works of this nature. The first iron bridge, as already observed, was erected upon the Severn, a little below Colebrook. Dale, where that river is narrow, and rapid. See Plate I. The abutments, which are of stone, are brought up to about 10 feet above the surface of common low water, where they have each a plat- form of squared freestoue for ten feet breadth, which serves for a hauling way, and a base for the arch to spring from. Upon this platform, cast-iron plates, four inches in thickness, are laid, and formed with sockets to receive the ribs. These plates, in order to save metal, have con- siderable openings in them. The principal, or inner ribs, which are five in number, and which form the arch, are 9 inches by 61. The second row behind them, and which are cut off at the top by the horizontal bearing pieces, are 6% by 6 inches: the third row are 6 by 6 inches; the up- right standards behind the ribs are 15 inches by 5 inches, but they have an open space in the breadth of 5%; the back standards are 9 inches by 6%, with projections for the braces; the dia- gonals, and horizontal ties, are 6 inches by 4, and the cast-iron tie bolts are 2} inches diameter. The covering plates, which are 26 feet in length, reaching quite across the bridge, are one inch in. thickness. The great ribs are each cast in two pieces, meeting at the keys, which, as the arch is circular, 100 feet 6 inches span, and 45 feet rise, are about 70 feet in length. There are circular rings of cast iron introduced into the spandrels, and there is a east-iron railing along each side of the road-way of the bridge: the weight of the whole of the iron work is 378% tons. Behind the iron work, at each extremity of the arch, the abutments are carried up perpendicularly of rubble masonry, faced with squared stone, and the wing walls are also of the same materials. The iron work was cast and put together in a very masterly manner, under the direction of Abraham Derby, of Colebrook Dale; and the whole was completed in the year 1779. The design was original and very bold, and was, as far as the iron work goes, well executed; but being a first attempt, and placed in a situation where more skill than that of the mere iron-master was required, several radical defects are now apparent. The banks of the Severn are here remarkably high and steep, and consist of coal measures, over the points of which vast masses of alluvial earth slide down, being impelled by springs in the upper parts of the banks, and by the rapid stream of the river, which dissolves and washes away the skirts below: the masonry of the abut- ments and wing walls not being constructed to withstand this operation, has been torn asunder, and forced out of the perpendicular, more par- ticularly on the western side, where the abutment has been forced forward about 3 or 4 inches, and by contracting the span, has of course heaved up the iron work of the arch. This has been re- medied under- the direction of that able mason Mr. John Simpson, of Shrewsbury, as far as the nature of the case will admit of, by removing the ground, and placing piers and counter arches upon the natural ground behind it. Had the abutments been at first sunk down into the natural undis- turbed measures, and constructed of dimensions and form capable of resisting the ground behind, and had the iron work, instead of being formed in ribs nearly semicircular, been made flat seg- ments, pressing against the upper parts of the abutments, the whole edifice would have been much more perfect, and a great proportion of the weight of metal saved“ We have already stated that one row of the principal ribs formed the 'r 2 1R0 140 IRO arch : the two rows behind are carried concentric with the inner row, until intersected by the road- way, which passes immediately at the level of the top of the inner ribs. This has a mutilated ap- pearance; the circular rings of the spandrels are less perfect than if the pressure had been upon straight lines; for a circle is not well calculated for r istance, unless equally pressed all round. We consider it our duty to introduce these obser- vations, in order to shew the necessity for great precaution in similar works, and how liable first attempts are to be defective; but they derogate nothing from the merit of projecting a great arch of cast-iron, introducing a material almost incom- pressible, which is readily moulded into any shape, and which is peculiarly applicable in the British Isles, where the mines ofiron are inexhaustible, and the means of manufacturing cast—iron unrivalled. The second iron bridge was built upon the same river, about three miles above the former one, at a place called Buildw‘as. An old stone bridge was carried away by a very high flood early in 1795, and the county of Salop was obliged to restore the communication. Mr. Telford, who was then, and is now, surveyor for the public works of that county, perceiving, that although, in a former repair, the middle pier of the four arches had been taken away, and that space, as well as the two adjacent arches, convertedinto one arch, yet that the water way had still been too much confined; and being aware that a few years previous to that time, the extensive low- lands in Montgomeryshire, which formerly acted as a reservoir, had been embanked, so that the flood—waters passed off more hastily, and in a greater body than formerly; in order, there- fore, to remove all obstacles out of the way of future floods, and on account of being within two miles of the best founderies in the world, he recommended a cast-iron arch of 130 feet span. (See Plate II.) The magistrates of the county agreed to this, and the Colebrook Dale Company became contractors, both for the iron work of the arch, and the masonry of the abutments. 1\’Ir. Telford, we understand, had some trouble in making that Company depart from their former mode of construction; but he at last prevailed in keeping the roadway low, and adopting the sus— pending principle, by means of a rib on each side of the bridge, which sprung from a lower base than the bearing ribs, and rose above them to the top of the railing: thus the bearing ribs were supported by the lower parts of those before— mentioned, and were suspended by their upper parts. The bearing ribs have a curve of 17in 130, or nearly one-eighth of their span. The suspending ribs rise 34 feet, or about one-fourth of their span. There are cast-iron braces, and also horizontal ties. There are forty-six covering plates, each 18 feet in length, and one inch in thickness. They have flaunches 41nches in depth, and are screwed together at each joint; so that, by taking the curvature of the bearing ribs, and being firmly secured at the abutments, instead of a load, they compose a strong arch. There being only one rib in the middle of 18 feet breadth of bridge, on each covering plate, a cross rib or flaunch, 4 inches in depth, is cast at an equal distance between the bearing ribs. The suspend- ing ribs are. each 18 inches in depth, and 2.} inches in thickness, exclusive ofa moulding. The hear— ing ribs are 15 inches in depth, and 2% inches in thickness, and each of the ribs is cast in three pieces only, of about 50 feet each; the braces are 5 by 3 inches. The principal king-posts are l0;— by 4% inches. The springing plates are each 3 feet broad, and 3 inches thick, with openings to save metal. The uprights against the abut- ments are 4% inches square. The strongest up- rights in the railing are 3 inches square, and those between them 1 inch. They are placed 6 inches apart, between middle and middle. The height of the railing above the surface of the roadway, is 4 feet 9 inches. In each spandrel, there are three circular arches formed with hard- burned bricks, which preserve most of the space open, but they are concealed by iron plates, one inch in thickness, which form the outside facings. 0n the eastern side of the river, although the banks are not so very high or steep, the quality of the ground being similar to that of the other iron bridge, particular care was bestowed upon the abutments: the space for them was excavated down to the rock, which lay considerably under the bed of the river, and the masonry was sunk into the solid part of the rock. It was built up chiefly of square masonry, and the rest of rubble, laid very close in regular courses, and having the back part formed in the shape of a wedge, point- ing to the bank. The wing walls were curved horizontally and vertically. At the height of 10 feet above the low water, there is a [rattling path mo 14! 7R0 I 1 gm“ on each side of the river. This bridge, which was completed in 1796, has never shewn any appearance of failure in any of its parts; nothing can be more perfect than the iron work; it is fitted as correctly as a piece of good carpentry. It has been objected to this structure, that by connecting ribs of different lengths and curva- ture, they are exposed to different degrees of ex- pansion and contraction. This appears just in theory ; and that no discernible effect has hitherto been produced, is probably from the difference being small. Another objection is, an apparent heaviness in the spandrels, from concealing the circular arches with iron plates. For appearance, these spaces had certainly better not been con- cealed, but they are not liable to the objections made to the former iron bridge, because the space around them is all closely filled up, and the roadway being formed with materials similar to this filling-up matter, distributes the pressure very regularly. Upon the whole, considering the strength acquired by placing the covering plates with their deep flaunches, in the form of an arch, we doubt whether a greater degree of strength can be had by any other distribution of the same quantity of cast iron, viz. 1735 tons: it appears to us, that the upright standards, braces, and king-posts, might be made of smaller dimensions. We have been informed, that each of these two first iron bridges, including abutments and road- ways, cost about £6000. The third iron bridge was constructed over the river Wear, near Sunderland, in the county of Durham. Its projector was Rowland Burdon, Esq. a gentleman of considerable landed property in that county, and who, for some time, represented it in parliament. The iron work was cast at the founderies of Messrs. Walkers, of Rotherham, and erected under the inspection of Mr. Thomas Wilson. The confidence in the use of iron, for arches of great extent, was by this time estab- lished. The span of the second arch, we have seen, is 30 feet more than that of the first; and in this third instance, the span is 106 feet beyond that of the second, although its rise is only the same as that of the suspending ribs at B'uildwas. The arch at Sunderland springs 60 feet above the level of the surface of low water; the span is 236 feet; the rise, or versed sine, is 34 feet; the width of the roadway 32 feet; and there are six ribs. See Plates 1. and III. In this arch, the mode of construction is very different from either of the former. Instead of working with pieces of iron from about 50 to 70 feet in length, each rib is here composed of 1‘23 small frames, each about two feet in the length or curve of the rib, and five deep in the direction of the radius. In each frame there are three pieces, of4 inches square, which run in the direc- tion of the curve of the arch; and these are con- nected in the direction of the radius by two other pieces, 4 by 3 inches. In each side of the larger pieces, is a groove, 3 inches broad, by three-quarters of an inch in depth; and oppositeeach cross piece there is a hole in the middle of the groove. When the abutments were brought up, and a scaffolding constructed across the river between them, six of these frames were placed against the abutments in the manner of arch-stones. VVrought-iron bars, of a length to embrace sundry frames, were then fitted into the grooves. Hol- low pipes of cast-iron, 4 inches in diameter, fitted to reach between each two frames, across the sofiit, were introduced. Upon the ends of these pipes are flaunches, in which there are holes, answerable to the holes in the four-inch pieces of the frames, and also to those of the wrought-iron bars. Through these holes, wrought-iron bolts were introduced, which brought all the before- mentioned parts together by means of fore-locks. The frames do not meet at the upright pieces, but on the three points of the four inch pieces only. On the ends of the hollow pipes, there are small projecting pieces, which embrace the upper and lower edges of the frames opposite each join- ing. These operations were repeated until the whole of the frames were placed, and the arch keyed, forming six ribs between the abutments. Upon the ribs, perpendicular pillars are placed; and between them are cast-iron circles, which come in contact with the extrados, the upright pillars, and the bearers of the roadway. The bearers and covering, we suppose for cheap- ness, are made of timber. The railing is cast- iron. The inclinations each way upon the arch, probably to save weight, are inconveniently steep. From its great elevation, and lightness of con- struction, this bridge is justly esteemed a bold effort of art, and a magnificent feature in the country. The wooden bridges in Switzerland, and that in America, are of greater span; but, 1R0 142 1R0 being placed near the surface of the water, and from the difference of material, their parts being of larger dimensions, there can be no comparison as to the fineness of effect. This arch. is an incon- trovertible evidence of what may be accomplished by means of cast iron, since it answers so well, charged, as it is, with the following, we conceive, material defects: 1. The frames are much too short, thereby multi- plying, very unnecessarily, the number of join- ings in the main ribs to 19.5 X 6:750; and in the same ratio, increasing the number of braces, ties, and bolts. The pieces of the frames being of unequal dimensions, is also improper. 2. The preservation of the due position of the frames is made to depend too much upon wrought-iron bars and bolts, which should be, as much as possible, excluded from structures of this kind. 3. The circles in the spandrels, placed as supports for the roadway, we have already stated, are im- proper in a situation where they are not equally pressed around. We shall observe nothing respecting the timber in the superstructure, because this is mere economy; if properly managed, any bad effects from the difference of expansion and contraction in the two materials, may be easily avoided; and the timber, not interfering with the essential parts, it may, when necessary, be removed, with little interruption to the intercourse over, and none to that under this noble arch. “7e cannot here resist drawing the attention of our readers to the perfection of this double accommodation, in crossing this deep ravine with facility, while vessels of 200 tons are passing full rigged below. A cast-iron bridge has lately been built over the river VVitham, at Boston, in Lincolnshire, from a design by Mr. Rennie. The span is about 85 feet, the rise is about 5 feet 6 inches, the breadth is 36 feet, and there are eight ribs, each rib is com- posed of eleven frames, 3 feet deep in the direc- tion of the radius. At each joining there is a cast-iron grating across the arch, which connects the frames, on the same principles as———-— prac- tised at Pontcysylte aqueduct. Instead of three pieces in the direction of the curve, as at Sunder- land, here are only two, but they are 7 inches by 4%. These are, in each frame, connected in the direction of the radius, by pieces, 4 by 3 inches. ‘Upon the back of the ribs, pillars, 4 by 3 inches, are placed perpendicularly to support the roadway. The superstructure resembles that of the first iron bridge at Colebrook Dale. The arch has been kept very flat, to suit the tide below, and the streets above. The rise being only about 1‘? of the span, is another proof of the facilites which may be acquired by using cast- iron. The frames being made about four times the length of those at Sunderland, and being connected with cast-iron gratings instead of wrought-iron, are essential improvements; but from the pieces in the frames, which are in the direction of the radius, being only 4» by 3 inches, while the main pieces in the direction of the curve, are 7 by 4%, a great proportion of the former are broken. This is a defect; and the pillars which support the roadway, being per— pendicular, do not correspond with the radiated pieces of the frames. The ribs, in springing from the perpendicular face of the masonry of the abutment, have also a crippled appearance. In improving the port of Bristol, Mr. Jessop found itnecessary to change the course of the river Avon, and to make two cast—iron bridges over the new channel. (See Plate IV.) The span of the iron work of each arch is 100 feet; the rise 12 feet 6 inches, or—g of the span; the breadth is .30 feet; and there are six ribs; each rib is composed of two pieces meeting in the middle, and they are connected crosswise by nine cast—iron ties, which are dovetailed, and wedged into the ribs; the cross sections of these ties are in the form of the letter T. The ribs stand upon abutment-plates, which are laid in the direction of the radius. These plates are 3‘2. feet in length, 2 feet 4 inches in breadth, and 4- inches in thickness; in each plate are five apertures, each 5 feet long and 9.0 inches in width. The ribs are 2 feet 4 inches in depth in the direction of the radius, and ‘2. inches in thickness, and have each 80 apertures, one foot square, separated by bars 3 inches broad, except- ing opposite the cross ties, where the solid is 19. inches broad. “fliere the ribs meet in the middle, they have flaunches 8 inches broad and '2 thick, and they are connected by cast—iron screwbolts 3 inches diameter. Between the ribs and the bearers of the road—way, perpendicular pillars, with cross sections formed like the letter T, are placed. The bearers are of the same form. The whole is covered with cast-iron plates, and there are railings of cast iron. 1R0 143 There is great simplicity, and much of correct principle in this design: 1. The springing plates being placed in the direction of the radius, and the abutments receding to produce a space be- kind the ribs equal to that between the upright pillars. 2. The ribs being composed of two pieces, and one joint only: and, 3. \Vrought-iron being wholly excluded. But we regret still observing the varying dimensions of the parts of the ribs; and that the supporting pillars are still placed perpendicularly; and which, as the arch has more curvature, has a still worse effect than at Boston. In the course of his employment as engineer to the board of parliamentary commissioners for making roads and constructing bridges in the Highlands of Scotland, Mr. Telford has lately made a design for a cast-iron bridge, now con— structing upon an arm of the sea, which divides the county of Sutherland from that of Ross, at a part where several of these roads unite. In this bridge, the defects noticed in the former works of this sort appear to be avoided. (See Plate V.) The arch is 150 feet span ; it rises ‘20 feet, it is 16 feet in width, and has four ribs. In the abutments, not only are the springing-plates laid in the direction of the radius, but this line is continued up to the roadway. The springing- ‘ plates are each 16 feet in length, 3 feet in breadth, and 4 inches in thickness, with sockets and shoul- der-pieces to receive the ribs. In each plate are three apertures, 3 feet in length and 18 inches in width. Each of the ribs, for the conveniency of distant sea—carriage, is composed of five pieces, 3 feet in depth in the direction of the radius, and 2%, inches in thickness. There are triangular apertures in the ribs, formed by pieces in the direction of the radius, and diagonals between them; but every part is of equal dimensions. At every joining of the pieces of the ribs, a cast- iron grating passes quite across the arch; upon these are joggles or shoulderings to receive the ends of the ribs: the ribs have also flaunches, which are fixed to the gratings with cast-iron screw-bolts. Each rib is preserved in a vertical plane, by covering the whole with grated flaunched plates, properly secured together, and to the top of the ribs, by cast-iron screws and pins. In the spandrels, instead of circles or upright pillars, lozenge, or rather triangular forms, are introduced, each cast in one frame, with a joggle at its upper and lower extremities, which pass into the sockets formed on the top of the ribs, and in the bearers of the roadway. Where the lozenges meet in the middle of their height, each has a square notch to receive a cast-iron tie, which passes from each side, and meets in the middle of the breadth of the arch, where they are secured by fore-locks. Next to the abut- ments, in order to suit the inclined face of the masonry, there are half-lozenges. By means of these lozenge or triangular forms, the points of pressure are preserved in the direction of the radius. The covering plates, in. order to preserve a sufficient degree of strength», and lessen the weight, are, instead of solid, made of a reticu- lated shape; the apertures widen below, to leave the matter between them a narrow edge; and contract upwards, so as to prevent the matter of the roadway from falling through. This disposi- tion» of the iron work, especially in the spandrels, also greatly improves the general appearance. In a printed report of a committee of the House of Commons, of the last session, we find some- new information, respecting centering for an iron bridge, which, as it promises to form a new aera. in bridge building, we are happy in being enabled to lay it before our readers. This subject has been brought under discussion in the course of investigating the most effectual mode of improving the mail-roads from Holyhead through North Wales. The island. of Anglesea- is divided from Caernarvonshire by the celebrated strait or arm of the sea named theMenai, through which the tide flows with great velocity; and from local circumstances, in a very peculiar manner. This renders the navigation difficult; and it has always been a formidable obstacle in the before-mentioned communication. It has hitherto been crossed by a ferry-boat at Bangor; but the inconvenience and risk attending this mode, has led to speculations of improvement for half a century past; wooden bridges, and embankments with draw-bridges, have been al- ternately proposed and abandoned. From a report of the House of Commons, of June 1810, it appears, that Mr Rennie, the engineer, had given plans and estimates for bridges at this place in 1802, and had been called on to revise them in 1810. His plans, which appear in the last- mentioned report, are, lst, One arch of cast- irou, 450 feet span, over the narrowest part of IRO 144 the strait, at a projecting rock named Ynys-y- Moch: and, 9d, Another upon the Swilley Rocks, [consisting of three castviron arches, each 350 span. The expense of that at Ynys—y-Moch is estimated at £259,140, and of that at the Swilley, £290,147. He prefers the latter, because he says, “ On account of the great span of the arch at Ynys-y-Moch, and the difficulty and hazard there will be in constructing a centre to span the whole breadth of the channel at low water, with- out any convenient means of supporting it in the middle, on account of the depth of water and rapidity of the tide, or of getting any assistance from vessels moored in the channel to put it up; I will not say it is impracticable, but I think it too hazardous to be recommended.” And, again, in the same report: “ I should be little inclined to undertake the building a bridge at Ynys-y- Moch.” But from the report of June 1811, it appears; that in May 1810, Mr. Telford was instructed by the Lords of the Treasury, to survey, and report upon the best method of improving the lines of communication between Holyhead and Shrewsbury, and also between Holyhead and Chester; and to consider, and give plans for passing the Menai. In the aforesaid report (of 1811) we have his plans and estimate. His ex- planations we shall give in his own words. “ The duty assigned me, being to consider, and report respecting a bridge across the Menai,I shall confine myself to this object. Admitting the importance of the communication to justify acting on a large scale, I not only consider the constructing a bridge practicable, but that two situations are remarkably favourable. It is scarcely necessary to observe, that one of these situations is at the Swilley rocks, and the other at Ynys-y-Moch. These two being so evidently the best, the only question that can arise is, to which of them the preference ought to be given. “ From the appendix to the second report to the Holyhead road-s and harbour, it appears, that a considerable number of small coasting vessels, viz. from 16 to 100 tons, navigate the Menai, and that there have been a few from 100 to 150 tons. By statements from the principal ship- builders in the river, made in the year 1800, to the committee for improving the port of London, it also appears, that vessels of 150 tons, when they have all .on end, are only 88 feet in height IRO J above the water-line; and farther, that even ships of 300 tons, with their top—gallant masts struck, are nearly the same height: these, in the Menai, are extreme cases, and, if provided for, ought, as to navigation, to satisfy every reason- able person; it may, indeed, rather be a question whether the height should not be limited to vessels under 100 tons, by which the expense of a bridge would be considerably diminished. “In the plansI have formed, provision is made for admitting vessels of 150 tons to pass with all on end; that is, in one design preserving 90 feet, and in the other 100 feet between the line of high water and the lower side of the soflit of the arch. The first design is adapted for passing across the three rocks, named the Swilley, Benlass, and Ynys-well-dog; which by their shape and position, are singularly suitable. To embrace the situation most perfectly, I have divided the space into three openings of 260 feet, and two of 100 feet each; making piers each 30 feet in thickness. Over the three large openings, the arches are made of cast iron; over the smaller spaces, in order to add weight and stability to the piers, semicircular arches of stone are intro- duced ; but over these, as well as the larger open- ings, the spandrels, roadway, and railing are con- structed of cast—iron. In this way the naviga. tion is not impeded, because the piers standing near the outer edges, are guards for preventing vessels striking upon the rocks; while the whole structure presents very little obstruction to the wind. From the extremity of the abutments, after building rubble walls above the level of the tideway, I propose carrying embankments until the roadway reaches the natural ground. The annexed drawing will sufficiently explain the nature of the design. I propose the bridge to he 32 feet in breadth: and, from minute calcu- lations made from detailed drawings, I find the expense of executing the whole, in a perfect manner, amounts to £158,654. “ The other design is for the narrower strait, called Ynys-y-h’loch. Here the situation is par- ticularly favourable for constructing a bridge of one arch, and making that 500 feet span, leaves the navigation as free as at present. In thisI have made the height 100 feet in the clear at high-water spring-tides; and I propose this bridge to be 40 feet in breadth. Estimating from draw- ings, as already described, I find the expense to 1R0 be £127,331, or £31,323 less than the former. From leaving the whole channel unimpeded, it is certainly the most perfect scheme of passing the Menai; and would, in my opinion, be attended with the least inconvenience and risk in the execution. “ In order to render this evident, I have made a drawing, (see Plate VI.) to shew in what manner the centering or frame, for an arch of this mag- nitude, may be constructed. ' Hitherto, the cen- tering has been made by placing supports and working from below; but in the case of the :Menai, from the nature of the bottom of the channel, the depth at low‘ water, and the great rise and rapidity of the tides, this'would be very difficult, if not impracticable. I therefore pro— pose changing the mode, and working entirely from above, that is to say, instead of supporting, . I mean to suspend the centering. By inspecting the drawing, the general principle of this will be readily conceived. - “ I propose, in the first place, to build the ma- sonry of the abutments as far as the lines AB, CD, and in thepparticular manner shewn in the section. Having carried up the masonry to the level of the roadway, I propose upon the top of the abutments to construct as many frames as there are to be ribs in the centre; and of at least an equal breadth with the top of each rib. These frames to be about 50 feet high above the top of the masonry; and to be rendered perfectly firm and secure. That this can be done, is so evident, I avoid entering into details respecting the mode. These frames are for the purpose of receiving strong blocks or rollers and chains, and to be acted upon by windlasses or other powers. “ I next proceed to construct the centre itselfzi it is proposed to be made of deal bulk, and to con- sist of four separate ribs; each rib being a con- tinuation of timber frames, 5 feet in width at the top and bottom, varying in depth from 25 feet near the abutments to 7 feet 6 inches at the mid- dle or crown. Next to the face of the abutments, one set of frames, about 50 in length, can, by means of temporary scaffolding, and iron chain bars from the beforemetioned frames, be readily constructed, and fixed upon the offsets of the abutinents, and to horizontal iron ties laid in the masonry for this purpose. A set of these frames (four in number) having been fixed against the face of each abutment; they are to be secured together by cross and diagonal braces, and there VOL. 11. 145 IRO .W being only spaces of 6lfeet 8 inches left between the ribs, (of which these frames are the com- mencement,)'they are to be covered with planking, and the whole converted into a platform, 50 feet ' by 40. By the nature of the framing, and its being secured by horizontal and suspending bars, I presume every person accustomed to practical operations will admit, that these platforms may be rendered perfectly firm and secure. “ The second portion of the centre frames, having been previously prepared and fitted in the carpenter’s yard, are brought, in separate pieces, through passages purposely left in the masonry, to the beforementioned platforms. They are. here put together, and each frame 'raised by the sus- pending bars and other means, so that the end which is to be joined to the frame already fixed, shall rest upon a small moveable carriage. It is then to be pushed forward, perhaps upon an iron rail road, until the strong iron forks, which are fixed on its edge, shall fall upon a round iron bar, which forms the outer edge of the first, or abut- ment frames. When this has been done, strong iron bolts are put through eyes in the forks, and the aforesaid second portion of the frame-work is suffered to descend to its intended position, by means of the suspending chain bars, until it closes with the end of the previously fixed frame, like a rule joint. Admitting the first frames were firmly fixed, and that the hinge part of this joint'is sufficiently strong, and the joint itself 20 feet deep, I conceive, that even without the aid of the suspending bars, this second portion of the centering would be supported; but we will for a moment, suppose, that it is to be wholly suspended. It is known, by experiment, that a bar of good malleable iron, one inch square, will suspend 80,0001b. and that the powers of sus— pension are as the sections; consequently, a bar 1% inch square, will suspend 180,000lb.; but the whole weight of this portion of the rib, in- cluding the weight of the suspending bar, is only about S0,000lb.or one-sixth of the weight that might safely be suspended; and as I propose two suspending chain-bars to each portion of rib, if they had the whole to support, they would only be exertingabout one-twelfth oftheirpower; and con- sidering the proportion of the weight which rests upon the abutments, they are equal also to sup- port all the iron work of the bridge, and be still far within their power. ' U IRO 146 [RC “ Having thus provided for the second portion of the centering, a degree of security far beyond what can be required, similar operations are carried on from each abutment until the parts are joined in the middle, and form a complete center- ing; and being then braced together, and covered with planking where necessary, the whole becomes one general platform, or wooden bridge, to re- ceive the iron work. “ It is, I presume, needless to observe, that upon such a centering or platform, the iron work, which, it is understood, has been previously fitted, can be put together with the utmost correctness and facility; the communication from the shores to the centre will be through the beforemen- tioued passages in the masonry. The form of the iron work of the main ribs will be seen by the drawing, to compose a system of triangles, preserving the principal points of bearing in the direction of the radius. It is proposed in the breadth of the bridge (1'. e. 40 feet) to have nine ribs, each cast in twenty-three pieces, and these connected by a cross grated plate, nearly in the same manner as in the great aqueduct of Pont- cysylte, over the valley of the Dee, near Llan- gollen. The fixation of the several ribs in a ver- tical plane, appearing (after the abutmeuts) to be the most important object in iron bridges, I pro- pose to accomplish this by covering the several parts or ribs, as they are progressively fixed, with grated or reticulated and flaunched plates across the top of the ribs. This would keep the tops of the ribs immoveable, and convert the whole breadth of the bridge into one frame. Besides thus securing the top,l propose also having cross braces near the bottom of the ribs. “The ribs being thus fixed, covered, and con~ nected together, the great feature of the bridge is completed. And as, from accurate experiments, made and communicated to me by my friend, the late William Reynolds of Colebrook Dale, it requires 448,0001b. to crush a cube of one quar- ter of an inch of cast-iron, of the quality named gun-metal, it is clear, while the ribs are kept in their true position, that the strength provided is more than ample. “When advanced thus far, I propose, though not to remove, yet to ease the timber centering by having the feet _of the centering ribs (which are supported by offsets in the masonry of the front of the abutment,) placed upon proper wedges; the rest of the centering to be eased at the same time by means of the chain-bars. Thus the hitherto dangerous operation of striking the centering, will be rendered gradual and perfectly safe; inasmuch that this new mode of suspending centering, instead of supporting it from below, may perhaps hereafter be adopted as an improve- ment. Although the span of the arch is un- usually great, yet by using iron as a material, the weight upon the centre, when compared with large stone arches, is very small. Taking the mere ring of arch-stones in the centre arch of Blackfriars’ bridge, 156x43x5, equal to 33,450 cubic feet of stone, it amounts to 2236 tons; whereas the whole of the iron work, in the main ribs, cross plates, and ties, and grated covering plates, that is to say, all that is lying on the cen- tering at the time it is to be eased, weighs only 1791 tons. It is true, that from the flatness of the iron arch, if left unguarded, a great propor- tion of this weight would rest upon the center- ing; but this is counterbalanced by the operation of the iron ties in the abutments, and wholly commanded by the suspending chain bars. “ When the main ribs have been completed, the next step is to proceed with the iron supporters of the roadway; and these, instead of being con- structed in the form of circles, or that of perpen- dicular pillars, as hitherto, are here a series of triangles, thus including the true line of bearing. These triangles are, of course, preserved in a. vertical plane by cross ties and braces. Iron bearers are supported by these triangles, and. upon the bearers are laid the covering plates under the roadway, which, instead of being solid, are, (in order to lessen the weight) proposed to be reticulated. “ Ifl have, throughout this very succinct descrip~ tion, made myself understood, it will, I think, be admitted, that the constructing a single arch across the Menai, is not only a very practicable, but a very simple operation; and that it is ren- dered so, chiefly by adopting the mode of work- ing from each abutment,without at all interfering with the tideway. “ In the case of the Swilley bridge, although the arches are smaller, yet being placed on piers, situated on rocks, surrounded by a rapid tide, the inconvenience of carrying materials, and working, is greatly increased; and supposing the bridge part constructed, an enormous expense is still IRON BRIDGE. mm 1. RIDGE builtover file RIflE'R SEVERMnear COALBBOOEDAEEjn file GUI/INTI?“ SAL 0P. 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Therefore, whether (economy, facility of per- formance, magnificence, or durability be consulted, the bridge of one arch is, in my opinion, infinitely preferable; and it is no less so, if considered in what regards the navigation.” This mode of constructing centres, applicable to stone as well as iron arches, being an original idea, and perfectly simple, and the effects of all its ope- rations being more capable of correct demonstra- tion than those of the former mode of supporting from below, we were glad of being enabled to communicate the outlines of the scheme, as given by the engineer in his report to the Lords of the Treasury. If this should be successfully practised on so large a scale at the Menai, all difficulties with regard to carrying bridges over inaccessible ravines or turbulent streams, will, in future, be done away, and a new aera formed in bridge building. \Ve have only given a plate of the centering, be- cause the construction of the iron work is pre- cisely the same in principle (though on a larger scale) as what has been adopted by the same en- gineer in Bonar bridge. See Plate VI. The above article upon iron bridges is taken from the Edinburgh Encyclopedia, by the permission of its able author, Thomas Telford, Esq. Since the publication of the article BRIDGE, and the foregoing part of the above, the Author has been favoured with two letters from John Rennie, Esq. correcting several errors in the information he had received upon these subjects: under the article BRIDGE, it is stated, that the aqueduct bridge near Glasgow is the work of that great engineer, Mr. Smeaton: but it was planned and executed under the direction of Mr. Robert Whit- worth, who succeeded Mr. Smeaton as engineer to the Forth and Clyde canals. In the same article, it is said that the foundation-stone of Vauxhall bridge was laid by General Sir David Dundas; but it was Lord Dundas who officiated for His Royal Highness the Prince Regent on that occasion. The iron bridge at Staines is also spoken of, as if it did then exist; whereas it failed by the giving way ofthe abutments,and was obliged. to be taken down and replaced by a wooden bridge, which had been completed, and was passable for several years before that article was written. In the beginning of the present article, the con- struction of the iron bridge over the river \Vitham at Boston, in Lincolnshire, is ascribed to Mr. Rennie: but he only gave the width and rise of the arch, and the abutments were founded and built under his direction; the iron arch itself being designed and executed by Mr. Thomas Wilson, of Sunderland; and unfortunately there is now a suit pending between the corporation of Boston and Mr. Wilson, relative to the iron work of this bridge, which is not yet settled. IRON CHArN, pieces of iron linked together. Iron chains are very serviceable under the roofs of circular buildings, where there is no intermediate tie, particularly at the bottom of stone domes, in order to prevent them from spreading or pushing out the walls, which, without this precaution, might be subject to separation, especially when the dome has to support an immense turret or lantern of stone. The dome of St. Paul’s Cathe- dral, London, has two chains let into a bondage of portland stone laid for the purpose. IRON KING-POSTS AND QUEEN-POSTS, are in many instances preferable to those constructed of wood, and are not more expensive where both bolts and straps are used. IRREGULAR, in the art of building, a term ap- plied not only to the parts of an edifice which deviate from the proportions established by an- tique monuments; as when the Grecian .Doric is made more than six diameters in height, the Ionic more than nine, and the Corinthian more than ten; but also to places where the angles are unequal, and to edifices whose counterparts do not correspond in the several elevations. A column is said to be irregular, not only when it deviates from the proportions of any of the three regular orders; but when its ornaments, whether in the shaft or capital, deviate from the established forms peculiar to the order. IRREGULAR BODIES, solids not terminated by equal and similar surfaces. IRREGULAR FIGURE, a figure whose sides and angles are not equal. ISAGON (from the Greek Zawydms) in geometry, 3. figure consisting of equal angles. [SIAC TABLE, one of the most considerable monuments of antiquity, being a plate of copper or brass, discovered at Rome, in 1525, and sup- posed by the various figures in has relief upon it, to represent the feasts of Isis, and other Egyp- tian deities. us 181 148 With regard to the history of this monument, we may observe, that the copper or brass ground wasov-erlaid with a black enamel, artificially ~in— termixed with small plates of silver., When, in the year 1525, the constable of Bourbon took the city of Rome, a locksmith bought it of a soldier, and then sold it to cardinal Bembo, after whose death it came into- the- hands of the duke of Mantua, and was kept in that family till it was lost at the taking of that city by the Imperialists, in the year 1630, nor has it been ever heard of since. By good fortune it had been engraved in its full proportion, and with all possible exactness, by JEneas Vico of Parma. This tablet was divided into three horizontal compartments, in each of which were different scenes, containing different actions. Those compartments are, as it were, different. cartouches, distinguished some- times by single strokes only, but oftener by a very large fascia, which is full of hieroglyphics, that is, of that mysterious writing, consecrated ISO by the ancient Egyptians to the mysteries of religion. The four sides of the table were en- closed with a border, filled up, like the ground, with several figures of the Egyptian gods, and with a great nuinber of the l1ie1oglypl1ics.The1e have been various opinions as to the antiquity of this monument: some have supposed that it was engraved long before the time when the Egyptians worshipped the figures of men and women. Others, among whom is bishop VVar- burton, apprehend, that it was made at Rome, by persons attached to the worship of Isis. Dr. Warburton considers it as one’of the most modern of the Egyptian monuments, on account of the great mixture of hieroglyphic characters which it bears. ISODOMUM, a species of walling used by the Greeks See WALL. ISOSCELES TRIANGLE, a triangle with two of its sides equal. 149 .m J 0G JACK PLANE, a plane about 18 inches in length, used in taking ofl‘ the rough of the saw, or the irre- gularities of the axe, and planing off any protube- A rant parts, to prepare the stuff for the trying plane. JACK RAFTER, a short rafter, such as those which are fixed to the hips. JACK RIBS, in a groin, or in a polygonal domic ceiling, are the ribs that are fixed upon the hips. JAPK TIMBER, any timber that is interrupted in its whole length, or cut short. JAMBS (French) the sides of an aperture, which connect the two sides of the wall. JAMB LINING, the two vertical linings of a door- way or aperture, which connect the two walls. JAMB Pos'rs, such as are sometimes introduced on the side of a door, in order to fix thejamb linings. They are particularly used when the partition is of wood. JAMB STONES, in stone walls, such as are em- ployed in building the sides of an aperture, in doing which, every alternate stone ought to be inserted the whole thickness of the walls. JERKIN HEAD, the end of a roof that is not hipped down to the level of the opposite adjoin- ing walls; the gable being carried higher than the level of the said walls. JETTE (French) the border made around the stilts under a pier, consisting of piles and planks, stones filling up the interstices, to secure the whole foundation. JlB—l)()OR, a door so constructed as to have the same continuity of surface with that of the par- tition in which it stands. The use of a jib—door is to preserve the symmetry of an apartment, where Only one door is wanted, nearer to one end of'the partition than the other. Instead of a jib-door, a real door and a false one may be used. “7 here jib-doors are used, it is obvious that they must be concealed as much as possible. JOGGLE, the joint of two bodies, so constructed as to prevent them from sliding past each other, by the application of a force in a direction per- pendicular to the two pressures, by which they are held together. The struts of a roof are jog- gled into the truss-posts and into the rafters; J. JOI \ when confined by mortise and tenon, the pressure which keeps them together is that of the rafter and the re-action of the truss-post. The same is also applied to the step and platform stones of a geometrical stair. JOGGLE PIECE, the truss-post in a roof, when formed to receivea brace or strut with a joggle. JOINER, the workman who joins wood for the finishing of buildings. JOlNERY,_in civil architecture, the art of framing or joining wood together, for internal and ex- ternal finishings of houses; thus the coverings and linings of rough walls, or the coverings of rough timbers, and the construction of doors, windows, and stairs, arejoiners’ work. Joinery requires workmanship much more ac- curate and nice than carpentry, which consists only of rough timbers, used in supporting the various parts of an edifice: joinery is therefore used by way of decoration only, and being always near to the eye, and consequently liable to in- spection, requires that the joints should be fit;ed together with the utmost care, and the surfaces made smooth. . The wood used is called stzfi and is previously formed by the pit-saw into rectangular prisms, which are denominated battens, boards, or planks, according to their breadths. Battens run from two to seven inches wide; boards from seven to nine inches wide; and planks from nine inches to any greater breadth that can be cut out of a piece of wood. The operations of joinery consist of forming sur- faces of various kinds, also of grooving, rebating, and moulding, and of mortising and tenoning; and lastly, of joining two or several pieces to- gether, so as to form a frame or solid mass. Surfaces, in joinery, are either plane 'or curved, but most frequently plane. All kinds of surfaces are first formed in the rough, and finally brought to a finish by means of appropriate tools. Grooving consists in taking away a part ofa rect- angular section from a piece of wood, so as to form a channel of equal breadth throughout, with three surfaces, one parallel, and the other two per- pendicular, to that'of the wood; whiqh‘channel JOI 150 JOI W is called ”a groove; and thus the piece that would fill the cavity, or which would restore-it to its original form, is a square prism. Rebating consists in taking away a part from a piece of wood of a rectangular section, so as to leave only two sides, one perpendicular, and the other parallel, to the surface ‘of the wood; the cavity thus formed is called a rebate. From this definition it is manifest, that a rebate can only be formed by reducing the piece of wood to be re— bated at the angle itself, and may therefore be considered as a semi-groove; and thus the piece which would restore the whole to its original form is a square prism, as in grooving. A mortiSe_is a cavity recessed within the surface of a piece of wood, with four sides perpendicular to the surface, and to each other. The act of , making a mortise is called mortisz'ng. A tenOn is a projection formed on the end of a piece of wood with four plane sides, at right angles to each other, and to a plane, from which it projects, called the shoulder of the tenon. In the following, all pieces of wood whatever are supposed to be rectangular prisms, and the length in the direction of the fibres; two of the sides of every mortise perpendicular, and the other two parallel, to the fibres; and the four sides of every tenon in the direction of the fibres, unless otherwise described: likewise, if two of the sur- faces of a piece of wood be of greater breadth than the other two, the latter are called the edges, and the former the sides; while each line of concourse, formed by two adjacent sides, is called an arm's. Moulding consists in forming the surface of a piece by plane or curve surfaces, or by both, in such a manner, that all parallel sections may be similar and equal figures. The first thing to be donein joinery is to select the stuff or boards, which ought to be well seasoned for every purpose in joinery, and then line it out; and if the stuff he not already at the size, as is most frequently the case, it must be ripped out with the ripping saw, or cross cut with the hand- saw, or both, as may he wanted. The next thing is the planing of the stuff, first upon a side, then the edge squared, and afterwards gaged to a breadth and thickness, should either or both be found necessary. Two or more pieces of stuff may be fastened to- gether, in various ways, by pins of wood, or by nails; but in work prepared by the joiner for building, the pieces are more frequently joined to- gether by making their surfaces planes, and plaster- ing them over with a hot tenacious liquid, called glue, then rubbing the surfaces until the glue has been almost rubbed out, and one piece brought to its situation with respect to the other. The best work is alwaysjoined by this method. When boards are required of a greater breadth than common, several primitive boards must be fastened together edge to edge, either by nailing them to pieces extending across the breadth, or by gluing them edge to edge, or byjoining pieces transversely together with small boards, tongued into grooves excavated in the edges. Two pieces of stuff are joined together at right or oblique angles by a mortise and tenon adapted to each other, and fastened together with glue. When a frame, consisting of several pieces, is required, the mortises and tenons are fitted to- gether, and the joints glued all at one time, then entered to their places, and forced together by means of an instrument called a cramp. A frame of wood in order to contain a panel, and surround it completely, cannot be made of less than three pieces, unless one or more of them be curved, because less than three straight lines can- not contain a space. The operation of forming a given surface, by taking away the superfluous wood, is called plan~ ing. and the tools themselves planes. The first tools used by joiners are bench planes, which generally consist of ajack plane, for taking away the rough of the saw and the superfluous wood, only leaving so much as is sufficient to smooth the surface; the trying plane, to smooth or reduce the ridges left by the jack plane, and to straighten or regulate the surface, whether it be plane or convex ; the long plane, when the surface is required to be very straight; and the smoothing- plane, in smoothing, as its name implies, and giving the last finish to the work. Besides the bench planes, there are others for forming any kind of prismatic surfaces whatever, as rebating planes, grooving planes, and moulding planes: but for a more particular description of these and the bench planes, we shall refer to the article PLANE. The tools employed in boring cylindric holes are a stock with bits, of various descriptions and sizes, gimlets, and bradaa‘ls of several diameters. The tools used in paring the wood obliquely, or JOI 151 w— — * across the fibres, and for cutting rectangular pris- matic cavities, are in general denominated chisels: those for paring the wood across the fibres are called firmers, or paring chisels, and those for cutting mortises are called mortise chisels. The sides of all chisels, in a direction of their length, are straight, and the side of a chisel which contains the cutting edge at the end is of steel. The best paring chisels are made entirely of cast steel. Chisels for par- ing Concave surfaces are denominated gauges. Dividing wood, by cutting away a very thin por- tion of the material of equal thickness throughout, to any required extent, by means of a thin plate of steel with a toothed edge, is called sawing, and the instruments themselves are called saws, which are of several kinds; as the ripping saw, for di- viding boards into separate pieces in the direction of the fibres; the hand saw, for cross cutting, or for sawing thin pieces in a direction of the grain ; the panel saw, either for cross cutting, or cutting very thin boards longitudinally; the tenon saw, with a thick iron back, for making an incision of any depth below the surface of the wood, and for cutting pieces entirely through, not exceeding the breadth of that part of the plate without the iron back; likewise a sash saw, and a dovetail saw, used much in the same way as the tenon saw. From the thinness of the plates of these three last saws, it is necessary to stiffen them by a strong piece of metal, called the back, which is grooved to receive the upper edge of the plate that is fixed to the back, and which is thereby secured and prevented from crippling. When it is required to divide boards into curved pieces, a very narrow saw without a back, called a compass saw, is used ; and in cutting a very small hole, a saw of a similar description, called a key-hole saw, is em- ployed. All these saws have their plates longer and thinner, and their teeth finer, as they succeed each other in the order here mentioned, excepting the two last, which have thicker plates and coarser teeth than either the sash or dovetail saws. The external and internal angles of the teeth of all saws are generally formed at an angle of 60 de- grees, and the front edge teeth slope backward in a small degree, but incline or recline from the straight line drawn from the interior angle per- pendicular to the edge in the plane of the plate, as the saw may be employed in ripping or in cross cutting, or cutting perpendicular to the fibres. The teeth of all saws, except turning and key- J01. hole saws, are alternately bent on contrary sides of the plate, so that all the teeth on the same side are alike bent throughout the length of the plate for the purpose of clearing the sides of the cut made by it in the wood. Of all cutting tools whatever, the saw is the most useful to the joiner, as the timber or wood which he employs can be divided into slips or bars of any size, with no more waste of stufi' than a slice, the breadth of which is equal to the depth of the piece to be cut through, and the thickness-equal to the distance of the teeth between their ex- treme points on the alternate sides of the saw, measured on a line perpendicular to them : where- as, without the use of the saw, cylindrical trees could only be reduced to the intended size by means of the axe; in the use of which there would not only be an immense consumption of stuff, but also much greater labour would be re~ quired to reduce it to a straight surface. Joiners use a small axe, called a hatchet, for cut- ting olf the superfluous wood from the edge of a board, when the waste is not of sufficient conse- quence to be sawed. The above are what are commonly denominated edge tools, but there are others required to regulate the forms. ,All angles whatever are formed by other reversed angles of the same number of de- grees; as an exterior angle by an interior one, and the contrary. The instrument for trying right angles is called a square, and those for try- ing oblique angles are called bevels. The two sides which form the edge of a square are always stationary, but those of bevels are generally move- able, one leg upon the other, round a joint. In some cases, where a great number of pieces are required to be wrought to the same angle, a sta- tionary bevel, called ajoz'nt-lcoolc, is used. When it is required to reduce a piece of stuff to a parallel breadth, an instrument called a gauge is used, which consists generally of a square piece, with a mortise in it, through which runs a sliding bar, at right angles, called the stem, furnished with a sharp point, or tooth, at one extremity, pro- jecting a little from the surface, so that when the side of the gauge, next to the end which has the point, is applied upon the vertical surface of the wood, with the toothed side of the stem upon the horizontal surface, and pushed and drawn alternately by the workman from and towards him, the. tooth will make an incision from the surface into the wood, at a parallel distance from the upper edge ‘of the vertical side on the right hand. This line marks precisely the intersection of the plane which divides the superfluous stuff from that which is to be used. 1 When a mortise is required to be cut in a piece of wood, a gauge with two teeth is used. The ‘ Construction of this instrument is the same as the ‘common gauge, except that the stem has alongi- ‘tudinal slider With a, tooth projecting from its end, :so that both teeth may be brought nearer, or re- moved farther from each other, at pleasure; and “also to any distance, from the face of the head or ".guide, .within the reach of the stern. if when a piece of wood {has been planed, it is required to be sawed across the fibres; to keep it stationary during the operation, and to prevent the sides or edges from being bruised, a flat piece of wood with two projecting knobs on op- posite sides, one at each end, called a side hook, is used. The vertical side of the interior angle of one of the knobs is placed close to the ver- tical‘side, and the under side upon the top of the bench; then the wood is pressed against the knob . whiCh projects from the upper surface while it is cutting. But the use of two side hooks 15 better, as they keep the piece 1n01e steady. When it is required to cut a piece of wood to a mitre with one side, that is, to half a right angle, .joiners use a trunk of wood with three sides, like a box without ends or a top, the sides and bottom being paiallel pieces, and the sides of equal heights; through each of the Opposite sides is cut a ke1f,1n a plane pe1pend1cula1 to the bottom, at oblique angles of 450 and 13 0with the planes of the sides; and another kerf is made with its plane at right angles to the two former. This trunk is called a mztre box. When the wood is to be cut, the mitre-box is fixed steady against two side hooks, and the piece, which must always be less than the interior breadth of the mitre-box, is laid in it and pressed against its fartherinterior angle, with the side downwards, to which the saw-kerf is intended to be perpendicular, and in this position it is to be cut. The two kerfs in the sides of the mitre-box are requisite, in order to form the acute angle on the right or left-hand side of the piece, as may be required. 'When a, piece of wood is required to be made straight in one direction, joiners use a slip of wood straightened on one edge, and thence called (:1 Ki . parallel planes. JOI: a straight edge. Its use isobvious; as by its ap- plication it will be seen whether there is a coin- cidence between the straightedge and the surface. When it is required to know whether the surface of a piece of wood is in the same plane, joiners use two slips, each straightened on one edge, with the opposite edge parallel, and both pieces of the same breadth between the parallel edges: each piece has therefore two straight edges, or two Therefore, if it were required to know whether aboard is twisted, or its surface plane, the workman lays one of the slips across the one’end, and the other across the other end of the board, with one of the straight edges of each upon the surface; then he looks in the longi- tudinal direction ofthe board, over the upper edges of the two slips, until his eye and the said two edges are 'in one plane; or, otherwise, the intersection of the plane, passing through the eye and the upper edge of~the nearest. slip; will intersect the upper edge of the farther slip. If it happen as in the former case, the ends of the wood under the slips are in the same plane; but should it happen as in the latter, they are not. In this last case, the surface is said to wind,- and when the surface is so re- duced as for every two lines to be in one plane, it is said to be out of winding, which implies its being an entire plane; from the use of these slips they are denominated winding-sticks. Before we proceed to the method of bringing a rough surface to a plane, it is necessary to shew how to make a straight edge. And here the joiner must not lose sight of the properties of a straight-line, viz. that which will always coincide with another straight line, however they may be applied together. The operation of making the edge of a board straight is called by joineis, shooting, and the edge so made is said to be shot. Straight edges may be formed by planing the edges of two boards and applying them together, with their superficies or faces in the same plane; if there be no cavity in thejoint, the edges will be straight; if not, the faces must be applied to each other, the edges brought together, and planed and tried as before, until they coincide. Another mode is by having aplane surface given: plane the edges of a board as straight as the eye will adtnit of, apply the face of it to that of the plane, and draw a line by the edge "J OI I w of the board; turn the board over with the other side upon the plane, bring the planed edge to the line drawn before, and the extremities of the edge to their former places, and draw another line; then if all the parts of this line coincide with the former, the edge is already straight, but if not, repeat the operation as often as may be necessary. Another mode is to plane the edge of a board as straight as the eye will admit of; then plane the edge of another board until it coincide with the former; plane the edge of a third board in like manner, to coincide with the edge of the first, and apply their edges together; then if they coincide, the operation is at an end, but if not, repeat it till they do. By any of these methods, the superficies of the boards to be shot, are supposed to be parallel planes, not very distant from each other; for if the faces be not parallel, or if the thickness be considerable, the operation will be more liable to error. To reduce tire rough sulfate (fa body to a plane.— This will not be very difficult, when it is known that a plane will every where coincide with a _ straight line. The most practical methods are the following: Provide two winding-sticks, and apply them as before directed, making the ends out of winding if they are not found to be so; then if all the parts of the surface are straight on which the edges of the winding-sticks were placed, it is evident that the whole surface must be plane. If the surface is hollow between the said lines, one of the ends, or both, must be planed lower, until the surface acquires a small convexity in the length, and then, if straightened between the straight lines at the ends, it will be a perfect plane. . Another mode of forming a plane, supposing the surface to be of a quadrilateral form: Apply a ruler along the diagonals, then if they are straight, they are in a plane; but if they are both hollow, .or both round, the surface to be reduced is either concave or convex, and must be straightened in these directions accordingly. Lastly, if by trying across the diagonals with the straight edge, it be found that the one is hollow and the other round, the surface of the board winds. In this case bring down the protuberant part of the convex diagonal, so as to be straight VOL. 11. "JOI W1 with the two extremities; then straighten the concave diagonal, by planing either of the two ends, or both of them, according as the thick- ness of the board may require. Both diagonals being now straight, traverse the wood, that is, plane it across the fibres, until all the protube- rant parts between the diagonals are removed; then smooth it by working in the direction of the fibres. ' Toljoin any number of planks together, so as to form a board of a determinate breadth, the fibres ofeac/z running longitudinal to those ofany other.— Shoot the two edges that are to be joined; turn the sides of the boards towards each other, so that the edges that are shot may be both upper- most; spread these edges over with strong glue of a proper consistence, made very hot;_one of the boards being fixed, turn the other upon it, so that the two edges may coincide, and that the faces may be both in the same plane; rub the upper one to and fro in the direction of the fibres till the glue is almost out of the joint; let these dry for a few hours: then proceed to make another joint; continue to join as many boards or planks in the same manner, till the whole in. i tended breadth be made out. If the boards, or planks of which the board is to be composer], be very long, the edges that are to be united will require to be warmed before a fire; and, for rub- hing and keeping the joints fair to each other, three men will be found necessary, one at each extremity, and one at the middle. Boards, glued together with this kind of cement, will stand as long as the substance of the deals or planks com— posing them, if not exposed to rain or intense heat, provided the wood has been well seasoned beforehand, and the grain be free and straight, and interrupted wi;h few or no knots. When a board which is to be exposed to the weather is to be made of several pieces, the cement to be used for uniting them should not be of skin glue, but of white-lead ground up with linseed-oil, so thin that the colour may be sensibly changed into a whitish cast: this kind of glue will require a much greater time to dry than skin glue. Boards to be exposed to the weather, when their thick- ness will admit, are frequently tongued together; that is, the edges of both boards are grooved to an equal distance from the faces, and to an equal depth; and a slip of wood is made to fit the cavity made in both: this slip should be made to'fill the: x JOI 154 m zygrooves, but not so tight as to prevent thejoint from being rubbed with proper cement. To glue any two boards together forming a given angle.—-This may be accomplished, either by shooting the edge of one board to the whole of the given angle, keeping the face of the other straight; and then, by applying the two surfaces together, and rubbing as before, they will form the angle required: or, if the two edges, being shot to half the given angle, be applied together, and rubbed and set as before, their faces will form the angle required. In both these methods, when only one side of the board is to be exposed to sight, which is most commonly the case, pieces of wood, called blocks, are fitted to the inside of the angle, and the sides glued across thejoint or legs Of the angle, being previously planed for that purpose. Tofvrm wooden architraves for apertures, by gluing - longitudinal pieces together.——Architraves maybe formed of solid pieces; but as this is attended with a waste of stuff and time, the most eligible method is to glue the parts longitudinally to- gether, as best adapted to the nature of the mouldings. Architraves of the Grecian form, for doors and windows, generally consist of one or two faces in parallel planes, one of which recedes only in a small degree from the other, while the outer edge is terminated with one or several mouldings, which have a very prominent projec- tion. In this case, make a board of sufficient thickness, and in breadth equal to the breadth of the architrave: prepare a slip of wood of a sufficient thickness and breadth, for the mould- ings on the outer termination of the architrave, and glue it upon the face, close to the edge of the board, with the outer edge flush therewith. In this operation, two men, at least, will be re- quired to rub the slip to ajoint with the board; and as it often happens that the side of the slip, which is to comply with the surface of the board, is considerably bent, it must be nailed down to the board; previously to this, small square pieces of wood, called buttons, must be bored with holes, one in each, and a nail put through the hole to the head; then the slip is also to be bored with a bradawl, and the nails, with the pieces thus described, are entered and driven home as far as the buttons will permit. These buttons may be about three-quarters of an inch thick, and the other two dimensions each equal to, or something JOI more than the breadth of the slip. Sometimes the slip is grooved; and the edge of the board tongued, glued, and inserted into the groove, instead of the above method. Or, the two faces may be made of different boards, tongued toge- ther at their joining, and the whole afterwards stuck into mouldings. T 0 form the surface 9“ a cylinder with wood, whose fibres are in planes perpendicular to the axis (f the cylinder, such as may be used in a circular dado, or the sofi‘its cf windows. METHOD l.——When the dimension of the cylin- dric surface, parallel to the axis, is not broader than a plank or board. This may be done by bending and gluing several veneers together; the first upon a mould, or upon brackets, with their edges in the surface of the proposed cylinder, parallel to its axis. This may be accomplished by means Of two sets of brackets, fixed upon a board, with a hollow cylindric space between them, of sufficient thick- ness for taking in the veneers, with double wedcres for confining them. If this operation be cacre- fully done, and the glue properly dried, the wedges may be slackened, and the work will stand well; but it must be observed, that, as the wood has a natural tendency to unbend itself, the curved surface, upon which it is glued, should be somewhat quicker than that intended to be made. Some workmen form a hollow cradle, and bendin the veneers into it, confine their ends with wedo-es, which compress them together; and by a vcery small degree of rubbing, with a hammer made for the purpose, the glue will be forced out of thejoint. . METHOD Il.—-Form a cradle, or templet, to the intended surface, and lay a veneer upon it; then glue blocks Of wood upon its back, closely fitted to its surface, and the otherjoints to each other, the fibres of the blocks corresponding to those of the veneer. METHOD Ill.———Make a cradle, and place the ve- neers upon it, confining one end of them; spread the glue between the veneers with a brush, and fix a bridle across, confining its ends either by nails or by screws; open the veneers again, put glue a second time between each two, and fix another bridle across them: and in this manner proceed to the other extremity. METHOD IV.——Ruu a number of equidistant 1.: J01 155 JO! M ‘ 1 grooves across the back of the board, at right angles to its edges, leaving only a small thickness towards the face; bend this round a cradle, with the grooves outwardly, and fill the grooves with slips of wood, which, after the glue is quite dry, are to be planed down to the surface of the cylin- dric board, which may be stiffened by glueing canvass across the back. Instead of using a grooving plane, workmen fre- quently make kerfs with the saw; but this mode is not—so strong when finished, as the uncertainty of the depths of the kerfs, and the difficulty of inserting the slips, will occasion a very unequal curvature. To bend a board, so as to form the frustum of a cone, or any segmental portion of the frustum of a cone, as the soflit of the head of an aperture.— Find the arch form of the covering, as shewn under the article ENVELOPE; cut out a board to this form, and run a number of equidistant grooves across it, tending to the centre: this being fixed to a templet made to the surface of a cone, finish it in the manner shewn in the last method for a cylinder. T 0 bend boards so as to form asphericsmface.—- Make a mould to the covering of a given portion of the sphere in plano, as shewn under the article DOME; complete the number of staves by this mould; make a templet or mould to a great circle of the sphere; groove each of the staves across, at right angles to a line passing through the middle, and bend it round the templet; put slips in the grooves; shoot the edges of the staves, so as to be in planes tending to the centre of the sphere; and these staves, being glued together, will form a spheric surface. To glue up the shqft of a column, supposing it to be the frastum of a cone—Prepare eight or more staves, as the circumference may require, in such ' a manner, that if the column be fluted, the joints may fall in the middle of the fillets, which disposi- tion will be stronger than if they were to fall in the middle of the flutes. Now suppose eight pieces to be sufficient to con- stitute the shaft of a column: describe acircle to the diameter of each end; about each circle circumscribe an octagon; from the concourse of each angle drawa line to the centre; then draw an interior concentric octagon, with its sides pa- rallel to those of the circumscribing one, the distance between any two parallel sides, on the D “I‘M: same side of the centre, being equal to the thick- ness of stuff intended: and thus the sections of the staves will be formed at each end, and conse- quently the bevels will be obtained throughout the whole length; any two pieces when joined together having the same angle, though the staves are narrower at one end than at the other. In order to join the column, glue two pieces to- gether, and when quite dry, glue in blockings to strengthen them; join a third piece to the former two, and secure it also by blockings. In this manner proceed to the last piece but one. In fixing the last, the blockings must be glued to the two adjacent staves, and their surfaces, on which the last stave is intended to rest, must be all in the same plane, that its back may rest firmly upon them. In closing up the remaining space, the part of the column that is glued toge- ther, should be kept from spreading, by fixing it in a kind of cramp, or cradle, while driving the remaining stave to close the joints. Instead of this mode, some glue up the column in halves, and then glue them together. When it is necessary to have an iron core, to support the roof or floor, the column must be glued up in halves; in this case the two halves are to be dowelled together, and the joints filled with white-lead. Instead of a cramp, a rope is used, twisted by means of a lever. In the act of bring- ing the two halves together, the percussive force of the mallet must be applied upon the middle of the surface of one half, while an assistant holds something steady against the middle of the other, that the opposition may be equal; and by this means, the surfaces will be brought into con- tact, and form the joint as desired. In this operation, pieces of wood ought to be inserted between the rope and the column. To glue up the Ionic and Corinthian capitalsfor carving—The abacus must be glued in parts, so that theirjoints may be in vertical planes. The leaves and caulicoles of the Corinthian capital may be first made of rectangular blocks, and fixed to the vase. To make a cornice round a cylindric body of the least quantity of wood, when the body is greater than a half cylinder, and when the members will nearly touch a right line applied transversely.“ Draw a section of the cylinder through its axis, and let the section of the cornice be represented upon the cylindric section. Draw a transverse x Q M JOI 1 _.line, touching the two extreme members of the .-cornice; and parallel to it draw another line Within, at such' a distance from the former, as may be necessary for thickness of stuff; produce - the latter line, till it meet the line representing the axis of the cylinder, and the junction will either be above or below, according as the cor— nice is applied to the convex or concave sides of ”the cylinder. This meeting is the centre of two _ concentric circles, whose radii are the distances between the nearest and farthest extremes of the section of the cornice. This is evidently an ap- plication. of the method of finding the covering of a cone. When mouldings are got out in this manner, viz. by a piece which does not occupy the space, when set to the place represented by -_ the height and breadth, they are said to be . sprung. When a cornice is to have much projection, the corona, or middle part, is got out of a solid piece, and the parts above and below, or one of them, as may be found necessary, only set to the spring, and supported by brackets. - Another method is, to bend veneers round the cylindric surface or surfaces; then work them to their form with moulding planes. Raking mouldings depend principally upon the nature of a solid angle, properly called a trihedral. In a trihedral angle, with two of its planes at ~ right angles to the third, let these two former make an obtuse angle; then suppose a moulding placed in the concourse of the two planes which form the obtuse angle of the solid, and another in the concourse of the two planes which form one of its right angles; and supposing the sec— tion of the moulding which stands in the line of . concourse of the obtuse angle to be given, it is required to find the section of the other, so as to mitre in a plane bisecting the remaining right angle of the solid. The trihedral will thus con- sist of three plane angles, two of which are right angles, and the other obtuse. Make an angle equal to that formed by the sides of the obtuse-angled plane of the solid; let one of the legs be called the mitre line, and the other the raking line; draw the position of the mould- ing at the point of concourse in respect of the mitre line without the angle; take any number of points in the curve of the moulding; through these points draw lines parallel to the mitre line; also draw lines through the same points parallel JO! to the raking line: draw a line perpendicular to the mitre line, cutting the other parallels at right angles; take the perpendicular, thus cut into several portions by the parallels of the mitre, and transfer it upon any part of the raking line, marking all the points of section: through the points of section, draw lines at right angles‘ to the raking line, to cut its respective parallels; through the points of section of the parallels and perpendiculars of the raking line, draw a curve, which will he the section of the moulding. The raking mouldings in pedirnents depend upon this. The raking line is the top of the tympa— num; the mitre line, the angle of the building; and the line of concourse of the obtuse angle of the solid, the level returning cornice, at right angles to the tympanum, or plane of the front of the building. _ The same is also applicable to a hollow trihedral, such as the inside of a room, of which the two vertical planes are at right angles to each other, the legs of the one plane forming a right angle, and those of the other an obtuse angle; and con- sequently the ceiling, which is the third side ofthe trihedral, will be inclined to the horizon, like the exterior side of a pediment, or triangular roof‘, with this difference, that the surface of the former is opposed to the floor, and the latter to the sky. Open pediments are not now in use, otherwise it might be shewn how the return mouldings were to be formed: if, however, the above general description is well understood, the reader cannot be at a loss to apply the principle to finding the section of such return moulding in an open pediment also. This, however, will be noticed under the article MOULDING. ' In a trihedral solid, with two of its planes at right angles to the third, as in the preceding case, let the two planes make an acute angle instead of an ob- tuse one; then the other two angles of the solid will be both right-angled, as also each of the planes forming the acute angle: now supposing one moulding to be placed in the line of concourse of the acute angle of the solid, and another in the line of concourse of one of the right angles; then if these mitre together upon a plane, passing along the line of concourse of the planes which form the remaining right angle of the solid, they will shew the principle of the formation of the angle-bars of a bow-window, consisting of three or more vertical planes. As the angle—bar J-OI "-1 57 J OI &_____~_ __-_-.MW stands in the concourse of two of the ver- tical planes, suppose those two planes to be cut by a third plane at right angles to their line of concourse, and the solid thus formed again divided in halves by a plane passing along the concourse of the two vertical planes, bisecting the angle-bar, or the angle of their inclination, two equal trihedrals will be formed, each having one acute angle and two right angles: and the mouldings fo1med on the two legs of the front plane will be those required to mitre together. One of these mouldings will be half of theo angle- bar, and the other half of the ho1izontal bar. The section of the horizontal bar being given, to fnd that of the angle-bar. ——Lay down the ho1i- zontal side of the trihedral, viz. that side which is contained by the acute angle; then calling one of the legs the mitre line, and the other the sash Zine; draw half the section of the horizontal bar perpendicular to the sash line, with the surface of the moulding opposed to the mitre line; take any number of points in the curve of the mould- ing, and draw lines through them perpendicular to the sash line, cutting it in as many points; take the length of the intercepted line between the extreme points, and transfer it upon a line perpendicular to the mitre line, with the several points of division from the mitre line towards the section of the horizontal bar; through the several points of division in the said perpendi- cular, draw lines parallel to the mitre-line; again, through the several points of division in the curve of the section of the horizontal bar, draw lines parallel to the sash-line, cutting the respec- tive lines parallel to the mitre-line, and the points of intersection will give the section of half the angle-bar, by drawing a curve through them. The counter part being drawn on the other side of the mitre-line, the whole section of the angle- bar will be complete. The reader will perceive that this principle is similar to the former, both depending upon the trihedral, or solid angle, consisting of three plane angles. The mitre passes through one of the lines of concourse, and a moulding along each of the two others. In both cases, that which is perpendicular to the other two is laid down. A circular sash-frame in a circular wall, is a solid of double curvature; its formation, therefore, depends upon the section of a cylinder, and the covering of, any portion ,of the cylinder. The gluing up of the arecular bars depends upon the developement of any portion of a cylind'ric surface. The radial bars are portions of different el- lipses, which intersect each other in one common line of concourse, or conjugate axis, being the sections of a cylinder at different inclinations, all passing through a line at right angles to the ax1s. Two of the sides of these bars are plane surfaces, and the other two curved surfaces are cylindrical; consequently they terminate the plane surfaces in curved lines, which are portions of elliptical figures. The head of the sash is generally got out of the solid in halves, or in four pieces, according to the size of the window; and when put together, ought to be so formed, that one concave surface may saddle upon a cylinder of a radius equal to that of the inner circle, which forms the plan, while the outer surface is every where equidistant from the cylindric surface; and that the other concave surface may coincide with the convex surface of another cylinder, whose radius is equal to that required to describe the interior curve of the Sash- head, while the outer surface is every where equally distant from the cylindric surface. An enlarged or diminished cornice has its parts, in height and in projection, of the same propor- tions as those of another, already given. Here it is only necessary to suppose the height 01 pro— jection given; thus, take one of them as the height to be given, and find a fourth p1oportional to the following thiee measmes, placed 1n order, viz. the height t,of the given cornice, the height of the required cornice, and the projection of the given cornice; then divide the height of the required cornice in the same proportion as the height of the given one, and the projection of theD one required, in the same propmtion as the piojection of that given The drawing of theb flutes ofadiminished pilaster, with curved sides, depends also upon the divi- sion of a line in the same proportion as one already divided: thus, a line equal to, or longer or shorter than the breadth of the pilaster, may contain the aggregate breadths of the number of flutes and fillets, in just proportion; then drawing several equidistant lines parallel to the base on the surface of the pilaster to be fluted, JOI 158 W 1 divide each of these equidistant lines in the same proportion; then a curve being drawn through each set of corresponding points will be the ter- minations of the flutes and fillets. For this pur- _ pose, an equilateral triangle, with one of its sides divided into the number of flutes and fillets, is sometimes used; for if lines be drawn to the point of concourse of the other two sides, any line parallel to the base will be divided in the same proportion as the base, which must be equal to, or greater than the breadth of the pilaster at the bottom. The same may also be conveniently done in the following manner: divide a straight line, equal to, or shorter, than the breadth of the pilaster at top; through the points of division draw lines parallel to each other, making any angle with the divided line: then if this series of parallels bc intersected by a line drawn in any _ direction, such line will be divided in the same proportion as the given line. Suppose, therefore, the parallels to be at right angles to the given line: to divide any line on the surface of the pilaster, take the extension of the line, and apply one end of it from any point in one of the ex- treme parallel lines as a centre, and describe an are cutting the most remote of the parallel lines : then a line drawn from the centre to the intersec- tion of the arc and the remote parallel, will be divided in the same proportion, equal to the breadth of the pilaster at the place required ; then transfer the line so divided, upon the line on the surface of the pilaster. In like manner, may every other line on the surface of the pilaster be divided, and the curve drawn as before. The method of diminishing and giving a graceful swell to the shaft of a column, depends upon the parabolic or sinical curve; both of which are easily described. The concoid of Nicomedes is also some- times employed for this purpose ; but the instru- ment required to describe it is very cumbersome, and the curve produced is not of abetter form than that of the parabola, or figure of the sines. ijoim'ng boards—A simple board, in its original state from the saw, is in one piece. A compound board is formed of several boards. Boards may bejoined together at a given angle, in various ways; by nails or pins, or by mortise and tenon, or by indenting them together; the latter mode is called dovetailz'ng, from the sections of the projecting parts, and those of the hollows, being formed to that of a dovetail. JOI Dovetailing is of three kinds, viz. common, lap, and mitre: common dovetailing shews the form of the pins or projecting parts, as well as of the excavations made to receive them. Lap dove- tailing conceals the dovetails, but shews the thick- ness of the lap in the return side, which appears like the edge of a thin board. Mitre dovetailing conceals the dovetails, and shews only a mitre on the edges of the planes at their surface of concourse; that is, the edges in the same plane, the seam or joint being in the concourse of the two faces making the given angle with each other. Dovetailing is used in fixing very wide boards together, where the seam or line ofjunetion is in the concourse of the two faces, and the fibres of the wood of each board are perpendicular to a plane passing through such line. Concealed dovetailing is particularly useful where the faces of the boards are intended to form a saliant angle; but where the faces form a re-en~ trant angle, common dovetailing will best answer the purpose; as it is not only stronger and cheaper, but is entirely concealed, the dovetails only shew- ing upon the saliant angle. Indeed, where the faces form a re-entrant angle, and each board is to be fastened to a wall, the two boards may be fixed together by means of a groove in the one, and a tongue in the other; and if Well nailed previous to their being brought to their situation, so that the nails may not be seen in the faces, this will answer as good a pur« pose as dovetailing. When several simple boards are glued together, to form a broad face, they are sometimes strength— ened by fixing another simple board across the end, or across each end, as may be required, by means of a groove and tongue, or by mortise and tenon, and reducing the face of the whole com- pound board to a plane; the transverse pieces are called clamps, and the compound board is said to be clamped. In simple and compound boards, where the faces are required to form an angle, and where the fibres of the wood are required to be parallel to the line of concourse of the two planes, or faces, which form the angle, the two boards are fastened together by tonguing the edge of one of them the whole of its length, and running a groove in the face of the other next to the edge to receive it, so that when the two boards are joined toge- ther, the re-entrant angle shews only a line at the 9 .E G H N E RY. FLA TEI] ’ my. 4. Fig. .3 [kg/.2. i » 1.4. M _ W /W ‘9‘ Fig.1}. my. 7. W /// . // ¢Z/ FM. 21. F131. 20. E 3; “5‘ , . 3.4 . . . 2 ‘ 23.. , 12‘ ' b 311M #2 view. . 7 1;, 'db 6W- 2mm ‘I/ I ( H London Bibliw/zal by 1’. A’L’Mnlu‘on 1- J. Bar/{eldWwdnm‘ .)71Yet,1813. ”‘51le J ‘ fl JOI 159 JOI- concourse of the two surfaces, but the saliant angle shews a line parallel to the line of con- course, which is the intersection of the inner surface of one board produced to meet the ex- ternal surface of the other; so that to form the saliant angle, the thickness of one board must be added to the breadth of the other, and thus the face of the one is lapped upon the edge of the other the whole of its thickness. The most common way of joining boards with the fibres thus disposed, in respect of the line of ‘ concourse of their inclination, is by lapping the face of one upon the edge of the other, and fas- tening them together with nails, driven through the lap into the substance of the other. Besides what has now been treated of, as princi- ples on which the practice of joinery depends, many particulars relating to the art, the definitions of the terms, and several articles which require long description, and a reference to plates, will be found under the following alphabetical order, viz. Bloc-kings, Boarded Floors, Bolt, Boxing of a VVindow, Brackets for Shelves, Brackets for Stairs, Brads, in Joinery, Buthinges, Butt- Joint, in Hand-Railing, Cap, in Joinery, Cased Sash-Frames, Casements, Casting, in Joinery, Cen- tre of a Door, Chamfering, Cheeks of a Mortise, Circular, Circular Work, Clamp, Clamping, Cloak- Pins and Rail, Communicating Doors, Curtail Step, Cut Brackets, Cut Standards, Cylindrical ‘Vork, Deal, Description, Diminished Bar, Dimiu nishing Rule, Dog-Legged-Stairs, Doors, Framed, Double-hung Sashes, Dovetail,Dovetailing, Draw- bore, Draw-bore-Pins, Dressings, Elbows of a Window, Face-Mould, Falling Mould, Feather- edged Boards, Fence, Fillet, Flaps, Floor, Fold- ing Doors, Folding Joint, Folds, Fox-tail-VVedg- ing, Frame, in Joinery, Franking, French Case- ments, Frieze Panel, Frieze Rail, Furniture, Gage, Grounds, Hand-Rail, Hand-Railing, Hanging of Doors, Hanging Stile, Heading Joint, Hinges, Hinging, Housing, and Impages. Gluing up of a Base refers to Base, Bridge Board refers to Notch Board, Curtail Step refers to the article Stair, Dog-legged Stairs refers to Staircasing, and ' Inlaying refers to Marquetry and Veneering. Among the, foregoing articles, Boarded Floor, Floor, Boxing of a Window, and Description, are of considerable length; Hand-Railing and Hinging are complete articles, accompanied with plates. ' Any thing omitted in the foregoing catalogue will be explained in the Subsequent part of this article. Mouldings—The names of mouldings in joinery according to their situation and combination, in various pieces of joiners’work. Figure ], edge, said to be rounded. Figure 2, quirked bead, or head and quirk. Figure 3, head and double quirk, or- return bead. Figure 4, double head, or double bead and quirk. Figure 5, single torus. Figure 6, double torus. Here it is to be ob served, that the distinction between torus mould- ings and beads, in joinery, is, that the outer edge of the former always terminates with a fillet, whether the torus be double or single, whereas in beads there is no fillet on the outer edge. Figures 7, 8, 9, single, double, and triple reeded mouldings; semi-cylindric mouldings are deno- minated reeds, either when they are terminated by a straight surface equally protuberant on both sides, as in these figures, or disposed longi- tudinally round the circumference of a shaft: but if only terminated on one side with a flush surface, they are then either beads or torus mouldings. Figure 10, reeds disposed round the convex sur- face of a cylinder. Figures 11, 12, 13, fluted work. When the flutes are semicircular, as in Figure 11, it is necessary that there should be some distance between them, as it would be impossible to bring their junction to an arris; but in flutes, whose sections are flat segments, they gene— rally meet each other without any intermediate straight surface between them. The reason of this is, that the light and shade of the ad- joining hollows are more contrasted, the angle of their meeting being more acute, than if a flat space were formed between them. See Figures 19. and 13. Figure 14, simple astragal, or half round bar, for sashes. Figure 15, quirked astragal bar. Figure 16, quirked Gothic bar. Figure 17, another form of a Gothic bar. Figure 18, double ogee bar. This and the preced~ ing forms are easily kept clean. Figure l9, quirked astragal and hollow. Bars of this structure have been long in use. Figure 20, double reeded bar. JOI 1'60 J OI" W1- Figure'm, .triple reeded bar. Figure 2.9, base moulding of a room, with part of the skirting. When the basemouldings are very .0. large, they ought, to be sprung, as in this diagram. A. The base mouldine. B. Part of the plintb.. In order to know of what thickness a board would be required, to get out a moulding upon the spring, the best method is to draw the mould- ing out to the full size, then draw a line parallel to the general line of the moulding, so as to -make it equally strong throughout its breadth, and also of sufficient strength for its intended purpose. Figure 23, a cornice. The part A forming the corona, is got out of a plank. B. A bracket. C. The moulding on the front spring. D. A cover board forming the upper fillet. E. A moulding, sprung below the corona. F. A bracket. Shutters to be cut must first be hung the whole length, and taken down and cut: but observe that you do not cut the joint by the range of the middle bar, but at right angles to the sides of the sash-frame; for unless this be done, the ends will not all coincide when folded together. In order to hang shutters at the first trial, set off the margin from the bead on both sides, then take half the thickness of the knuckle of the hinge, and prick it on each side from the mar- gin so drawn towards the middle of the window, at the places of the hinges, put in brads at these pricks, then putting the shutter to its place, screw it fast, and when opened it will turn to the place intended. Mouldings are mitred by means of a templet, which is a small piece of wood, moulded in a reverse form to the mouldings that are to be mitred, so that the surface of the templet may coincide with that of the surface of the mould- ing, and to a portion of the plane surface of the framing, both on the face and on the edge adjoin- ing: the ends of the templet are cut to an angle of45 degrees in a plane perpendicular to the face, the one end forming a right angle with the other. To scribe one piece qf board or surf to another.— VVhen the edge end, or side, of one piece of stuff is fitted close to the-superficies of another, it is said to be scribed to it. Thus the skirting boards of a room should be scribed ‘to the floor. In moulded framing, the mould- ing upon the rails, if not quirked, are scribed to the styles, and muntins upon rails. T o scribe the edge of a board against any uneven surface—Lay the edge of the board over its place, with the face in the position in which it is to stand; with a pair of stiff compasses opened to the widest part, keeping one leg close to the uneven surface, move or draw the compasses forward, so that~the point of the other leg may mark a line on the board, and that the two points may always be in a straight line, parallel to the straight line in which the two points were at the commence- ment of the motion: then cut away the wood between this line and the bottom edge, and they will coincide with each other. To rebate a piece of stzgfii—VVhen the rebate is to be made on the arris next to you, the stuff must be first tried-up on two sides : if the rebate be not very large, set the guide of the fence ot' the moving fillister to be within the distance of the horizontal breadth of the intended rebate; and screw the stop so that the guide may be some- thing less than the vertical depth of the rebate from the sole of the plane; set the iron so as to be sufficiently rank, and to project equally below the sole of the plane; make the left—hand point of the cutting edge flush with the left-hand side of the plane, the tooth should be a small matter withoutthe right-hand side. Proceed now to gauge the horizontal and verticaldimensions of the rebate: begin your work at the fore end of the stuff; the plane being placed before you, lay your right hand partly on the top hind end of the plane, your four fingers upon the left side, and your thumb upon the right, the middle part of the palm of the hand resting upon the round of the plane between the top and the end; lay the thumb of your left hand over the top of the fore end of the plane, bending the thumb downwards upon the right—hand side of the plane, while the upper division of the fore-finger, and the one next to it, goes obliquely on the left side of the plane, and then bends with the same obliquity to comply with the fore end of the plane; the two remaining fingers are turned inwards; push the plane forward, without moving your feet, and a shaving will be discharged equal to the breadth of the rebate; draw the plane towards you again to the place you pushed it from, and repeat the operation: proceed in this manner until you JOI 161 .101 L have gone very near the depth of the rebate, move a step backward, and proceed as before, go on by several successive steps, operating at each one as at first, until you get to the end; then you may take a shaving or two the whole length, or take down any protuberant parts. In holding the fillister, care must be taken to keep the sides vertical, and consequently the sole level: then clean out the bottom and side of the rebate with the skew-faced rebate plane, that is, plane the bottom and side smooth, until you come close to the gauge-lines: for this purpose the iron must be set very fine, and equally prominent throughout the breadth of the sole. If your rebate exceed in breadth the distance which the guide of the fence can be set from the right side of the plane, you may make a narrow rebate on the side next to you, and set the plow to the full breadth, and the stop of the plow to the depth: make agroove next to the gauge-line: then with the firmer chisel cut off the wood between the groove and the rebate level with the bottom; or should the rebate be very wide, you may make several intermediate grooves, leaving the wood between every two adjacent grooves of less breadth than the firmer chisel, so as to be easily cut out; having the rebate roughed out, you may make the bottom a little smoother with the paring chisel; then with a common rebate plane, about an inch broad in the sole, plane the side of the bottom next to the vertical side, and with the jack plane take off the irregularities of the wood left by the chisel: smooth the farther side of the bottom of the rebate with the skew rebate plane, as also the vertical side: with the trying plane smooth the remaining part next to you, until the rebate is at its full depth. If any thing remain in the internal angle, it may be cut away with a fine-set paring chisel; but this will hardly be necessary when the tools are in good order. then the breadth and depth of the rebate is not greater than the depth which the plow can be set to work, the most expeditious method of making a rebate, is by grooving it within the gauge-lines on each side of the arris, and so taking the piece out without the use of the chisel: then proceed to work the bottom and side of the groove, as before. By these means you have the several methods of rebating when the VOL. II. rebate is made on the left edge of the stufi“: but if the rebate be formed from the right-hand arris, it must be planed on two sides, or on one side and an edge, as before; place the stuff so that the arris of the two planed sides may be next to you. Set the sash-fillister to the whole breadth of the stuff that is to be, left standing, and the stop to the depth, then you may pro- ceed to rebate as before. To rebate across the grain.—Nail a straight slip across the piece to be rebated, so that the straight edge may fall upon the line which the vertical side of the rebate makes with the top of the stuff, keeping the breadth of the slip entirely to one side of the rebate; then having set the stop of the dado grooving plane to the depth of the rebate, holding the plane vertically, run a groove across the wood; repeat the same operation in one or more places in the breadth of the rebate, leaving each interstice or stand- ing-up part something less than the breadth of the firmer chisel: then with that chisel cut away these parts between every two grooves, but be careful, indoing this, that you do not tear the wood up; pare the bottom pretty smooth, or after having cut the rough away with the chisel, take a rebating plane with the iron set rather rank, and work the prominent parts down to the aforesaid grooves nearly. Lastly, with a fine-set screwed rebating plane, smooth the bottom next to the vertical side of the rebate. The other parts of the bottom may be taken com- pletely down with a fine-set smoothing plane: in this manner you may makea tenon of any breadth. Stairs—Are one of the most important things to be considered in a building, not only with regard to the situation, but as to the design and execu: tion: the convenience of the building depends on the situation, and the elegance on the design and execution of the workmanship. A staircase ought to be sufficiently lighted, and the head-way uninterrupted. The halfpaces and quarter paces ought to bejudiciously distributed. The breadth of the steps ought never \to be more than 15 inches, nor less than 10, the height not more than 7, nor less than 5 ; there are cases, however, which are exceptions to all rule. When you have the height of the story given in feet, and the height of the step in inches, you may throw the feet into inches, and divide the height of the story in inches by the height of the step; if there be no v . JOI 162‘ JOI W remainder, or if the remainder be less than the half of the divisor, the quotient will shew the number of steps: but if the remainder be greater than the half of the divisor, you must'take one step more than thenumber shewn by the quo- , tient; in the two latter cases, you must divide the height of the story by the number of steps, and the quotient will give the exact height ofa step: in the first case you have the height of the steps at once, and this is the case whatever description the stairs are of. In order that people may pass freely, the length of the step ought never to be less than 4 feet, though in town-houses, for want of room, the going of the stair is frequently re- duced to 2% feet. Stairs have several varieties of structure, which depend principally on the situation and destina- tion of the building. Geometrical stairs are those which are supported by one end being fixed in the wall, and every step in the ascent having an auxiliary support from that immediately be- low it, and the lowest step consequently, from the floor. Bracket stairs are those that have an opening or well, with strings and newels, and are sup- ported by landings and carriages, the brackets mitering to the ends of each riser, and fixed to the string board, which is moulded below like an architrave. Dog-legged stairs are those which have no open- ing or well-hole, the rail and balusters of both the progressive and returning flights fall in the same vertical planes, the steps being fixed to strings, newels, and carriages, and the ends of the steps of the inferior kind terminating only upon the side of the string, without any housing. For farther particulars, see DOG-LEGGED STAIRS. In order to eradicate a prevalent false idea which many workmen entertain, when the outer edge of the mitre-cap is turned so as to have the same section as that of the rail, they suppose this to be all that is necessary for the mitering of the above: but from a very little investigation they will easily be convinced that the sides of the mitre can never be straight surfaces or planes, but must be curved. Bracket stairs.——The same methods must be observed as to taking the dimensions, and laying down the plan and section,as in dog-legged stairs. In all stairs whatever, after having ascertained the number of steps, take a rod, the height ofthe story a from the surface of the lower floor to the surface of the upper floor: divide the rod into as many equal parts as there are to be risers, then if you have a level surface to Work upon below the stair, try each one of the risers as you go on, this will prevent any excess or defect, which even the smallest difference will occasion; for any error, however small, when multiplied, becomes of con- siderable magnitude, and even the difference of an inch in the last riser, being too high or too low, will not only have a bad effect to the eye, but will be apt to confound persons, not think- ing of any such irregularity. In order to try the steps properly by the story-rod, if you have not a level surface to work from, the better way will be to lay two rods or boards, and level their top surface to that of the floor, one of these rods being placed a little within the string, and the other near or close to the wall, so as to be at right angles to the starting line of the first riser, or, which is the same thing, parallel to the plan of the string; set otf the breadth of the steps upon these rods, and number the risers; you may set not only the breadth of the flyers, but that of the winders also. In order to try the story-rod exactly to its vertical situation, mark the same distances on the backs of the risers upon the top edges, as the distances of the plan of the string- board and the rods are from each other. The methods of describing the scroll and all ramps and knees, are geometrically described in the articles HAND—RAILING and STAIRCASING. This so far relates to every description of stairs; but to return to the particulars of this kind of stair. As the internal angle of the steps is open to the end, and not closed by the string, as in com- mon dog—legged stairs, and the neatness of work- manship is as much regarded as in geometrical stairs; the balusters must be neatly dovetailed into the ends of the steps, two in every step; the face of each front baluster must be in a straight surface with the face of the riser; and as all the balusters must be equally divided, the face of the middle baluster must in course stand in the middle of the face of the riser of the preceding step and the face of the riser of the succeeding one. The risers and treads are all glued and blocked previously together; and when put up, the under side of the step nailed or screwed into the under edge of the riser, and then roughu JOI 168 501 bracketed to the rough-strings, as in dogJegged stairs, the pitching-pieces and rough-strings being similar to those. In gluing up the steps, the best method is to make a templet, so as to fit the external angle of the steps with the nosing. Geometrical stairs—The steps of geometrical stairs ought to be constructed so as to have a very light and clean appearance when put up: for this purpose, and to aid the principle of strength, the risers and treads, when planed up, ought not to beless than 1;, inch, supposing the going of the stair, or length of the step, to be 4-feet; and for every 6 inches in length, you may add 1, part more; the risers ought to be dovetailed into the cover, and when the steps are put up, the treads are screwed up from below to the under edges of the risers; the holes for sinking the heads of the screws ought to be bored with a center-bit, and then fitted closely in with wood, well matched, so as to conceal the screws entirely, and to ap- pear as one uniform surface without blemish. Brackets are mitered to the riser, and the nosings are continued round: in this mode, however, there is an apparent defect, for the brackets, instead of giving support, are themselves unsupported, depending on the steps, and are of no other use in point of strength, than merely tying the risers and treads of the internal angles of the steps together; and from the internal angles being hol- low, or a re-entrant right angle, except at the ends, which terminate by the wall at one extre- mity, and by the brackets at the other, there is a want of regular finish. The cavetto or hollow is carried all round the front of the slip, returned at the end, returned again at the end of the bracket, thence along the inside of the same, and then i along the internal angle 0fthe back of the riser. This is a slight imitation of the ancient mode, which was to make the steps solid all the way, so as to have every where throughout its length a bracket-formed section. This, though more natural in appearance, would be expensive and troublesome to execute, particularly when winders are used, but much stronger. The best mode, however, of constructing geome- trical stairs, is to put up the strings, and to mitre the brackets to the risers as usual, and finish the soflit with lath and plaster, which will form an inclined plane under each flight, and a winding surface under the winders. In elegant buildings, the soflit may be divided into panels. If the risers are got out of two—inch stuff, it will greatly add to the solidity.. The method of drawing and executing the scroll and other wreathed parts of the hand-rail, will be found under HAND-RAILING. In order to get a true idea of the twist of the hand-rail, the section of the rail by a plane pass. ing through the axis of the well-hole, or cylinder, is every where a rectangle ; that is, the plumb or vertical section, tending to‘the centre of the stair. This rectangle is every where of an equal breadth, but not of an equal vertical dimension in every part of the rail, unless that the risers and treads were every where the same from the .top to the bottom: the height is greatest above the winders, because the tread is of less breadth, and it is of less height above the flyers; the tread being the greatest. If you cut the rail, after squaring it, perpendicular to any of its curved sides, the section will not then be a rect- angle, three of the sides will at least be curved. Hence two falling—moulds laid down in the usual way, will not square the rail, though in wide openings they may do it sufliciently near. Hence in squaring the rail, the square can never be ap- plied at right angles to any one of the four arrises, for the edge of the stock will not coincide with the side of the rail, being curved; this would be easily made to appear by making a wreathed part of a rail of unusual dimensions, and cutting it in both directions. Therefore, to apply the square right, keep the stock to the plumb of the stair, and to guide the blade pro- perly, the stock ought to be very thick, and made concave to the plan so as to prevent the possibility of its shaking or turning from side to side; as a little matter up, or a little down, in the direction of the blade, would make a great difference in the squaring of the rail. All this might easily be conceived from the cy- linder itself, for there is no direction in which a straight line can be drawn on the surface of a cylinder, but one, and this line is in a plane pass- ing through the axis of the cylinder, and as the two vertical surfaces of the rail are portions of cylinders, there can be no straight line upon such surface, but what must be vertical; all others, from this principle are curves, or the sections of the rail are bounded by curves, or by a curve on that side. In gluing up a rail in thicknesses, it will be Y 2 JOI 164 sufficiently near to get out a piece of wood to the twisted form by two falling moulds, provided the well-hole be not less than one foot diameter; the thickness of this piece, as is there stated, must be equal ,to the thickness, or rather the horizontal breadth of the rail, together with the thickness which the number of saw-kerfs will amount to, and also the amount of the substance taken away by planing the veneers. We are now supposing the plan of the rail to be semi- circular, with two straight parts, one above and one below, a plan more frequently adopted from motives of economy, than from any propriety of elegance. ‘ The first thing to be done is to make a cylinder of plank to the size of the well-hole. Draw two level lines round the surface of this cylinder at the top and bottom; upon each of these lines set ofi‘ the treads of the steps at the end next the well—hole. Draw lines between every two corre- sponding points at the head and foot, and these lines will be all parallel to the axis of the cy- linder. Upon each of the springing lines, and also upon a middle line between these two lines, set the heights of the winders, and the height of one of the flyers above and below, or as much as is intended to be taken of? the straight of the rail. Take a pliable slip of wood straight on one edge, and bend it round, and keep the straight edge of it upon the three corresponding points, at the height of the last riser of the flyer; then draw the tread of the first winding step by the straight edge from the line where the cylindric part commences to the first perpendicular line on the curved surface; take the next three points higher, and draw a line between the second and third perpendicular lines, proceed in like manner with the next three higher points, and draw a line between the next two adjoining cylindric lines, and the lines so drawn between each three points will be the section of the treads of the succeeding winding steps. Having thus gone through the cylindric part, draw a step at the top, and another at the bot- tom, and thus the sections of the steps will be completed; draw the hypothenusal or pitch lines of the flyer on the lower part, and that of the upper part, and whatever (lili‘erence you make in the height of the rail between the flyers and the winders, you must set it up from the nosings of the steps of the winders upon two of the per. JOI pendicular lines: draw a line through the two points by bending a straight-edged slip round the cylinder, the straight edge of the slip co- inciding with these points; this line willrepresent the top of the rail over the winders, and the hy- pothenusal lines at the bottom and top that of the flyers; then curve of? the angles at the top and bottom where the rail of the winding parts meets that of the flyers above and below, and a line being drawn parallel to this, will form the falling mould. The reason of making the verti- cal elevation of the rail more upon the winders than the flyers, is, that the sudden elevation ofthe winders diminishes the height of the rail in a direction perpendicular to the raking line, and by this means persons would be liable to fall over it. To lay the veneers upon the cylinder, if bed- screws or wedges are used, you may try the veneers first upon the cylinder, screwing them down without glue; prepare several pieces of wood, to lie from 6 to 12 inches apart, ac- cording to the diameter of the well-hole, with two holes in each, distant in the clear some- thing more than the breadth of the rail. Then having marked the positions of the places of these pieces on the cylinder, pierce the cylinder with corresponding holes on each side, of the depth of the rail. If the cylinder be made of plank 2 inches thick, it will be sufficient for the screws: but if of thinner stuff, it will be con- venient to set it on end upon stools, to get under- neath, confining the top with nuts. Unscrew one half, three men being at work, one holding up all the veneers, another glueing, and the third laying them down successively one after the other, until all are glued; screw them down im- mediately. Unscrew the other half, and proceed in like manner, and the rail will be glued up. The glue that is used for this purpose ought to be clear, and as hot as possible; the rail ought likewise to be made hot, as otherwise the glue will be liable to set before all the veneers are put down, and ready for the screws: this opera- tion should therefore be done before a large fire, and the veneers thoroughly heated previous to the commencement, in order that the heat may be as uniformly retained as possible throughout the process. The glue in the joints of the rail will take about three weeks to harden in dry weather. lJOlNERY. 111" |1|||1|11|11||1|1|||ll 1|111||11|1||11|| 1|1||11||1|1|111111111111|11|1||11|1|1||"11111111111111 HHIHIIIIIHNIIIHHHIIIIHIMIINI|||HHI|II|H|I 1111111111111111111111111111111111 t 1111111111111111111111111111111 “111.1 :11; 111fl1M111[31111311111111 1111111111111 I III 1||||11||1111111111|1|||||1l|||111 W111"!11111111111111111111111111lIll1111111III[1111111111111111111111||I1111|l|||llllllllllllllllllllllLL“~ 1 fi*—_%fi_—, _-_ #_,,i___ iAw“, ,,,,,, , . ‘ 1 1,1 W, . , 1 1 EE 11 1221111111 111 11.111111111111111 * ‘ 1111111111!" E; g ‘E 111111 35‘ 111W " a: 1 11111 ~,' .. ‘1‘},1 f1 1111111|l111||||l|11|||1|1|111||||11 1|1|1111|||11||111|I|||11||11|l||||| ‘ 1111111111111 1 "‘1‘1 é?" ' ‘1‘ “ 1111111111 1 151 ! T11111111111111 . 11 111111.111 1111 111111111111111111‘ 1 “11111111111111 I|I111||1111||1|111|||111||111||1|1| E 1|||l||11| ||1|||11111111111111111111111111111 111ml ' E1 11 1 111 11l111||11111||1|111||1|| ‘5' 111111 1 Imummnmm 11 11111111 17me 1 11.11 1.111111111121111 1111111111 ‘ 1111‘ 111.“ 1.1111111111111111... .1.11.1.11uf1;u111. _ _—;— s 11111111111111111111111111111111111111111111111111111 11 1 1111 JOI 16 J01 W Doom—When a board is made to fit an aperture in a wall, for the purpose of preventing ingress or egress at pleasure, it is called a door, or closure. Doors are seldom constructed of one entire board, from the difliculty of procuring a simple board of sufficient size; neither are they often con- structed of simple boards joined edge to edge, to form a compound board, without having trans- verse pieces fastened to one side, or being clamped at the ends; as without such appendages, the door of this construction~would be liable to break in the direction of the fibres, or be subject to crack or split, if not entirely seasoned, or when the texture is unequal in consequence of knots, or the resin not being uniformly disposed. The most common kind of doors are constructed of several simple boards, not fixed with glue, or any tenacious substance, but by nailing transverse pieces upon the hack of the boards, laid edge to edge. The transverse pieces, thus nailed, are called ledges, or bars, whence the door is said to be lodged, or barred. In this case, one of the edges, at every joint, is headed on both sides, or at least on the face which is the outside, the ledges being placed to the inside. Doors of this description are generally employed in the cottages of the poor, or in the out-houses of superior buildings. ‘Vhere doors are required to combine strength, beauty, and durability, a frame,joined by mortise and tenou, must be constructed, with one or more intermediate openings, each of which must be en- tirely surrounded by three or more parts of the frame, which have grooves ploughed in the edges, for the reception of boards to close the openings. ‘Vhen any parts of the framing are intended to lie in an horizontal position, after the door is hung, or fixed upon its hinges, they are called rails; if there are more than two rails, the ex- treme rail next to the floor is called the bottom rail, and that next to the ceiling, the top rail. Doors are seldom framed with less than three rails; in which case the middle one is called the lock rail; but most doors have two intermediate rails, of which the one next to the top rail is called the frieze rail. When there are more than two intermediate rails, those between the lock and frieze rails have no particular name. The extreme parts of the frame to which the rails are fixed, are called stiles, and the intermediate parts, mountings, from their vertical position. The 1 boards by which the-interstices are closed, are called panels. The stiles are first defined, on account of. some doors being made narrower at the t0p than at bottom, in the manner of ancient doors. , Figure 24.——A four equal paneled door; this for is only used in common work, and frequently without mouldings. Figure 25.———A nine panelled door, with square panels at the top. This form is frequently used in street doors and the back lined with boards. Figure 26.——-A six equal panel pair of folding doors, two panels in breadth and three in height. Figure 27.—A double margin or folding door, with three panels in height, and two in breadth ; being all equal. Figure 28.—-—A double margin, or pair of folding doors, with four panels in height and two in breadth, and with two lying panels below the top rail, and two above the lock rail. Figure QQ.——A ten panelled pair of folding doors, five in height and two in breadth, with two lying panels under the top rail, two above the bottom rail, and two in the middle: of this form is the ancient door of the Pantheon at Rome. Figure 30.——An ancient door, narrower at the top than at the bottom: of this form is the door of the temple of Vesta, at Rome, and that of Erech- theus, at Athens. This construction may be use- ful for causing the door to rise as it opens, in order to clear a carpet, or to make it shut of itself. Figures 31 and 32.—Doors of communication, or such as shut out of the way ofthe floor. Figure 31, folds round upon the partition, by means of hang- ing styles : Figure 32, is made to shut occasionally in the partition, so as to be entirely concealed. The two middle parts open, like ordinary folding doors, upon hinges fastened to the extreme parts. Figure 33.—A jib-door, which when shut may be as much concealed as possible. Jib—doors are used to preserve the uniformity of a room, or to save the expense ofa corresponding door. Doors ought to be made of clean good stuff, firmly put together, the mitres or scribings brought together with the greatest exactness, and the whole of their surfaces perfectly smooth, particularly those made for the best apartments of good houses, in order to effect this, the whole of the work ought to be set out and tried up with particular care; saws and all other tools must he in good order; the mortising, tenoning, JOI 166 JOI plowing, and stickingof‘the mouldings,.ought to be correctly to the gauge lines; these being strictly attended to, the work will of necessity, when put together, close with certainty: but if 1 otherwise, the workman must expect a great deal of trouble in paring the different parts be- . fore the work can be made to appear in any degree passable: this will also occasion a want V of firmness in the work, particularly if the tenons , and mortises are obliged to be pared. In bead-and-flush doors, the best way is to mitre the work square, afterwards put in the panels, and smooth the whole off together, then marking the panels at the parts of the framing they agree to, take the door to pieces, and work the beads on the stiles, rails, and mountings. If the doors are double margin, that is, re- presenting a pair of folding doors, the staff stile, which imitates the meeting stiles, must be en— tered to the top and bottom rails of the door, by forking the ends into notches cut in the top and bottom rails. . Oflmnging Doors.—Having treated fully on the - various kinds of hinges under the article HING- ING, we shall here make afew observations upon, and give some rules for, hanging of doors, so as to clear the ground or carpet. First, Raise the floor under the door as much as may be necessary, according to the thickness of the carpet, 8L0. Secondly, Make the knuckle of the bottom hinge to project beyond the perpendicular of the top hinge about one eighth of an inch: this will throw the door off the floor. Note—rThe centre of the top hinge must project a little beyond the surface of the door, if the hinge is let equally into the door and into the jamb; otherwise, if the centre lie in the surface of the door, it ought to be placed at the very top, which is seldom done, except when hung with centres. Thirdly, Fix the jamb, on which the door hangs, out of the plumb line, so that the top of the jamb may incline to the oppositejamb about one- eighth part of an inch: this will contribute to the effect of clearing the door from the floor. Fourthly, Make the door, when shut, to project at the bottom towards the inside of the room, about one eigth of an inch, which may be effected by giving the rebate the quantity of inclination .. requisite. .Noten—Although any of the above methods, pro- perly applied, will make a door swing sufficiently clear- of the floor, yet as each one separately will require to be done in so great a degree as to offend the eye, I do not recommend it in nice work, but would rather advise a combination of them all to be used, thus: Raise the floor about one-eighth of an inch under the door; make the jamb on which the door hangs incline to the opposite jamb about one quarter of an inch; make each rebate that stops the door project at the bottom one eighth part of an inch to that side of the room on which the door opens. Now these several methods practised in the above small degrees, which will not be perceptible, will throw the door sufficient- ly out of the level when opened to a square; that is, it will be at least half an inch when the height of the door is double its width. Fifi/sly, An invention has lately been introduced called rising hinges, which are made with a spiral groove winding round the knuckle; this con- struction of hinge requires that the door should be beveled at the top next to the ledge or door catch, as much as the hinge rises in one quarter of its revolution. Sixth/y, This may also be effected by adopting a door in the form of the antique doors ; that is, the bottom to be wider than the top, the jambs having the same inclination. Mouldings of Doors.—-The different denomina- tions offramed doors, according to their mouldings and panels, and framed work in general. The figures in the Plates, to which these descriptions refer, are sections of doors, through one of the stiles, taking in a small part of the panel; or they may be considered as a vertical section through the top rail, shewing part of the panel. Figure 34, the framing is without mouldings, and the panel a straight surface on both sides: this is denominated doors square and flat panel on bot/c sides. Figure 35, the framing has a quirked ovolo, and a fillet on one side, but without mouldings on the other, and the panel flat on both sides: this is denominated doors quirked ovolo, fillet and flat panel, with square back. Figure 36, differs only from the last in having a bead instead of a fillet, and is therefore denomi- nated quirked ovolo, bead and flat panel, with square back. , W,.....,... IQ~-‘ou'» ‘ 'I‘ ,. ,2.“ ‘3. ”3, www. . In:~:,figwbiflryh£~ilwoy «5, wk <, . - WJWOIVNERY. ' 1 “ ‘ murky”! ‘ fig). 34. [51.35. [11:1]. .761. [1}]. JR Fifi :‘M’. [’40. . 310 If NJ +————7—\J U L————— ‘ r \| __J ‘ I 1 Hg]. ‘10. 143,. 4/. x l r—————fl_| K I Pflfl I i 2 a l : 173,. 45;. . ["13]. A/ z). Hg). 44. my. ./.:. ["13] ll“. Fly. 10‘. k] 1 x \ 1 ( £3.— fl Olav/3mm] by /’.\'..\’-/)mu'n , . ‘ lfl‘Jl .1 .\'."1‘/I.'/.I't'll Arm/NILl‘ub/ILJ-lml lgr/thv'w/(rnn A" 9/ [fur/I'M],"Fin/var.)'frr¢'t,(’.I'/i’rd £9.91; lz'Iw/wrm' [5r Itlfull‘c'. ‘ ' 14.3? w JOI Figure 37, has an additional fillet on the framing, to what there is in Figure 36, and is therefore de— nominated quirked ovolo, bead, fillet, and flat panel, with square back. . Note. When the back is said to be square, as in Figure 35, 36, 37, the meaning is, that there are no mouldings on the framing, and the panel is a straight surface on one side of the door. Figure 38, the framing struck with quirk ogee and quirked head on one side, and square on the other; the surface of the panel straight on both sides: this is called quirked ogee, quirk bead and flat panel, with square back. Figure 39, differs from the last, only in having the bead raised above the lower part of the ogee, and a fillet. This is therefore denominated quirked ogee, raised bead, and flat panel, with square back. Figure 40, is denominated cove, raised bead, and flat panel, with square back. Figure 41, is denominated quirked ovolo, bead, fillet, and raised panel on front, with square back. The rising of the panel gives strength’to the door, and on this account they are often em- ployed in street doors, though the fashion at pre- sent is discontinued in the inside of buildings. Figure 42, the framing is the same as the last, but the panel is raised in front, and has an ovolo on the rising. This is therefore denominated quirked ovolo, bead, and raised panel, with ovolo on the rising on front of door, with square back. Figure 43, is denominated quirked ogee, raised panel, ovolo and fillet on the rising, and astragal raised on theflat of panel, and square back. Note. The raised side of the panel is always turned towards the street. Figure 44, is denominated quirked ovolo, bead, fillet, and flat panel, on both sides Doors of this description are used between rooms, or between passages and rooms, where the door is equally eXposed on both sides. When the panels are flat on both sides, or simply chamfered on one side and flat on the other, and the framing of the door moulded. on the side which has the flat panels: .such doors are employed in rooms where one side only is exposed, and the other never but when opened, being turned towards a cupboard or dark closet. Figure 45, is denominated bead, but, and square, or more fully, bead and but front, and square back. In bead and but work, the bead is always ‘16? "301 4% struck on theouter arris of the panel, in the di- rection of the grain. Figure 46, is denominated bead and flush front and quirked ogee, raised panel, with ovolo on the rising, grooved on flat (3)" panel, on back. Bead and flush, and bead and but work are al- ways used where strength is required. The mouldings on the inside are made to correspond with the other passage or ball doors. Figure 47, is a collection or series of mouldings, the same on both sides, and project in part with- out the framing on each side. The mouldings are laid in after the door is framed square and put together. If bradded through the sides of the quirks, the heads will be entirely concealed; but observe, that the position of the brads must not be directed towards the panels, but into the solid of the framing. The mouldings of doors which thus project are termed belection mould- ings; belection—moulded work is chiefly employ-v ed in superior buildings. I Geometrical Descriptions in Joinery. To find the true bevel for hanging any door. Figure 48.———Let a be the centre of the hinge; on a b, the width of the door, describe 'a semicircle, bceda, cutting the other side of the door at c and d. Join ad and be, which will be the proper edges of the door, in order to make it open freely. Note—The bevelling on the side ad is of no other consequence than to make the sides- uniform. To find thejoint for a pair offolding doors. Figure 49.-—Let h and g be the centre of each. hinge; bisect hg by a perpendicular, a b, cutting the thickness of the door at a and b; biseet ab by the perpendicular ed at e,- :make e c and e d each equal to half the thickness that you intend the rebate to be. Suppose you intended the flap, ga cdf, to open, draw a line from dto the centre of the hinge at g; on dg describe a semicircle, dfig, cutting the other side of the door at f; join fd, and through c draw ck parallel to df; then kc df will be the proper-joint. Note—If you put a head at thejoint, it ought; to be equally on each side of the points a and b. To find the bevel on the edge (f a door, when it is executed ona circular plan, and the door to turn. towards the space on the convex side of the circle. Figure 50.-—-VVith regard to the circular door, all that is required is to make the angle a b c either a right angle or greater than a right angle (for a. JOI right angle is the least that any door will admit of) formed by the edge of the door, and a line drawn from the centre of the hinge to the oppo- site angle. For the Folding Doors. Figure 51.-—-Let a and b be the centres of the hinges on the plan; join the points a and b by the right line a l), and bisect it by a perpendicular, cde, at c, cutting the thickness of the door in e; bisect d e by a perpendicular, gfh; make fh and fgeach equal to half the thickness of the rebate; join h b; on it describe the semicircle hi k [2, cutting the opposite side of the door, on which is placed the knuckle of the hinge ati; join i h; through g draw glparallel to it; then will lg hi be the properjoint for the meeting of the two doors. To find the meetingjoint of folding doors when the hinges are placed on the concave side of the doors. Figure 52.-—Let a and b be the centres of the hinges; join ab, and bisect it by a perpendicular, e de, at c, cutting the thickness of the door at d and e; bisect d e by aperpendicular, gfh, cutting de atf; makefh andfg each equal to half the thickness of the rebate; join bh; on it describe a semicircle, hi k 1), cutting the other side of the door contrary to the hinge at i; join ih, and through g draw gl parallel to ih, cutting the con- cave side of the door at l; then will i h gl be the joint sought. Denzonstration.——Let the door a lg hi remain in its place; now the angle bih being a right angle, consequently the perpendicular hi will be the shortest line that can be drawn from the point p b to the line i h; then suppose the half door to be turned round the hinge at b; the point i will then describe a circle, whose centre is the hinge at I); then will ih be a tangent to that circle at 1'; therefore the angle ati will touch no other part of the edge of the other door, but at i. If round the centre of the door which opens, as Figure 53, you describe circles on each side of the rebate, and the edges of each door he made circular, it is plain it will also open in this case. The plan of the doors here shewn,are two or three times thicker than those used in practice, in order to shew the principle clearly. Figure 54, a section of the jamb post, jamb linings, grounds, and architraves, with partof the plan of a door. 168 MI I JOI ._.I J Bl). Sections of the grounds, flush, or in the same plane with the plaster. E, e. Outside and inside architraves. ggg g. Line of the plinth. C. Jamb lining. H. Hanging style. I. Door style hung to the hanging style H, by means of the hinge m. Figure 55, half of the plan: shewing the door folded back; the parts in this having the same references as those in Figure 54. Figure 56, meeting styles. Figure 57, the moulding of the door, shewn to a larger size. This method is adviseable where you have no opportunity of making the doors slide into the partition, as is shewn in Figure 3'2, but whenever that opportunity offers, it should be preferred, as no door can be seen when shut into the partition, which not only keeps them entirely out of the way, but makes the most complete appearance. Elevation ofapair ofjolding doors, to be shut quite out of the way, in order to open a communication between two rooms, or to throw both into one on any occasion. Figure 58, Plan of half the door to a small size. A. Plan of the outside‘style. B, C. Plans of the hanging styles. .D. One of the meeting styles. G G G, ,gg g. Framed partitions,'distant from each other, in the clear, the thickness of the door. F F F. The space or cavity for the door to work in, which must be made sulficiently wide to receive one half of the door entirely within, or nearly so: doors of communication for general uses may be constructed in this larger door, in which case the middle doors may be hung to the flaps on the flanks, so that they will open like any other com- mon folding door; this method therefore com- bines utility and convenience, and is a complete deception. The first leaf of the door, must run in a groove at the top, to make it steady. Figure 59, a section of the style next to the par- tition, to a large size, with part of the plan of the bottom rail, shewing a small part ofeach partition. Note.——In setting out work of this kind for prac— tice, one half of the plan ought to be completely drawn out. . Tofiud thejoint ofa jib-door, so that it shall open free/y at the hanging side, and the joint to be a plane sur/izce. .EZAIfi'flK 4 j JOINERY. M A 1 1 1-\ 11111111 ._ ”1%: _ EE." 1 '1 g l: 1!“ 1 , 1111‘. 1:111“ 1 11:11 1 1 1111: H , 111 1 ‘\ ”I 1" *x /' j 1' t1! 1 X // 111‘ 1 ‘ l1 / 111313116111 11“ x ‘Hal 1/ I 11; 1 rf 11E: Wfl" 1MAA; _‘ - _ I 7 [ill / / / /. .T/r/nr/w/I A“ f/lz/I'fl'rlzl, Him/Mll- 'I‘frz Ely/rural (11' /I'. [fur/('1 ' f’o’INié'kY. 123;. 53. 6/71/17 / //// :/ /////////////////////////////1Z//Z{///l F157- L ‘ " ¢ // ,7 7/ ,7 "y H ,;/,/,,.// F :%¢ W; l/ 7/; __--"‘ —'___‘ 'l/ -_.—- -“‘—_---rl/// 4M5, ////////// ///////////////;/ ////////////////////// /// 4 J l V \Mikx/ 7“ ~ ‘. , . " / //7//’i ,% A Drawn 11vJL-im‘olzuldwz. [07241072, Pub/(what b ‘, [EVII'Iw A}. 011.1% J b’arfl' rid, War: inur J‘We [’ 181;. Ely/rural 111' [bibs/h". «i? JOI 169 501 W Figure 60. —Let C, the centre of the hinge, be 111 the same plane with the dado, and placed within the substance of the lining, in order to give strength to thejamb. C E. tiThe thickness of the door at the joint, which produce till it cut the opposite side of the base moulding at A; make A B equal to AC; join BC, and from B draw BD perpendicular to BC; then will BD be the true line through which the surbase moulding must be cut in a plane perpendicular to the floor. The shadowed part shews a part of the jamb lining cut out suffi- cient to let the surbase moulding move in it. Note. If the centre of the hinge had been placed in the plane of the side of the rebate, parallel to the jamb lining, a deep cavity through thejamb would have been brought into view in the open- ing of the door, the exposure of which would have been very unsightly. If the upper part of the door he hinged, the axis of the hinge should be in a straight line with the axis of the centre below, and both the axis of the hinge and the axis of the centre should be in the plane ofthe face of the door, so that the joint upon the hanging side will always be close. Figure 6], the elevation of the surbase at the joint. T he construction of a saskframe, and the manner of putting the several parts of it together. Figure 62, the elevation of the sash frame. A BC D. The outer edge of it. The dark perpendicular lines EF, G H, are grooves whose distances from the edges L M and K I of the sash frame, are equal to the depth of the boxing, together with three-eighths of an inch allowed for the margin between the shutters and the bead. Figurelis, ho1izontal section of the sides, shew- ing also the plan of the sill. Figure 64, a vertical section of the sill and top, shewing the elevation of the pulley-style m and n, the pulleys let into the pulley-piece. Figure 65, the horizontal section of the sides, shewing also a plan of the head of the sash-frame. Figure 66, the elevation of the outer side of the sash frame: the outside lining being taken away in order to shew the work within the sash-frame. fg, the parting strip fastened by a pin: ed, one of the weights connected with the sash by means of a line going over the pulley c; the other end fixed to the edge of the sash. VOL. II. Note. The weight d e is equal to half the weight of the sash. Figure 67, part of the head of the sash-frame be- fore put together. Figure 68, the edge of Figure 67. Figure 69, the edge of the bottom, shewing the manner of fixing the styles. Figure 70, the plan of Figure 69. Figure 7], and 79:, sections of window sills, with sections of the under rail of the sash, shewing the best modes of constructing them in order to pre- vent the weather from driving under the sash-rail. A. Section of the bottom rail of the sash. B. Section of the bead tongued into’the sill. C. Section of the sill. Figure 73, sections of the meeting rails, with the side elevations of the upright bars. C. Rebate for the glass. D. A square. E, F. An astragal and hollow moulding. G. Fillet. Note. The small letters denote the same parts of the under sash. Figure 74, section of an upright bar, with the plans of two horizontal bars, shewing the frank- ing or manner in which they are put together, so as to keep the upright bars as strong as possible. The thickness of the teuon in general comes about one-sixteenth of an inch to the edge of the hollow of the astragal, and close to the rebate on the other side. kit, A dowel to keep the horizontal bars still firmer together. Note. The same parts in this have the letters of reference the same as Figure 73. Note also. There is no rebate made for the glass on the inside of the meeting-bar; a groove being made to answer that purpose. Figure 7 5.——Section of common shutters 8y sash-frame. A. Section of the architrave. B. Ground for the architrave. F. Back lining of the boxing, tongued into the ground B, and into the inside lining G, of the sash-frame. G. The inside lining of the sash-frame. H. The inside head. I. The pulley.style. K. The parting bead. L. Outside lining. M. Back lining. 'JOl i —__—— C C C. The frontshutterhung to the inside lining of the sash-frame, G, by means of the hinge a. D D D. Back flap or shutter hung to the front shutter by means of the hinge l). EEE. Another back flap hung to DDD, by means of the hinge c. As in a window the whole of the light should be shut out, the principle of setting out the shutters is, that each boxing should contain as many shut— ters as will cover one half; the horizontal breadth of which is from the axis of the hinges to the central vertical line of the windows. 0 P Q R. Plan of the lower sash. 0. Rebate of the glass. P. A square. Q. An astragal moulding. R. A small square, or fillet. Figure 76, the method of hinging two back flaps together, shewing the manner of placing the hinge, when room is scanty in the boxings. Elevation and plan (f halfa window, adapted, when the wall of the building is not sufficiently thick, to admit of room for boxing. Figure 77', elevation of half the window. Figure 78, plan of the window to double the size of the elevation, in order that the parts may be more distinctly seen. E L. The breadth of the shutter, which is hung to a hanging style G, and the hanging style G is hung to the sash-frame by the hinge at h. The whole breadth of the shutter E L, together with the breadth of the hanging style at G, that is, ih, ought to cover exactly half the breadth of the window; viz. from the axis of the hinge at h, to the central vertical line of the window. H. Architrave. 1. Back ground. K. Back lining. The panel, ABCD, Figure 77, represents the shutter, of which E F, Figure 78, is the breadth. The hanging style and shutter are hung together by means of a rule—joint, as before described, unde1 the article HINGING. Under the shutter A B C D, is a bead R, which is continued across the sash- frame to serve for capping; P is a vertical bead continued in a line with the edge, at D, ofthe rule-joint. O and N. Sub-plinth of window, flush with the bead P. M. Plinth, or skirting board. I 70 JOI r Figure 79.——A. Architrave moulding. B. Ground. C C C. Back lining. D. The lining, or return of the window. E E E. The shutter hung to the hanging style, F, which is hung to the sash—frame by the hinge at a. G. The inside lining of the sash-frame. H. Inside bead. I. Parting bead. K. Outside bead. L. Back lining. M. The parting slip for the weights N and O. N and O. \Vcights. P. Ground fixed upon the plug, Q. Q. The plug, for securing the finishings. Pt. Pulley-style. The plan, front side elevation, and settion 0] a window proper for a building ztheie the walls are not thick enough to admit of room for boamgs, which will shew the same finish as if the shuttezs folded into boxings. Figure 80, front elevation of the window. The dotted lines a hdc, represent a piece of framing. The other side, A BC D, represents a sliding shutter in the wall. The haming IS supposed to be removed, in order to shew the shutter. Figure 81, the side elevation and section, sup- posing the shutter removed. a. An architrave moulding. b. Sofiit. c. Top of the sash~frame. d. Capping, tongued into the sash-frame sill. Figure 82, horizontal section and plan of the window, twice the size of the elevation. gg. Section of the framing, as shown by a I) c (I, Figure 80, by dotted lines. hh. Plastering on the wall. ii. A shutter hung to the sash-frame at m. ff. Section of the sliding shutter, which runs on rollers. lt‘ k. A flap, which 15 let into a rebate and hinged at the edge pp, so that when the flap is turhed round, the hinges out of the rebate, and the shut~ ter ii turned to tDthe face of the window, there will be a clear passage for the shutterjf to run out. Note. Although there is only a stop for the back of the shutter at the bottom, yet'it is quite setti- w. m m P m ///// 7M” 4 ...................... d JOINERY. // W/ ,\ ////%,/ /%¢%Z¢flflflfl%fi Eng/”11741 Jr If . [Bo/i}. fired, 1316’ ‘ [undwbfizlilzflml by 1’. A7}'lzz,IZ.rw/1 a" J lj’nlfic'ld, [1711210111' z % x mm by Jf/l. "\?}']147/d't711. my: J o INE RY. ' mm t; E I . I a i E \ E i dim-"mic I C D . I Hg]. (92 g ,, E Z i Iv i lc P p t .1 ! ‘5 .1 T [2;]. (m. [If/.87, WW {_ I// v %%7% 1243,11 / .; ,/}///c ,r7/‘7I///CZ%/////‘ V/(Cfi' ’; /% '2’“? [KB ' A L i H i h .5 § 1 o __ i P r } -, o — 1 N M L K F Drawn [41' 111-1. A’I'z'lwlwn. [wedonlAIIZill'MaZ by 1% A 'Ik'lwlwm Jul BzI/fit‘dflZnimzr J'trmf, 1818. £715”;sz by RRofii’» QMMH f! JOI if J— cient, as it is stopped on both sides at the top, and as the edge of the shutter should never be entirely out of the boxing. This is more clearly shewn by the parts drawn larger in the next plate. Diflerent sections Qf the foregoing Plate. Figure 83, horizontal section through the side of the window. . Architrave moulding. Part ofa piece of framing. . Part of the shutter. . Plaster or rendering upon the wall. . The front shutter hung to the sash-frame at y. . Back lining. . Inside lining of the sash-frame. 11. Inside bead of the sash-frame. I. Pulley-piece. i K. Parting bead. L. Back lining of the sash-frame. IVI. Parting stripe. N. Outside lining. Figure 84, vertical section through the top of the window. a. Architrave moulding. T. Ground over the window. C. Section of part of the shutter. O. Soffit. 1’. Top of the sash-frame. N. Horizontal outside bead. Ii, [1. inside horizontal bead. Figure 85, vertical section through the sill of the window. B. Edge of the framing, C. Edge of the shutter. Q. Capping, rebatcd out at S, and tongued into the sash-frame sill. ‘ S. A flap hung to Q, by means of the hinge at i n; then by turning the front shutter upon the window, and by turning up the smallflap, S, there will be aclear passage for the shutter, C, to run in. Qmeofi> Plan, elevation, and section, of a window with shut- ters, which will shew uniform and complete, whether the shutters are in the borings, or closing the aper- ture (f the window. Figure 86, plan or horizontal section at AB. Figure 87, elevation or front of the window. Figure 88, vertical section at C, D, Figure 87, and side of the window. E. Thickness of the pilaster or architrave. 171 J01 F. A bead stuck on its edge, parting the edge of the pilaster from the shutter. G. The breadth of the shutter. H, I. A head and square to correspond to the thickness of the architrave and bead, so as to shew the same finish on each edge of the shutter: one edge of this finishes against the sash-frame above, and the same edge below finishes against the back of the window down to the plinth. K. Another square, equal to the projection of the capping. L. Bead of the sash-frame. M. Thickness for the under sash to run in. N. Parting bead. O. The thickness for the upper sash to run in, P. Outside lining and bead. Q. The breadth of the reveal or outer brick-work. This is farther explained in another figure, where the principal sections are shewn to a larger scale. a a. Lintels, made of strong yellow deal or oak. l). The top of the ground. 0. The architrave fixed upon the ground 6. dd. The sofiit tongued into the top of the sash- frame e, and on the other edge into the head architrave C. ff. A hollow space between the soFfit dd, and the lintels aa; the under edges of the liutles a a, are generally about four inches and a half above the camber of the outside of the window; but it may be less when there is any necessity for it, as for example, when very narrow grounds are used, it may come down within a quarter of an inch of the soflit. The face of the pulley-style of every sash-frame ought to project beyond the edge of the brick- work about three-eighths of an inch; that is, the distance between the face of each pulley-style ought to be less by three-quarters of an inch than the width of the window on the outside, so that the face of the shutters ought to be in the same plane with the brick-work on the outside. Parts of the foregoing at large. Figure 89. Plan of the shutters. A. The outside lining. B. The pulley-style. C. Inside lining. D. Back lining. E, F. Weights. G. Parting slip of weights. H. Parting bead of sashes. z 2 JOI . I. Inside bead. K L M N. Plan of the sash-frame. K L. Sill of the sash-frame. M. Plan of the inside bead. N. Plan of the capping. R R. Hanging style, hung to the sash—frame at a. S S. A shutter, hung to the hanging style at e. T T. Another shutter, hung to S S at n, ifnecessary. P P. A door, hung to the architrave at m, falling upon the hanging style R R by means of a rebate. Note. The door must fall in a rebate at top and bottom. U. A ground to fix the architrave upon. V. The architrave fixed upon the ground. \V. Back lining. When the aperture is shut, the door PP must ’ be turned round the hinge m, parallel to the face of the sash—frame : then the shutters R R, S S, T T, being drawn out and turned on the hinge a, and on the hinges c and n, will cover that part of the window for which they were intended. The door P may then be closed, and the whole will have an uniform and neat appearance. . 'ofind the splay of the ground b c.—-—Draw a line from the centre of the hinge at a to the edge of the ground at b; on a b, as a diameter, describe a circle cutting the back lining of the boxing at o; join 0 b, and it will be the bevel requiredg Front and two side elevationsof a window, the sash- frame being out of the square, or an oblique-angled parallelogram: shewing how to construct the sidesry“ the window, so that the shutters shall make an equal margin round the edge of the sashframe, when the window is shut; and also to fit their boxings. Figure 90. Elevation of the window; AB CD being the edge of the sash-frame next to the bead, and E F G H the margin between the shutters and the inside beads. The difficulty of fitting up a window of this kind may be surmounted if the following observations are attended to: the points K and I, Figure 91, being taken at the distance EF, Figure 90, and the point R, Figure 91, being made to correspond to K, Figure 90, the middle of the meeting rails; then make the angle R K L, Figure 91, equal to the angle K E H, Figure 90: through R and I draw R S and 1M parallel to K L; then K I M L will be the front shutter, and RS the parting bead, in case the shutters are to be cut. Figure 92, is constructed in the same manner as 172 JO! Figure 91 ; that is, by making the angle T O P equal to the angle L H E, Figure 90; the points 0, T, N, being previously made to correspond to the points H, L, G, as on the other side. In Figures 9] and 92, A and B, are lintels. C. The top of the sash frame. I). The soffit. e. Ground. G. Sash-frame sill. F. Stone sill. Plan and elevation (f the shutters to the foregoing example,- shewing the manner of hanging and cutting the shutter when the sash-frame is an oblique—angled parallelogram, or out of the square, as workmen call it. Let Figure 93, be the plan of the window, and let A B and D C, Figure 94, be the bottom and top ends of the shutters parallel to each other; now, in order that the shutters may fit close into their boxing and also close into the window-frame, the centres of the hinges to each flap must be set in lines perpendicular to D C or A B. To set out the shutters. —-— Make A e and Df, Figure 94, equal to the breadth of the front shutter, and draw the line fe; then will ADfe repre- sent the front shutter, andf e the edge on which the flap willjoin to it; then if the angle Dfe be not a right angle but obtuse, from f draw fg perpendicular to D C; then willfg be the line of the hinges. In the same manner, B C q r will re- present the shutter on the other side; B rq being the obtuse angle, and rs a perpendicular to A B, for the line of the hinges: the two extreme joints being made, all the other joints, h i, kl, m n, and op, ought to be all perpendicular to the ends D C and A B of the shutters: then will the centres of the hinges be parallel to, or in the same line with, the joint. To find the breadth of the flaps which hang to the front shutters, so that they may be as wide as possible—From the points A and C, the obtuse angles, draw A v, C u, perpendicular to A B and D C, the ends of the shutters; make u a and A 6 equal to the breadth of the rebate; and from the pointj, and in the line of hinges, make fc,fh, and gd, gi, respectively, equal to fa,fv, and g b,gA; then will efhi be the flap required; and it is plain, from the nature of this window, that the other flap, oq rp, must be the same figure as the flap e f h i, but inverted. gm . ”any: - < 99525 ”My. is ,fiA Q .q 3%. at . NNFNN‘ aVNNN. ”A a A “a. . u «a M. «A n- \ NW”). «a .0} ,u «try w MW 3 . fir ‘ _» , \ 13. 1A1 ‘ 1 :14 .11 . , fill .23.: «1, .. z r. .7 ”v «said: At ; V i: «ya-N: fléagfi . _ ,4 » x ‘ ‘ , . . i , ,. n ‘ , by 1mm . d EIIwa/e 1818 . r I 5h H|||I “III.” “fil|'1l|\llqlllllln Hi londom-MZIQIM by flle'cfiobcw X: Jflar/‘wjld, Wandaw- J'W, d! . .« ‘fiuh JOl 173 The other flaps may be filled in as the width of the window will admit. Note—VVe have given this example, because the method is general, and will apply to all cases; the workman ought never to trust to the sash—frame being absolutely square, for they seldom are; and if the variation be ever so small, there will be a very considerable error in the ends of the shut- ters when enclosed in the boxings. Such distort- ed examples as the above generally occur in old buildings; in such this method must be adopted: but also, for the above reason, it ought not only to be employed in old work, but even in new, where the shutters are cut, so that the ends of the shutters may not only coincide when folded, but also with the sill and top of the sash frame, and also with the meeting rail. Customary bleasures in. Joiners’ Work, for Zabour only. Preparation of boarding by the foot super. —— The different distinctions are—edges shot; edges shot, ploughed and tongued; wrought on one side, and edges shot; wrought on both sides and edges shot; wrought on both sides, ploughed and tongued; boards keyed and clamped; mortise clamped; mortise and mitre clamped. The price per foot is also increased according to the thick- ness of the stuff. If the longitudinal joints are glued, so much more is added to the foot: and if feather-tongued, still more. Floors—Are measured by the square, the price depending upon the surface, whether wrought or plain, and the manner of the longitudinal and heading joints, as well as upon the thickness of stufi“; or whether the boards are laid one after the other, or folded; or whether the floor be laid with boards, battens, or wainscot. Skirtings are also measured by the foot super; the price depending upon the position, whether level, raking, or ramping; or upon the manner of finishing, whether plain, torus, rebated, scribed to floor, or to steps; or upon the plan, whether straight or circular. The price of every kind of framing depends upon the thickness, or whether the framing be plain or moulded; and if moulded, what kind of mould- ings,'and whether stuck on the solid, or laid in; whether mitred or scribed; and upon the number of panels in a given height and breadth; also upon the nature of the plan. Jot ' The various descriptions of wainscoting, window- linings, as backs and elbows, door-linings, as jambs and soffits, back linings, partitions, doors, shutters, are all measured by the foot super. Sashes are measured by the foot super, as well as the sash-frames. The sash and frame are either measured together or separately. Sky—lights are measured by the foot super, their price depending upon the plan and elevation. Framed grounds, at per foot run. Ledged-doors, by the foot super. Dado is measured by the foot super; the price depends upon the plan being straight or circular, or upon the elevation being level or inclined as in staircases. In staircasing the risers, treads, carriages, and brackets, are generally classed together, and mea- sured by the foot super; sometimes the string- board is also included. The price must be difi- ferent, as the steps are flyers or winders, or as the risers are mitred into the string-board, the treads dovetailed for balusters, and the nosings returned, or whether the bottom edges of the risers are tongued into the step. The curtail-step is gene- rally valued as a whole. Returned nosings are sometimes valued at so much each, and if circular are double the price of straight ones. The hand-rail is measured by the foot run; the price depending upon the materials and diameter of the well-hole, or whether ramped, swan-necked, level circular, or wreathed; or whether made out of the solid, or in thicknesses. The scroll is paid at per piece; as is the making and fixing of each joint screw; three inches of the straight part at each end of the wreath are included in the mea— surement. Deal balusters are prepared and fixed at so much each; as likewise, iron balusters, iron column to curtail, housings to step and riser, common cut brackets, and brackets circular upon the plan, preparing and fixing. Extra sinking in rail for iron balusters is charged by the foot run, the price depending on the rail being straight, circular, wreathed, or ramped. The price of the string-board is regulated by the foot super, according to the manner in which it is moulded, or whether straight or wreathed, or the manner in which the wreathed string is con- structed, if properly backed upon a cylinder. The shafts of columns are measured by the foot super, the price depending upon the diameter, or J OI 174.: -—— JOI . whether it be straighter curved on the side, and Upon its being properly glued, and blocked. If the column .be fluted or reeded, the flutes or reeds are measured by the foot run, and their ‘price depends upon the size of the flute or reed. '. The headings of flutes and reeds are so much each. Pilasters, straight or curved in the height, are measured in the same way, and the price taken per foot super. In the caps and bases of pilasters, besides the mouldings, the mitres must be so much each, according to the size. Mouldings, such as double-faced architraves, base and surbase, or straight mouldings stuck by hand, _ are valued at per foot super. Base and surbase, and straight mouldings wrought by hand, are generally fixed at the same rate per foot, being something more than double-faced architraves. . The head of an architrave in a circular wall is . four times the price of the perpendicular parts, not only on account of the time required to form the mouldings to the circular plan, but on account of the greater difficulty of forming the mitres. All horizontal mouldings, circular upon the plan, are three or four times the price of those on a straight plan; being charged more as the radius of the circle is less. Housings to mouldings are valued at so much each, according to the size. The price per foot super of mouldings is regulated by the number of quirks, for each of which an addition is made to the fool. The price of mouldings depends also upon the materials of which they are made, or upon their running figure, whether raking or curved. The following articles are measured by the foot run. Beads, fillets, head or ogee capping, square angle-staff rebated, beaded angle-staff, inch ogee, inch quirk ogee, ovolo and bead, astragals or reeds on doors, or on shutters; small reeds, each in reeded mouldings stuck by hand up to half an inch, single cornice or architrave, grooved space to let in reeds, and grooves. Note. In grooving, the stops are paid over and above, and so much more must be allowed for all grooves wrought by hand, particularly in the parts adjoining the concourse of an angle; and circular grooving must be paid still more. The other running articles are, narrow grounds to skirting, the same rebated, or framed to chimneys; . and rule-joints, cantalivers, trusses, and cut brackets for shelves, are rated at per piece. Water-trunks are measured by the foot run, the rate depending upon the side of their square. These ought always to be properly pitched,and put together with white-lead, and the joints ploughed and tongued; the hopper-heads and shoes are valued at so much each; moulded weather-caps at so much each; thejoiuts at so much each. Scaf- folding, Stc. used in fixing, to be paid for extra. Flooring boards are prepared, that is, planed, gauged, and rebated to a thickness, at so much each, the price depending upon the length of each board: if more than 9 inches broad, the rate to be increased according to the additional width; each board listing at So much per list. Battens in the same way, but at a different rate. RatesofLahour in Joiners’ Work from the Bench, according to the universal Method described in pages 162 and 163 of the First Volume of this Dictionary. The column on the left hand of the Table denotes the number of panels, the middle column the species of work, and the right hand column the rate in decimals, being the rate of the part or parts of a day required to the quantity signified at the head of the column; therefore, this rate being multiplied by the wages per day, gives the real rate of the work per foot, in shillings or pence, according as multiplied by shillings or pence. DESCRIPTION OF 1;- INCH DOORS. No. of Rate per szels. ft. super. 2. Both sides square .............. . . ...... . . . . . . . . . .06 Both sides square . ............ ................... .07 Bothsidessquare.... ..... ..... ....... .......... .08 . Quirk, ovolo, and bead front, and square back . . . ...... . .1 Quirk, ovolo, and bead front, and square back. ......... .11 Quirk, ovolo, and bead front, and square back . . . . . . . .12 Bead and flush front, and square back ..... . . . . . ...... .1 Bead and flush front, and square back ...... . ........ .11 Bead and flush front, and square back ..... . ......... .12 Bead and but front, and square back . . . . . ..... . . . . . . .09 Bead and but front, and square back . . . . . ........... .10 Bead and but front, and square back . . . . . . . . . . . . . . . . .1 1 Quirk, ovolo, and head, on both sides. . . . . . . . . . . . . . . r. .14: 919599529E®9£9$°9§r999t§5°99w99 Quirk, ovolo, and bead, on both sides. . . . . . . . . ........ .15 Quirk, ovolo, and bend, on both sides . . . . . . . . . . . . . . . . .16 Bead and but on both sides . .......... . ....... . . . . . .12 Beadandbutonbothsides ..... ................... .13 Beadandbutonbothsides.................. .. .14. Bead and flush on both sides . . ......... . .......... . .14 Bead and flush on both sides. . ...... . ...... - ...... . . I .15 Bead and flush on both sides . . . . . . . . . . . . ........ . . . .16 For every additional quarter of an inch inthick- ness, add .005 to the rate per foot super. If the panels are raised on one side, add .002; and .101 175 301 if on both sides .004: and if an astragal or ovolo I fits-(151,12: on the rising on one side, add .003; and if on both sides .006; to the rate per foot super. If the price of a foot of a square door, and the number of panels are given, and the price of a foot of a door square on one side, with the same number of panels, and. with extra work on the- other side; then, the price of a door with the same number of panels, and the same extra work on both sides, will be found by subtracting the rate of the first from that of the second; and adding the difference to the second, will give the rate per foot extra on both sides. Thus the rate per foot super'for 1}; inch two panel door, square on both sides, is .06; and the rate for 15 inch two panel door, square upon one side, with quirk, ovolo, and bead upon the other, is .1, their difl‘erenee is .04, which added to .1 gives.14, for the rate per foot of 1% inch two panel, with ovolo_ and bead on both sides of the framing. The difference of workmanship between square- framed door—linings, backs, elbows, sofiits, or wainscoting and doors that are square on both sides, supposing the panels and thickness to be alike in both cases, can only arise from planing the panels and the framing on the other side of the door; therefore if the difl'erence of the rate per foot of a door square on both sides, and one square on one side, with any extra work on the other, be added to the rate per foot of door-linings, backs, elbows, soi’fits, or wainseoting, framed square, will give the rate per foot for door-linings, window-linings, or wainscoting, with the same extra work. In these rates the stiles or rails are supposed without rebating. Framed linings for walls or apertures, may be made of stuff 1 of an inch thinner than doors. In common cases, the thick- ness of linings may be about an inch, as the are rendered sufficiently stifl“ by being fixed to the wall; this, however, must depend (upon the distance, that the panel recedes from the face of the framing, or upon the depth which the mould- ings are run in the thickness of the said framing. No. of FRAMED INCH LININGS. Rate per panels. . ft. super. 1. Square,asinbacks...... ....... .................. .051 3. Square, as in backs and elbows, measured together. . . . . . .071 4. Square, as in backs, elbows, and sofl‘its . . . . . . . . . . . . . . . .061 3. Moulded, as in backs and elbows, together. ..... . . . . . . .087 4. Moulded, as in backs, elbows, and sofiits, measured together .077 3. Quirk moulded, as in backs and elbows, measured together .095 4. Quirk moulded, as in backs, elbows, and soflits, measured together......... ... .085 Semicircular moulded soliits in two panels, seven times the straight. . For every'additional quarter of. an inch, add .005 to the foot super. In the column of panels, the backs, elbows, and soflits, are numbered 3 and 4- panels, as being classed together, though this is the case, they are intended to be framed in single panels. = 1% INCH DOOR LININGS, Having only one panel in height. Rebated.... ............ ..... ........... .......... .051 Rebated and headed ........... . .................... .058 Double rebated, not exceeding seven inches wide ...... . . . .067 Double rebated, and one edge beaded ................... .071 Double rebated, and both edges beaded ................. .075 If the plan be circular, the price will vary as the diameter is less. Semicircular heads, straight on the plan, five times the straight. _ —.__. SHUTTERS. Inch framed, uncut, shutters or flops, two panels in. height. Mouldings, when described, are understood to be laid in, but g‘fstuck on the framing to add .012 to the rate; for every extra panel, to add .016 to the rate; for any extra height, to add .012 to the rate: y” quirked moulded, add .008 to the rate if moulded. Square ....... ......... ......................... .. .071 Bead, but, and square . . . . . . . . . . ............... . ..... .1 Bead, flush, and square. . . . ........... . ........ . ...... .111 Bead flush, and head but . . . ............... . . . . . . ..... .131 Inch and quarter uncut shutters, two panels in height, to add for extras, as above. Moulded and square .1 D’Ioulded bead and but ............ .......... . ........ .111 Moulded bead and flush. . . ...... . . . . . . . .............. .135 Moulded on both sides ........... . . . . . .............. .111 Ovolo and bead, or quirk ogee front, and squarelback. . . . . . .103 Ovolo and head, or quirk ogee front, with head and but back .123 — —— 1—}; INCH WAINSCOTING, Two panels high, including square facia, framed up to ceiling. Square ....... ............ ....... . ...... ..... .039 Moulded ..... ..... ...... ............ .055 Quirked moulded.... ...... ..... ......... . ......... . .063 Bead and but ..... ........ ........ . ............. ... .051 Beadandflush ....... .......... ....... .....-....... .059 Bead and flush, with3 reeds ....... . ....... .. ...... .075 If any of them are framed with raised mouldings, add .008 to the rate; or, if framed with more panels in the height, add .006 for every additional panel. JOI n '- —, 1% INCH DWARF WAINSCOTING. With one panel, including square skirting. Rate per ft. super. Square ....................................-....... .047 Moulded...... .063 Quirkmoulded .071 Bead andbut....... 'ooo--.Io‘ooooooo-ooooso.c-onuoo :059 Bead and flush ...... .067 Bead and flush,with3reeds .......................... .083 If any of the above descriptions of dwarf wainscoting are framed with two panels in height, add .016 to the rate, as in full wainscoting. If made raking to stairs, to be paid for extra. 023, and if with raised mouldings .007. All cappings to be measured, and paid for as in running articles. All skirting to stairs, to be paid for separate from wain- scoting. = TH REE-QUARTER INCH DEAL, From the bench, called Slit Deal. Edgesshot .... . .004 Wroughtononeside.................. ............. . .016 \Vrought on one side, grooved, tongued, and beaded . . . . . . . .008 \Vrought on two sides, and edges shot. . . . . . . . . . . . . . . . . . . .028 Wrought on two sides, grooved, tongued, and beaded . . . . . .04 It'gluedjoints,add perfoot . .00-1 INCH AN D QUARTER DEAL. Wrought on one side, and edges shot . . . . . . . . . . . . . . . . . . . .02 \Vrought on two sides, and edges shot . . . . . . . . . . . . . . . . . . .032 Wrought on one side, ploughed, and tongued . ...... . . . . .036 Wrought on two sides, ploughed, tongued and beaded . . . . . .052 If glued joints, add .004 to the rate :1...- INCH AND HALF DEAL. Edgesshot . .008 Ploughedandtongued ..... ....... .024 \Vrought on one side, with edges shot . . . . . . . . . . . . . ..... .02 \Vrought on both sides, with edges shot. . . . . . . . . . . . . . . . . . .036 Wrought on both sides, ploughed and tongued. . . . . . . . . . . . .052 If glued joints, add .012 to the rate. = TWO INCH DEAL, From the bench. Edgesshot................. ....... ................ 02 Ploughedandtongued............................... .036 Wroughtononeside.....v... ..... ..... .028 Wroughtonbothsidcs... ..... ....... .............. .044 \Nrought on both sides, ploughed and tongiled. . . . . . . . . . . . 056 It glued joints, add .016 to the rate. — TWO AND A HALF INCH DEAL, From the bench. Edgesshot .... .. .028 Plollghed and tongueduuu...-o...”nun-...”... .048 1’76 JOI Rate per ft.super. Wroughtononeside......................."........ .048 Wroughtonbothsides...... W. .063 Wrought on both sides, ploughed and tongued . . . . . . . . . . . .083 If glued joints, add .016 to the rate. THREE INCH DEAL. Edgesshot.. ............... ...... .032 l’loughed andtongued............................... .056 Wroughtononeside ..... .. ............ ............. .056 Wrought on two sides .................. .08 Wrought on both sides, ploughed and tongued If glued joints, add .016 to the rate. .103 “ _— INCH BOARDING. ONE SIDE PLANED. Ploughedandtongued....................... ...... .. .0354 rGluedjoint ..... ........ ..... ..... ....... .......... .03 Clamped . . ................. . .......... . ........ . . . .056 lVIortise-clamped .......... s . . . . . . . . . ....... . . ....... .0015 Laid with straight joint in floors . .......... . . .......... .02 Dado keyed . . . . . . ........ . . ..... . - . ............... .014 Keyed in backs and elbows . . . . . ................. . . . . . .056 INCH BOARDING, WROUGHT ON BOTH SIDES. Ploughed and tongued ......................... . . . . . .036 Glued joints. ........... . . .' ................... .04 Groove—clamped flaps to shutters, In one height .......... .053 Clamped flaps to shutters, in two heights. . . . . . ........... .071 Inch mortise-clamped outside shutters. . . . . . . . . . ........ . .063 Ledged doors with plain joint ........................ .044 Ledged doors, ploughed, tongued, and beaded. . . . . . . . . . . . .056 _ —.——. PREPARING FLOORING BOARDS, To be gauged to a width, and rebated to a thickness not more than nine inches wide. Rate or Inch Deal. each boil r d. Tenfeetlong....................... ............ .063 Twelvefeetlong................ . .. .075 Fourteenfeetlong.... ...... .. .087 15 Inch Tenfeet.............. ......... ................... .071 Twelvefeet..................... . .. ........... . .083 Fourteenfeet....................... ... 1 Buttens 1;} inch. Tenfeet.......................................... .044- Twelve feet.............................. Fourteenfeet........................... .056 ............ .075 Rate per ft. MOULDINGS. super, from the bench. Double-faced archilraves . . . . . . . . . . . ..... . . ....... . . . . .111 Baseorsurbase ........ ....... . ....... .137 Above four inches girl, stuck by hand. .................. .127 If a collection of mouldings have more than two quirks, add .016 for each. JOI RUNNING ARTICLES. Per foot lineal. Beads and fillets.................................... .004 Beadorogeecapping._......................... ..... .016 Inchogee... ..... . .......... .. ...... ............ .016 Inch quirked ogee or ovolo and bead. . . . . . . . ..... . . . . . . . .023 Squareangle-staffrebated. .028 Angle-stat? rebated and headed ......... . . . . ...... . . . . . .048 Single cornice or architrave. . . . . . . . . . . . . . ..... . . ..... . . .048 Small reeds, in reeded mouldings stuck by hand, to half an inch ........ . . ..................... . . . . ...... . .004 Reeds above half an inch, stuck by hand, including grooved space ........ .. ......... ...... .......... .008 Grooves in ornamental work. . . . ....... . . . . ............ .004 Narrow ground to skirting ..................... . . . . . . . .011 Narrow ground to skirting, rebated or grooved . . ..... . . . . . .016 Narrow grounds framed to chimneys. . . . . . . . . . .......... .032 Double-beaded chair-rail ................ . . . ..... . . . . . .023 Plugging included in the above rates. Such of the above running articles as are circular on the plan, must be rated at double the straight. Legs, rails, and runners to dressers ............ . . ....... .055 Rule—jointstoshutters................................ .063 — _—. INCH AND INCH AND QUARTER FRAMED GROUNDS TO DOORS. Rate per run from the Bench. Both edges square .................... . . . . . . ........ . .028 One edge square, and the other rebated and headed ...... . .032 Rebated on one edge, and both edges beaded ............ .036 It framed to a circular plan with a flat sweep, the head to be three times the straight, but the less the radius the greater the price. = STAIRS. 1,],— inch nailed Steps with Carriages. Rate per ft. super fired. Flyers........... ......................... . ........ .08 Winders .......... . .......................... ..... .111 Flyers moulded and glued with close string-board. . ........ .103 Winders moulded and glued with close string-board . . . . . . . . .135 Moulded planceer under steps . . . . . . . . . . . . . ....... . . . . . .04 Housings to fiyers, .127 each. Housings to winders, .2 each. Common cut brackets to fiycrs, .143 each. Common cut brackets to winders, .286 each. All fancy brackets to be paid for at per value. = HAND - RAIL. 2 inches deep by 2% inches broad. Rate per ft runjired. Dealmoulded... ..... ................. .111 Deal moulded and ramped ........................ . . . . .495 Deal moulded, level circular ...... . . . . . ...... . . . . . . . . . .413 Deal moulded wreathed . . ............... . . . . . . . . ..... 1.2 Mahogany moulded straight. . . . ....... . . . . . . . . . . ..... . .263 Mahogany moulded ramped . . . . . . . . . . . . ...... . . . ..... .831 Mahogany moulded swan-neck ......... . . . . . . . . . . . . . . . .927 Mahogany moulded, level circular ........... . ......... 1.08 Mahogany moulded wreath, from 12 inches and above . . . . . 1.6 Mahogany moulded wreath, under 12 inches ..... . . . , . . . . 1 8 Mahogany moulded wreath, not less than 12 inches opening. 2. 8 Mahogany moulded wreath, under 12 inches opening . . . . . . 3 4- V 0 L. I I . .101 W Mahogany moulded cap, wrought by hand,.495 each. Mahogany moulded cap, turned and mitered, .4 each. Mahogany scroll, 1.8 each Making and fixing each joint, with joint screw, .231. Making model, and fixing iron balusters, each, 2.095. Making model, and fixing iron columns to curtail, each, 2.142 Preparing and fixing deal bar balusters, each, .04. Preparing and fixing deal bar balusters dovetailed to steps, .056. Extra sinking to rail, for iron rail or balusters. . . . . . . . . . . . . . .032 Extrasinkinginramporwreath . .....................\. .1 Every half rail to be measured two-thirds of a whole. All rails to be measured three inches beyond the springing of every wreath or circular part. All cylinders used in rails glued up in thicknesses, to be paid for extra. Articles rated at so much each. Clamp mitres. Cuttings to standards. Housings in general. Housings to steps. Housings to mouldings. Each scribe of skirtings to nosings of steps. Elbow cappings. Curtall step. Returned moulded nosidgs to steps. Caps to hand-rails. Scroll of hand-rails. Making and fixing joints of hand-rails with joint-screws. Fixing iron columns in curtails of stairs and p1eparing mould. Fixing non balusters, and preparing mould. P1epar1ng and fixing deal baluste1s. Brackets to stairs. Mitres of pilaste1s according to their size. Headings offlutes and reeds. Hopper- heads to water-trunks. Shoe to water-trunks. Moulded weather caps to water-trd‘rlks. Joints to water-trunks. Preparing flooring boards. Preparing battens for floors. Listing boards. Articles rated at per foot lineal. Sinking to shelves. All raised panels on the extremity of the raising to be charged extra. Moulded raisings of panels. . Coping to wainscoting. Level circular string-boards to stairs. Hand-rails. Newels to stairs. Moulded planceer in stairs. Sinking to rail for iron rail or balusters. 2 A J OI 178 JOI’ Pilasters under 4 inches wide Boxings to windows. Water trunks. Skeleton grounds. Flutings to columns. Beads or fillets. Bead or ogee cappinoa Square angle-staff rebated. Beaded an gle-stafi“ rebated. Inch common ogee. Inch quirk ogee. 0volo and bead. Astragals on doors. Reeds on doors. Reeds on shutters. Single cornice. Single-faced architrave. Ornamental grooving. Narrow ground for skirting. Narrow grounds for chimneys. Legs, rails, and runners of dressers.. Rule-joints. Framed grounds. Skeleton grounds. Articles rated at per foot super. Planing, ploughing, tonguing, beading, gluing, and clamping deals. Skirtings. Sash-frames. Sashes. Sashes and sash-frames, Sky-lights. Framed back linings. Back elbows and soflits. Shutters. Door linings. Doors. VVainscoting. Partitions. Dado. Steps to stairs, including carriages. Cradling. Double-faced architraves. Mouldings wrought by hand. Shafts of columns. Articles done by the square. Laying floors. Articles at per value. Belection mouldings. All fancy-works. The English writers who have treated upon W joinery, are, Moxon, in his Mechanical Exercises, second edition, printed 1693; Halfpenny, in his Artqf Sound Building, small folio, 1725; Oakley, in his Magazine qurchitecture, folio, 1730; Price, in his British Carpenter, quarto, 1735; Hoppus, in his Builders" Repository, quarto, 1738; Batty Langley, in his Builders’ Complete Assistant, royal octavo, 1738; Salmon, in his London Art of Building, third edition, small quarto, 1748; Mr. Abraham Swan, in his Architect, folio, 1750; Pain, in almost every one of his works, particularly in The Carpenters’ and Joiners’ Repository, The British Paladio, The Practical Builder, and in The Prac- tical House Carpenter; and the Author of the Architectural Dictionary, in The New Carpenters’ Guide, published in quarto, 1792; in The Carpen- ters’ and Joiners’ Assistant, quarto, 1792; in Rees’s Cyclopedia; and in the Mechanical Exercises, octavo, 1812. From these Authors we shall here collect such ex- tracts as relate to mechanical principles, or to geometrical construction, in the order of the above list. Moxon treats the subject merely as a manual art. The following is extracted from Halfpenny’s Art of Sound Building; he seems to have been the first writer who considered Joinery in a geometri- cal point of view, his knowledge, however, is en- tirely confined to Hand—railing. “ Tofind the raking arch, or mould,for the hand- rail to a circular pair ofstairs, in such manner that it shall stand perpendicularly over its base, or arch of the (cell-hole. Figure 95. “ First describe a circle equal to the breadth of the well-hole, whose diameter is U W; as also another from the same centre, whose diameter is A G, to represent the plan of the rail; and divide the circumference of the greater circle into the same number of equal parts as you would have steps once round the circle. “ This being done, take the back, or rake, of the bracket, equal to CF, in your compasses, and setting one foot in A, with the other strike the arch h: also take the height of one step, as A C, Figure 96, and setting one foot in B, with the other strike the arch i; and when this is done, take the distance from A to h in your compasses, and setting one foot in h, with the other strike the arch k, and take the height of two steps, and With one foot in C, draw the arch l, to inter~ sect the arch k, and so on. ; J01 J01 W “ The intersecting pointsof the arches h i, and kl, _ and no, and rs, and tu, are all at the same dis- tance from one another, and the lines B h, C 1:, D71, Ep, Fr, and G t, being the risings or heights of the steps, in Figure 96, Bh being the height of one step, Ch of two, D n of three, E1) of four, Fr of five, and G t of six. Now if these lines are raised up perpendicular on the circle A D G, it is evident that the point of intersection of the arches h and i, will stand perpendicularly over the point B; of the arches k, I, over C; of the arches n and 0, over D; of the arches p,g, over E; of the arches r and s, over F; and of the archest and u, over G. Now if nails be struck into the intersecting points of the said arches, and a thin rule be bent round them, you may describe the arch, A h h” n p r t, by the edge thereof, being the mould to strike the arch of the rail with. “ The arch or mould of the rail being found, as above, how to prepare the stufl' of which the rail is to be made, and work the twist thereof without setting it up in its due position. Figure 97. “ First strike two circles, whose dia- meters are equal to UVV and A G, in Figure 97, and next consider into how many pieces you glue the rail, which in the semicircle let be six, as in the example. “ Now divide the semicircle into six equal parts, as EF, FM, MS, SL, LD, and DK; from each of these points of division, draw lines to the centre A, as A E, AF, AM, AS, A L, AD, and A R. Then from F, raise F G, perpendicu— lar to A F, and equal to the height of one step. Also at the point M, raise M N, perpendicular to A M, equal to the height of two steps; and in like manner at the points S, L, D, and R, raise the perpendiculars ST, L Y, D E, and RL, re- spectively equal in length to the height of three, four, five, and six steps. Then draw a line from G to R, parallel and equal to AF; as also an- other from N to 3/, parallel and equal to AM; another from T to W, parallel and equal to S A ; another from Y to B, parallel and equal to LA; another from E to H, parallel and equal to D A ; and another from L to P, parallel and equal to RA. From the point A draw the line A B, per- pendicular to AE, and equal to the height of one step; also at the points By, W, B, H, P, draw the lines RL, Y Z, ‘V X, BC, H I, PO, all equal to the height of one step, and re- spectively perpendicular to R G, g N, TW, Y B; E H, L P, and draw the hypothenuses EB, LG, ZN,TX,YC,-EI,LO. _ “ This being done, set of? the width of the rail from E to d, Gtoi,N to o, Tto u, Y to a, E tof, and L to m; and set the stem of a square on the line EB, till the blade touches the point d, and draw the line cd. Moreover, set a square on the line G L, and where it cuts the line R G, as in the point i, draw the line hi; and in like manner draw the lines p0, un, za, gf, and um. Then the angles Edc, Gih, Npo, 8m. and the rest of the little black spaces, as you see in the Figure, do represent the twisting of eachpiece, and what must be taken ofi“ from the back at the lower end, to make the twist of the rails. The lines being drawn, you are next to consider after what manner they are to be applied in the working of the rail. - “ Take the piece of timber, of which you design to make the first length, which is represented in Figure 98, and plane one side thereof straight, and cut it to its bevels ac, bd, answering to D RA and RDA, Figure 97, and both ends thereof being also cut to the raking-joint of the rail, proceed thus: Take that part of the raking-arch in Figure 95, which answers to the first length of the rail, as A h in the arch A z, and lay it on the upper side of Figure 98, from [to h, and strike the arch lh, then take Ec, equal to G h, or Np, in Figure 97, and set it on the line bd from h to m, Figure 98, and strike a square stroke at pleasure from m to g; also take cd equal to hi, orpo, dye. and set it on the line from m to g, and draw the line hg, which represents the back of the rail when it is worked, and is equal to Ed, or G i or N 0, the. This being done, represent the lower end of the rail h g hi at right angles to h g; as also the upper end to o n at right angles to lo, and baste out the inward arch cm square from the upper side a bed, as mg; and take a thin lath, and bend it close to the side thereof, from c to g, whereon strike a line along the edge of the lath, and so the lines [/2 and cg are your guides in backing the rail: which, when done, turn the piece upside down, and with the mould strike an arch equal to Zh, from u to k, and baste out the side to the lines lh, and ok: then you have one side and the back squared, which is the greatest difliculty in the formation of a twisted rail, because the ,two other sides arefound by gauging from them. 0 A Q 'd JOI 180 “ Note. If the triangles in Figure 97, and lines, whereon they stand, be supposed to be raised up perpendicularly, then will the lines AB, K L, yZ, W-X, BC, H l, and P O,join to each other, and produce one line perpendicularly over A, equal to seven risings or heights of the steps. But in working a rail of this kind, you have need of but one triangle, A B c Ed, because they are all equal, and of but one effect in working, they being drawn only to satisfy the curious in the nature of the thing.” He finds the moulds for elliptical staircases in a similar manner, viz. by finding an arch line divided into equal parts, so that each of them may be equal to the liypothenuse of the pitch-board and the distance of the points of division in succes- sion respectively equal to the heights of the steps : this principle is to be understood in all staircases where the steps are equally divided at the well- hole, whatever be the form of the plan: but in elliptic staircases, the degree of twist is different, and therefore requires a pitch-board to be made for every portion. It is hardly possible to conceive any method so distant from principle, as what is here shewn: the squaring of the wreath is altogether guessed at, not to mention the great disadvantage in making the rail in so many pieces. If the rail were really executed, the above method would then be a property, but the moulds never can be obtained from any construction in plano upon the same consideration. It is rather astonishing that any attempt should be made at demonstration, for the support of a method so entirely destitute of prin- ciple as the above. “ How to form the arch or mould to the hand-rail of‘a pair of stairs that sweeps two steps, so as to stand perpendicularly over its ground, and the man- ner of'squariug the same, without setting it up in its position. “ First, draw Figure 99, to represent the ground— work of the rail, whose arch, G C, consists of two different arches, one whereof is a quarter of a circle, the other a quarter of an oval. AB (equal to AC, equal to C D, equal to BD) is equal to one-third of a step; and D is the centre to the arch C B; also, B F is equal to two-thirds of a step, and F G is equal to one step and two-thirds; by means of which, and B F, is the arch G B de- scribed. G K represents the straight part of the rail to one step, and the arch H D is drawn by J 01 I 4 gauging from the archG C; that is, it is drawn parallel to it, and the straight part I H is found by gauging from KG, or is drawn parallel to it. Figure 100, “ shews the manner of drawing the rake or arch of the rail, which is done thus: draw I L equal to G K of Figure 99, and represent the tread of the steps as before, by pricked lines. Then divide that part of the ground-work of the rail which belongs to each step into any number of equal parts, as AF into five, and F K into four. This being done, draw A B, BC, C D, in Figure 101, to represent the rising and tread of the steps; and continue out the line C B, at pleasure, towards T, in which set the five divisions on the ground of the rail to the first step, F E, of Figure 100, being equal to C l, of Figure 10]; also, ED equal to ik, DC to k l, C B to l u, and BA to u T. Then will the line CT, in Figure 10], be equal to the arch AF, of Figure 100; draw the line D T; then is the triangle C D T the bracket to the first step, according to the sweep of the rail; and as T C is the length of the ground to the first step, so is T D the length of the rail an- swering to it. Then from the points i, k, l, u, raise the perpendiculars i P, k Q, Z Z, and u S, to CT; and take the four divisions on the second step, and set them in the line C T, from C to B, and draw the line BD; and then is BC the length of the ground to the second step, and B D the length of the rail answering to it. Draw lines through these divisions, as from F to m, G to n, and H to o, perpendicular to C B; and so your perpendiculars are found according to the com- pass brackets of each step, and may be pieced thus. “ In Figure 101, take T S in your compasses, and with that distance, setting one foot in A, in Figure 100, strike the arch m, and take S u be- tween your compasses, and with one foot in B strike another arch to intersect the arch m. Again, take SZ, or S T, in your compasses, and with one foot in the intersection of the arch m and this latter arch, describe the arch n; and take [Z in your compasses, and with one foot in C, describe an arch to intersect the arch n; and thus proceed on, so that z 9 be equal to n 0, Q P to op, P D topq, q ztoB o, zsto o n, st to nm, and tu to m l); as also kQ to Do, iP to Ep, CD tqu,Ho toGz,Gn to H S,Fm toIt, EDto K a, L to to three times A B. The points u, o, p, q, r, s, t, u, '0, to, being found by the .intersec‘ JOI 181 .101 [W tion of arches, as above, stick a nail into each point, and bend a thin rule about the nails, till it touches them all, then with a pencil describe an arch round the edge thereof, which will be the arch A 02), being that of the rail to work by. “ Figure 102 shews the manner of squaring the rail,which is thus: first,describe A F, the square, or ground of the rail, being the same as that of Figure 99, and find the centres to answer to the different arches of the ground; from whence draw pricked lines to the places where you design to join the rail, as from G to B, from G to C, from from H to E, and from H to d. Because the first step is to he joined in three equal pieces, you must take one-third of the rising or height of the step, and set it from B to I, perpendicular to B G, and draw the line hi I, parallel and equal to G B. Now from M to n draw a perpendicular to M I, to rise so much as the rail rakes over, which is one-third of the rising or height of the step, be- cause that part of the rail is one-third of the length on the first step; and draw the line I n, by which means we shall have the first triangle I M n. Then from the point C draw C q, perpendicular to G C, and equal to two-thirds of the height of one step; and draw the line 9 z, equal and parallel to C G; and from 2 raise a perpendicular, z s, to 2 (1, equal to one-third of the height of one step, and draw the line q s, and you will have a second triangle. Again, from d draw d T, perpendicular to H d, and equal to the height of one step, and draw the line T W equal and parallel to H d; and from “7 erect the line W X, perpendicular to W T, and equal to the height of one step, be- cause that part of the rail over the second step will be one piece, therefore the triangle must rise one height of the step; and draw the line T X, and so you will have a third triangle, VVX T. This being done, from I, in the line 1 M, set off I 1:, equal to the width of the rail; also set off the same from g to o, and T to u, and setting the stem of a square on the hypothenusal line, so that the blade thereof touches the point It, draw the line I: l; and in like manner draw the lines p o, u v; and then the little triangles I It l, q op, T u e, do represent what must be taken off from the lower end of each piece, to bring the rail to its true twrst.” The form of the scroll is only a subject of fancy, but what has been quoted from this author, will shew the difference of taste between the time when such were in use, and those of the present day. No elegant geometrical forms seem then to have been employed. _ As to the construction of the raking-mould for the scroll, it is done in a simi- lar manner to the twist of the rail, before shewn ; and therefore equally destitute of principle. Mr. Edward Oakley, in his Magazine of Architec- ture, has copied Halfpenny’s descriptions and dia- grams; to which we refer the reader. The next work under review is The Britisk Car- penter, by Francis Price. The article joinery is almost confined to hand-railing, as in the preced- ing authors. Mr. Price proceeds as follows : “ Tofind the proper kneeling and ramp (3)“ rails.— In Figure 103 is represented a short flight of four steps, and part of a half—pace, on which are shewn two balusters on a step ; a bis the rise or height of one step, and b c is the newel, generally two feet four inches and a half high, and sometimes two feet six inches high, Ste. and c d is the thick- ness of the rail; the kneeling, o, is in the middle of the first baluster; from e to f is also the height of the first step on the half-pace; andf g the height of the newel, agreeable to that of b c; and g It is the thickness of the rail; from It to i is generally the same as from o to c, which line, It 2', continue at pleasure; for on it is the centre for the ramp. With your compasses find the centre, k, which touches the back of the rail, 72, and the point of the ramp, 2'; find the point of touch, 72; draw the line kn; describe the ramp, and also the turned part of the balusters, as may seen by the pricked line. “ Over this is represented the alteration, that ought to be made, if you place three balusters on a step; that is, that the kneeling ought to come to the back-side of the first and last balusters, as at p and g. If it be said, the method in Figure 103 is not fully expressed; to find the height of the ramp agreeable to the kneeling, let Figure 104 be the rail, the bottom is continued as by the pricked line appears at u and to; take the distance, ut, and set from w to x; from 1‘ set one rise, or the height of one step, as at y, and that gives the height of the ramp, and is the same as the method in Figure 103, notwithstanding they differ in appearance. “ In Figure 105 is shewn the manner of fluting newels forstairs, as 3“; and also balusters, as 1*; the newel having twelve flutes, and the balusters eight. If the stuff be large, the flutes may vary; thus the newels to have sixteen flutes, the balusters twelve.” JOI 189 'J OI We cannot comment any farther on the above, than that it shews the method of describing the ramp of a rail, and the difference of taste in the age of Price, from that now in use. vThe de- sign, the quantity of work, and the massy parts, which characterised that time, when contrasted with the slightness and plainness ofwork executed in the present day, are really astonishing. Our hand-rails are very light, but very neat; when ornamental work is used, it is chiefly confined to iron, being rarely constructed in wood. “ Whatever may appear difficult in this method of forming scrolls proper for the plans of twisted rails, due application will make easy and expe— ditious. “ First, form a scroll with chalk, or a pencil, agreeable‘to the bigness of the place in which it is to stand; next resolve on the bigness of your stuff to be used for your rails, and also your mould- ings on the side thereof, as in Figure 106. Let d be the centre of your chalked scroll in Figure 107; on which describe, with the projection of your mouldings from Figure 106, the small circle (1; take from Figure 106, half the bigness of the stufl‘, as e g, or ef, which add to the small cir- cle, and form the circle It i t, which is the big- ness of the eye of the scroll: this done, take the distance from i, tothe inside of the rail, as the supposed chalked scroll, which suppose k; with it, make a diminishing scale, by setting that dis- tance up, from t to I; draw the line kl; place one foot of your compasses in k, describe the part of a circle t 8, which divide into eight equal parts, because here your supposed chalked scroll was to come into its eye, or block, at one revolu- tion of a circle. (Scrolls may be made to any number of revolutions desired, by the same rule, witness that above, in Figure 108.) “ Place one foot of your compasses in d, describe the large circle to Z I 21, which always divide into eight parts, because you strike one-eighth part of a circle every time, till you come into the eye, or block, itk; from the said divisions on the large circle, draw lines through, for on them your sections meet, which form the scroll. It is observable in drawing your sections, that they do not end in the line drawn through the great cir- cle, only the outside scroll; for those of the in- side scroll end on a line drawn to each respective centre. I suppose A and B to be two steps; the “rest I think cannot fail of being understood, by observing the letters and figures, which shew each part distinctly.” Mr. Price’s advice, to make a scroll first of chalk, is altogether ungeometrical, and therefore unv worthy of notice. The method of forming it is of Italian invention. A similar construction is used in describing the Ionic volute in Daviler’s Cours d’Arclzitecture, dated Paris, 1720. He ascribes the invention to Vignola. But, in our opinion, it is far from producing that agreeable variation of curvature required. The opening next to the eye expands too rapidly towards the extremes. A much more perfect method, and not very dissimilar in construction, is that pub- lished in the Joiner’s Assistant, by the Author. See the articles SPIRAL and SCROLL. “ In order to make the squaring of a twisted—rail ‘ easy, see the plan, Figure 109, which is the same as that in the foregoing Figure 107, and find the point of touch, I). From these curves a mould must be traced out, in order to form a sweep, which when applied on the rake, is agreeable to this of a b, c d, as that of Figure 110. (It is first to be observed, that you will want wood extraordinary, both on the top of the rail, as in Figure 111, at e, a; and also under the same, as g, It.) To find which, observe where your sweep begins, in the plan Figure 109, as at a c; also observe that o and n is the end of the twisted part. There- fore, from a to n, divide into a number of equal parts, so as to transfer them on some line, as in 112, from a to 7:; also divide the inside of 109, as from c to 0, into equal parts, so as to transfer them on some line, as in 113, from c to 0; take the distance e a, in 109; apply it to the pitch-board, as from g to 6; take the pitch-board, 114, with it place e to c, in 113-, draw the line (i q, and make the point 3; divide from d to 3 into eight equal parts, also from d to 0 into the same number; draw the lines, which form a sweep, whose use shall be hereafter shewn. “ Likewise take the pitch-board, 114, and apply e to a, in 112; draw the line ep, and make the point r; from e to r divide into eight equal parts; also from e to u do likewise; draw straight lines from each division: that curve shews how much wood is wanting on the back of the rail, as b t, which describe in 111, from e to a; and there describe the bigness of the rail; which sbews how much wood is wanting, as may be observed by what was said above. The other part of the twist is cut ii 5.11..) :...an.1.4 . .4524! A .11. 1A... . 1.1, .. . . . . . . .. . . I . 2.. J. , . .. :1 ; .15.... .. _...~.....;.,.m..w_ .. j r. ,.., . .. 4...... .. 13. .4 . .. {A e P .3 H .. . . . $\.\\ ..\\.\m..\.\ . M. F . \..\,\\\\ x. \ \\\\\ x . . .. $\.... ‘ .PIATE I Engraved by Wlmly. L n . » __. n. _ _ M n _ . M v m. _ . ' F9103. Immanuel“ 3...... , if £14m? _ m__.§:.;_ JOINERY ....\\ $ \ \\ \\ 65 \\\\ x W\ -P ,' £4ndon,-Mldrhed éqfiNMobonéjflwfidd,Wwdow$mM.. ...-.. . . .. _.,_. ._ w \ .. .11.»: A; ”Lu-(Lug... Z . 4M 2... -Dnzwn. by Efifi'dwb'zm. .101 ‘183 101 M out of a parallel piece, as 115; which thickness extraordinary is shewn in 111, at e a. “ To square the twisted part of the rail, having so much wood extraordinary on the top and bot- tom, observe in 109, from a to e, and from c to], must be traced, as was above mentioned. Take a e, in 109, apply it to the pitch-board 114, it shews g i, which length place in 110, from k to 2'; also, take from 109, the distance 6 d, apply it to the pitch-board 114, it shews g m, which length place in 110, from [to m. This done, trace out the raking- mould 110, agreeable to the plan 109, which by inspection and a little practice will become easy, and without which nothing is known truly. I say, the wood extraordinary being accounted for in 11 1, both on the top and the bottom of the rail, observe to place your strokef, in its true place, that is, at the beginning of the twisted part; take the raking-mould, 110, set i tof, in 111; there strike it by; with the angle ofyour pitch-board describe the pricked linef, by the side of the rail; then apply the mould, 110, to the bottom; set i to this prickcd line, and there describe by it, with your pencil. Lastly, cut that wood away ; also cut the remaining part of the scrOll out of the block, as _ 115 ; then glue these together, and bend both moulds, 112 and 113, round the rail; strike them by that, and cut the wood away; so will the back of your rail be exactly square, and fit to' work.” This method of squaring the twist of the scroll is correct; the principle is that of the section of a curved prism at right angles to a given plane, and amounts to no more than tracing a common angle- bracket. The construction, however, requires a very considerable addition to the thickness of stuff; and even this thickness will be variable, ac- cording to the place of the pitch-board. This method, though much superior to that of Half- penny, is not to be compared with that of springing the plank, introduced by the Author. Mr. Price says, that his method will apply to any twist or wreath whatever: we grant that it will, but then the stuff would require to be from four to eight inches in thickness, and some- times more. In drawing the section upon the plank, in order to be cut out, the shank of the . mould is always applied parallel to the arrises; this application occasions also a great waste. in the breadth as well as in the thickness. In the construction of the face-mould of the scroll, he employs the pitch—board of the flyers. He giVes no example of forming a wreath over winders, but if the same principle isto be applied, recourse must be had to a developement of the steps. It is unnecessary to make any farther observations, as the Author of the Architectural Dictionary in. tends to place these and his own before his readers, in order to compare and point out the specific dif- ferences of each, by proper diagrams, at the end of this article. ' “ You are always to observe this general rule, viz. To conceive each respective paragraph, as it oc~ curs, before you begin another; the neglect of which, appears by some who cannot conceive the particulars of the foregoing Figure, although I had put it in so clear a light. “ I have here described three distinct methods of squaring the twisted part of a rail, which may be known, and the rail squared, with more ease than in the foregoing Figure. But when done, they will not have that agreeable turn in their twisted part, as they would have, if done by the foregoing unerring rule, as may more clearly appear by the following explanation. “ That of Figure] 16, is the raking-mould, taken from Figure 110 (whose use and application was therein clearly shewn ;) that of 117, is the pitch- board, taken from 114; which gives the rake or declivity of the rail. “In Figure 118 is shewn how to square a rail, without bending a templet round the twisted part thereof; and which is by being guided by the back; first, describe the bigness of the stuff to be used, as a I) h 2', which shews how much wood will he wanted at bottom, supposing S to be the side of the rail. And because the grain of the wood should be agreeable to the falling of the twist, therefore consider how many thicknesses of stuff will make the wood required to cut the twist out of; as here three. Therefore, as in S, continue the line a I); place one foot of your compasses in a, make the section, or part of a circle, c d; di- vide it into four parts, as 1, £2, 3, 4, because the rail, S, must be always reckoned as one; this by inspection shews how the grain of the wood is to be managed, as appears by the shape of the seve- ral pieces, 119, 120, 121, which are better, if cut so by the pitch-board, before glued together. “ In 122 is shewn how to square the twisted part, making the bottom your guide; the section shews how much wood is wanted on the back. JOI “ In 123 is shewn how to square the twisted part, making a middle line on the back your guide; the section shews the wood wanting on the back, and at the bottom. “ That of 124 may be cut out ofa parallel piece, of the thickness of the intended rail, which, when it is glued to the twisted part, will want little or no humourinor. " N.B. There is a nicety in working the mitre ‘ thereof, as k l m.” The abOve method of forming the wreath by glu- ing different thicknesses together in parallel blocks, perhaps originated with Price, or might be in use among workmen in his time. The pro- cess is quite mechanical, and what might occur to any well-informed workman. And though the wreath might be got out of much less stufi' than by the former principle, it is tedious, and much more uncertain. To apply these properly, would require the workman to understand the method of orthographical elevations ; and though Mr. Price seems to have had a notion of this, his re- presentations of the wreaths are all drawn by guess, and are therefore not to be depended upon. Another method by which this might have been ascertained, is by a plan and developement of the twist, where the risings of the blocks might have been ascertained according to their several thick- nesses; we shall shew this improvement at the end of this article, accompanied with a diagram. “ You are to observe, the foregoing Figures must be well understood, and then, in these Figures the lengths of the newel and balusters that stand under the twist or scroll are truly described; that is, their lengths and bevels may be known before the rail be put up in its place; and, that it may prove easy, observe, the plan, Figure 125, of the twist or scroll is the same as before, and so are the two steps, Pand Q, and the pitch-board, 19.6. “ First, resolve on the bigness of your balusters, as a, b, c, d, e, f, and also the newel. Divide the said balusters truly on a line drawn in the middle of the rail; for then what is wide on one side, is narrower on the other. It is for that reason I choose to divide them on a middle line. Describe the plan of the balusters, asp q, r s, t u, u av, :c y, and z, for there your twisted part ends; from thence to the eye is level. “ Observe where your scroll begins, as at I, and on some line, as above in 127, first make a point at I; then from your plan take the distancesp q, 184: JOI W _ r - r s, t 'v, u w, x y, and 2, which transfer, as above, observing to have regard to place truly each distance from I, both ways, as p q, r s, t v, u w, .r y, and z. Observe also, to take from the plan the distance from I to m, which apply to the pitch-board R, as from h to n,which gives the length h 0; take this pitch-board, and apply it on the line above, which by inspection the letters will shew; this gives the slope of the rail, as It 0 8;. From 0 to h, and from It to 3/, form the curve by equal divisions, and drawing straight lines, as was before shewn. “ Lastly, having the lengths of your fixed ba- lusters, as a b, Figure 197, describe the steps Sand T,with the pitch-board; so that by continuing per- pendicular lines, from the points on the line first terminated, to the said curve and to the steps, you have the accurate lengths of the balusters, as a, b, c, d, e,f: the newel, g, being the same length asf, because atf, or z, the twisted part ends. “ The curve of the first, or curtail-step, Figure 125, is formed by the same rule as delivered for the plan of the rail. “ It may not be amiss to observe particularly the point of the sweep, or curve‘s beginning, and be- ing particular also in its application, by which this, and the foregoing, though represented with but two steps, is the same in fact, as though I had described a whole flight, to shew its use." To ascertain the height of the balusters is not of very great importance to workmen of the present day. The method is however correct, and though it might be laid down and expressed more clearly, it is as eligible as any that can be applied to the purpose. Price’s remark for taking the middle line fur the division of the balusters, is judicious. “ Zealous to promote what may be useful, I have made easy the difficulty of squaring a rail that ramps on a circular base. “ Observe, Figure 128 is the plan ofa staircase ; and at the landing is a quarter-circle: to make this easy, in 129, is three steps, described by a larger scale, and the same method as shewn in 103, 104. Likewise, 109, is the plan of the rail. It was shewn in 110, Ste. how to trace out a mould on the rake, agreeable to this plan, or indeed any other. A con— siderable thickness of wood more than usual is required on the back of this rail, as in 8r, at p, b, which will appear more plainly by inspecting 116, Ste. as also the method to trace your moulds that shall bend round the said rail. Let the sides be SOENERY. PLATE A. 4 [12,. 12 7. 124. 128. [7137. Z35. Drawn by -11 (14 (Mu/Jun. [mu/m1, Iii/1:111:11 /r‘1/ EJTI'fin/xnn X4 J. fiar/SHJ, [flirt/111w J‘h‘ec’f, 1314. £3157": wd 1’}! J [3. Taylor. 301. 18 W J squared, as was shewn in 109, 110, 111, 112, 113, 114, 1 l5. Observe here in Figure 129, the line k, p, 0,- take the distance [c p, and place it on some line, at pleasure, as in 130, then divide the outer circle, in 130, intoanumber of equal parts, as into six, as from g to h, which transfer to 131, as g, 1, 9., 3, 4, 5, 6, h. The point of the ramp may be ob- served to fall within the fifth division, as at s, so that by the intersection of straightlines, and equal divisions, you describe the sweep for the ramp, g I), which makes 131, the mould, to bend round the outside of the said rail. “ Observe also in 130, from b to]; divide it into six equal parts, which transfer to 132, as from c tof; and (observe again)the ramp falls within the fifth division, as at 1'. So divide the distance from e tog, and from g to 6, into equal parts, and by drawing straight‘ lines, you have the sweep b c. From the point I), to p, is the thickness you want to be added extraordinary on the back of the rail 139., and which is the inner mould; so that by bending both these moulds round the rail, and by drawing them with a pencil, and cutting away the superfluous wood, you have an exact square back. “ There seems no difficulty now left unmen- tioned, to square twisted rails in any form what- ever. “ Because I have all along strove to give variety, observe 133, in which is shewn a method to have your newel under the twist, the same length as the rest; by which means also the rail twists no farther than the first quarter, and consequently the remaining part may be cut out ofa plank, of thc thickness of your rail, without twisting at all. 'J'ln-re seems no explanation wanting to clear this point, but inspection, and a good conception of figures 109, 110, 111, 112,113, 114, 115: in this of 1:13, lfis the thickness of wood extraordinary wanting 011 the back of the rail.” rl‘he method which Mr. Price employs at 139, for ascertaining the thickness of stuff by a falling- mould, or (levelopement of the side of the rail, is incorrect; nor can it be found in a determinate manner without an orthographical elevation of the part of the wreath to be formed. This con- cludes the whole substance advanced by Price in the article Joinery, and shows improvement only in its infancy. Mr. Price has also shewn the method of forming raking-mouldings for pediments, as follows: “ And in consideration that no pediment can be V0 1.. 11. JOI w performed without two kinds of cornice, (exCept it be knee’d at its bottom or springing, which is reckoned a kind of defect,) therefore to give each of the cymas such a shape, or curve, as shall strictly agree in their mitre, do thus: Describe the curve of the level cornice F, Figure 134, as a b c, by two such portions of circles, as that the centres for forming each may be on a horizontal or level line, drawn through the middle of the said cyma; as 3“ ”’9, c, d; being the projecture thereof. Draw lines from the points of the said cyma, agreeable to the slope of the pediment, which gives or ter- minates the bigness of the raking cornice or cyma G; so that by drawing a line through the middle of the said member, on’ it are the centres * *, by which the curves efg are described; the pro- jecture, h g, being as before. In case a break or return be made in the pediment, then another kind of cyma must be formed, which shall agree with the two former, as H; the centres for form~ ing each curve being on an horizontal line drawn through the middle of the cyma, as before; 2' k l is the curve, whose projecture, as before, is lm. These three kinds of cornice being thus formed, will agree with each other, without the trouble of tracing. But if the given curve be not described as before, then observe the method proposed in 135; by which the curve ofany raking-mould what- ever may be truly described. Admit the cornice given were K; n o 1) being its curve, and p 9 its projecture; by making points on the said curve, draw lines from them, agreeable to the slope of the pediment, on which place each respective pro- jecture from K to L, so is r s 1‘ its curve, the projecture being t u, as before. And if a break or return be made, as M, then transfer the several projectures from K, observing that the points he on the lines drawn agreeable to the rake of the pediment, so will to avg be the curve, and y z the projecture, asbefore : which no doubt but in- spection explains.” The scheme forraking-mouldings, shewn at 134, is not to be depended upon. It is evident that since the figure is a prism, and since the given curve is composed of circles, the curves required must be composed of elliptic segments, unless the sec- tions are parallel to each other, which is not the case. ' The second method, shewn at 135, is perfect, and is the first thing of the kind that is to be found in any English publication. 2 B 301 We come now to the London Art of Building, by William Salmon ; and as it is our province to repeat only the inventions and improvements in joinery, we shall therefore omit what Mr. Salmon has said on the formation of the scroll; being, in method and substance, the same as that which we have detailed from Mr. Price, who certainly gave the first rational method of squaring the twist for the scroll part of the rail, either from his own invention, or from a practice known among work- men. And as Mr. Price has only shewn the formation of the twist of a scroll, and of a rail upon a quadrantal plan in a level landing, we shall here detail the application made of the same principle by Salmon to a winding stair, where the treads of the steps are all equally divided around the circumference; but first it would be necessary to notice the candid acknowledgment which Mr. Salmon has made in respect to the principle. “ I must confess, for this method of forming twist rails, I have had my eye upon, and am obliged to, my ingenious friend, Mr. Francis Price, in his Treatise on Carpentry, lately published; though on comparing them, you will not find them alike. This method of forming the raking-mould will serve for all twist rails whatsoever, with due ap— plication, as shall be shewn in another example of a staircase, having a circular well-hole. “Figure 136,is the plan of a circular rail having six- teen steps in the whole circumference; but here it is proposed to find the raking-mould to a fourth part thereof, or four steps,it being to asmall scale. The plan being laid down, as a c d e, Figure 136, divide the outer circle into a number of equal parts, so as to transfer them on some line, as a c, Figure 137 : and setting up the rise of four steps, as a I), gives the pitch-board, due to them all. Then taking b c, in Figure 136, applied to the pitch-board, Figure 137, from c to d, it gives 0 e, which transfer to Figure 138, from b to 0. Also, from Figure 136, take a d, placed in Figure 137, from c to g, gives c f, which transfer to Figure 138, from a to d ; and there tracing, as before taught, you will form the raking-mould required.” In such a staircase as the above, the waste of stuff is great: but when does it ever come into practice, that the steps are equally divided? In every stair there must be a landing, and this would require much thicker stuff: Again, if the stair is mixed with flyers and winders, the waste 186 W JOI :2 stuff would in many cases be enormous, and still more so, if the joint were brought over the flyers, in order to secure the wreath and straight parts more firmly by a screw, as is the case in modern practice. The greater number of stairs now in use, are constructed upon this plan. “ Some able workmen have another method of forming this rail. “ First, they make a cylinder, equal to the whole well—hole, f, e, in Figure 136, or part thereof, either solid (if the well—hole be small) or (if large) by fastening boards together upright, in the exact form of the plan. “ Then they proceed to set on the said cylinder, as Figure 139, the height and breadth of each step, as a, b, c, d, e, f; 8m. and to the extreme points, b, d,f, they bend round several thin pieces of the breadth of cf, in Figure 137, and being glued, or otherwise fastened together, till they make the thickness of the rail, as E; I say these, when taken off from the cylinder, will be the rail, and exactly squared to the right twist. “ This is a very safe and sure method, though not very frequently made use of. ' “ Either of these ways will serve, should the well- hole he an ellipsis, or any other figure for its plan ." The first idea of gluing a rail in thicknesses is here shewn, but the description, and the figures accompanying it are very imperfect; nor will the rail come off squared, as Mr. Salmon asserts, without the veneers are all different in pro- portion to the radius of their plan, except, indeed, upon the plan which he has shewn, where the rail is supposed to be continued, and there- fore requires much amendment to be brought into general use. Langley’s improvements are as follow: “ To describe a twisted MIL—Let the lines B D E, Figure 140, represent the edges of the two lower stairs of a staircase. “ Divide b 9, the tread of the second stair, into nine equal parts, continue the line D towards the left at pleasure. Draw N F, parallel to 9 b, at the distance of seven parts, also draw the line 14 d at the distance of three parts, then db is the breadth of the hand-rail. Draw A 13 parallel to 9 b, at the distance of b 9, then the point it is the centre of the eye of the scroll. On the point (1 describe the quadrants b c and de, which is the length of the twisted part of the rail, the remaining part, to n, the eye, being level. On it describe the circle J01 J01 W :xp, whose diameter, sup, must be equal to db, the breadth of the hand-rail. Divide the radius, up, into four equal parts, and through the first part, at o, draw the line r 1, cutting the line N F in .r; on x describe the quadrants c f and e g, make at equal unto two parts of up, and draw the line ts parallel to A n. On the point t describe the quadrants fit and g 2, make new equal to three parts of up, and through the point an draw the line z k, parallel to 7‘1“; on z describe the qua- drant It 12, and on w the quadrant up, and then is the plan completed.” This is a very anomalous attempt at the de- scription of the scroll of a hand-rail with compasses, the first centre being at a,the second at x; the third centre is said to be at z, but it proves to be at o; neither t nor to answer to the remaining centres. “ T 0 describe the mould for the twist—Continue b 9 towards M, and F N towards b, in Figure 14l, also draw L I parallel to b N ; at the distance of N K, in any part of N b, as at c, draw the line afat right angles to b N; and on c describe the semi- circle abf: make ad andft each equal to the rise of one stair, and draw the line dc t. Make cN equal to ct, divide be into any number of equal parts, and draw. the ordinates l5, 1; 16, 2; k 3, 8LC. divide c N into the same number of equal parts as in b c, and make the ordinates thereon equal to the ordinates on b c, and through their extremes trace the curve N f, which is the curve of the outside ofthe mould. Make 6 k equal to the breadth of the hand—rail, and on c, with the radius ck, describe the inner semicircle. Make C/t equal to rt. On kt, the semi-diameter of the ' inner semicircle, make ordinates, which transfer on c It, as before, and through their extremes trace the curve of the mould, which will complete the whole, as required. For as the outlines of the plan of the twisted part of the rail, 6 c and de, are quadrants, therefore the outer and inner curves of the mould will be both a quarter part of two ellipses; because the twisted rail, strictly consi- dered, is no other than the section of a cylinder, as L M IK, whose diameter, af, is equal to twice a b, in Figure 140, and its transverse diameter equal to d t, and conjugate diameter to a f “ The twist of a rail over a circular base at a half pace, as ab, Figure 142, is the very same thing as the preceding, as being the fourth part of an ellipsis, made by the section of a cylinder, whose diameter is equal to twice a c.” This method of forming the section is the same in effect as that already shewn by Price. The impu- dence of this author is however astonishing, in writ- ing upon this diagram,as well as upon every other, “ Batty Langley invent. 1738.” See Figure 1, and Figure 4, Plate LXVII. of his Builder’s Com- plete Assistant. The only difference between Price and Langley is, that Price forms the face-mould of the rail from the intersection of straight lines drawn from two lines of sines placed at right angles to each other, and tracing a curve through the diagonals of the rectangles, beginning at the extremity of one of the perpendiculars, and ending at the extremity of the other. Whereas Langley divides the breadth of the plan and the length of the face-mould of each into the same number of parts, and draws lines at right angles through the points of division, and makes the respective per- pendicular of the face-mould equal to those of the plan, and then traces curves through the ex- tremities for the concave and convex sides, and thus completes the face-mould of the twist. Figures 143, 144,—“ To find the mould of a twisted rail, to a circular or elliptical staircase. —-—Figure 143. Let A B C D be the plan of a cylin- drical staircase, whose base is a circle, and whose stairs wind about the cylinder a b d, 8a. The plan of the stairs being divided, continue out the diameter, d a, towards the left hand, as to f, of length at pleasure. Make af equal to the girt of the semicirclea b d, which divide into the same number of equal parts as there are stairs in the plan of the semicircle a b d, as at the points 1, 2, 3, 4, dye. from which erect perpendi- culars, as 1 a, 2 a, 3 a, 8m. of length at pleasure. Consider the rise of a stair, and make the per- pendicular,fg, equal to the rise of all the twelve stairs that go round the semicircle a b d; and divide the perpendicularfg into twelve equal parts, as at the points 1, 2, 3, 4, dc. from which draw lines parallel tof d, continued out towards the right hand, at pleasure, which will intersect the perpen- diculars on the linefa d, in the points a c, a c,a c, die; and which are the breadths and heights of the treads and risers of the twelve stairs, at the side of the semi-cylinder a b d; for were the whole Figure g f a applied about the semi-cylinder, then the parts a c, a c, dye. would be in the respective place of each stair. Let a e represent the breadth of the hand-rail, and the semicircle e 10 c its base, over which its inside is to stand. Divide its 9. B 2 —_: JOI‘ 188 diameter, ec, into any number of equal parts, as at 1 2 3 4, Src. and draw the ordinates 1, 6; 2, 7; 3, 8 ; 4, 9, 8yc. which continue upwards, so as to meet the horizontal lines drawn from the perpen- dicular gf, in the points 28, 27,26,25,8rc. through which trace the ogee curve 28, l4,a, which is the sectional line of the cylinder, over which it stands. Make the distances 15,21; 19,14; 18,13; 17, 12; and 16, 11, equal to the ordinates 10, 5; 9,4; 8, 3; 7,2; and 6, 1; and through the points 20, 19, 18, 17, 16, to a, on the linefd, trace the curve, 20, 16, a, which is the inside curve of the mould, and whose out-curve,21 a, being made concentric thereto, will be the mould required, whose end, 21, 20, when set up in its place, will stand per- pendicular over its base I) 10. “ Note. This mould, though made but for one- fourth part ofthe cylinder,will serve for the whole, by repeating the same, or adding three or more others of the same kind, to the ends of each other, as often as there are revolutions in the cylinder.” It is not possible to conceive any thing so void of truth as the method here shewn. Over and above the absence of principle, the description is contradictory to the diagram. We are told to “ divideits diameter, ec, into any number of equal parts) as at l 23 4, SLC. and draw the ordinates l 6, 2 7, 3 8, 49, &c. which continue upwards so as to meet the horizontal lines drawn from the perpendicular gf:” but instead of being drawn through the diameter, they pass through the divisions which divide the concave circumfer- ence of the plan into equal parts. Langley has presumed to differ in method from Price in finding the curvature of raking-mould- ings, but in this he has been much mistaken, as may be observed in the following: “ Tofind thecurvature or mould oft/re raking ovolo, that shall mitre with the level ovolo.—Let up, Figure 145, be a part of the level cornice, and a n the points from which the raking cornice takes its rise; also letfa and g n represent a part ofthe raking cornice. On it erect the perpendicular n b, and continue I a to b; divide b 71 into any number of equal parts, at the points 1, 2; 3, (SC. and from them draw the ordinates, 1 2, 3 4, 5 6, (ST. In any part of the raking ovolo, as at c, draw the perpendicular c m, and make c d equal to I) a, the projection of the level ovolo. Dividec m into the same number of equal parts as are in I) n, as at the points I, S, 5, 7, 650. from which draw ordinates equal to the. JOI ordinates in bn, and through the points 2, 4, 6, fire. trace the curve required. In the same manner the curvature or mould maybe found when the upper member is a cavetto, cyma-recta, or cyma- reversa, as is exhibited in Figures 146, 147, 148.” “ Tofind the curvature or mould of the returned moulding, in an open or broken pediment.-—Let the pointf, Figure 145, be the given point, at which the raking—moulding is to return. Continue up to- wards ]: at pleasure, and from the pointf, let fall the perpendicularfh; drawfe parallel to h p, and makefe equal to b a, the projection of the level cornice. Draw e 2' parallel to fh, and divide e g into the same number of equal parts, as are con- tained in b u, as at the points 1, 3, 5, 7, tire. from which draw the ordinates 2 l, 4 3, 6 5, 8% Equal to the ordinates in b 1:; through the points 2, 4, 6, 8, Eye. trace the curve required. In the same manner the curvature or mould may be found when the upper member is a cavetto, cyina-recta, or cyma- reversa, as is exhibited in Figures 146, 147, 148." In the treating of a subject in order to make it as perfect as possible, it ought to embrace everv article hitherto known, that is intimately cori- nected with it: and no author ought to be ashamed to copy an article from another, when it comes within his plan; but then he ought to acknow- ledge his authority, provided that it has not become common property; in this case he may either use it with or without such acknowledge- ment, as he pleases. There are some authors, however, who, rather than follow the principle of another, will shew a different method in order to have the appearance of originality; but as this has every chance of being detected, and exposed in future, it must reflect a double disgrace upon their memory. This circumstance is applicable to Langley: it would have redounded to his credit to have copied Price’s second method, and to have made honourable mention of his name. Mr. Abraham Swan has also contributed some— thing to the practical improvement of joinery; his method of describing the scroll is that in- vented by Vignola, we shall therefore refer the reader to our review upon Price for the detail; but though his face-mould and its application are the same as given by Price, the manner in which he constructs his diagram, in order to obtain it, is more obvious to the practicaljoiner, as the corresponding parts of the section may be ~ 1.: M1!» ,3 A. . 1 fr. , JOINERY. My. 133. £13,146. F4”. V [31:0, 14 7. if". 1419. ' \1\\ [ZN-W. I r' (I L I ('1 I .x _. , . . 1 l ' : ,.'u . {"2' " 4‘ ’, r .’l. I, .- . 4:4 ‘ , VJ. .' I ‘r’. '. 7:7 .,,.-..‘.r , I“ e '- . , 1 ( £2,117”. ' ( o r L ,q a». 1.3.1 . \ . '\ \- 1m ‘1 . :H'W ~ m nun %: Drawn [{M (MAJVIb/lu/n-vn. [om/4m,lich/(lv/u‘ll It}; /? [1’11'1’10/a'on X‘././)’ur/}}’/a/, Hun/0111‘ .‘7I-.’n‘i1,'.. /:'n‘m'.n‘n/ If” .1 /)’. 'liz‘II/ul'. J01 189 W turned into the same position with regard to the plan, that the section of the solid itself has with regard to its base. The manner of squaring twist-rails. Figure 149, “ exhibits the pitch-board,-to shew what part of the step the twisted part of the rail contains; the three dotted lines drawn from the rail to the pitch-board represent the width of the rail, that from the middle shews the ridge, or middle of the rail, which is to be kept level. The dotted lines a and b, shew how much half the width of the rail turns up from its first begin- ning to 3. 1"igure150, “ sheWS the same pitch-board, with the manner of the rails turning up. If the sides of the twisted part of the rail be shaped by the rail-mould, so that they direct down to its ground- plan; that is, the upper side of the rail being first struck by the mould, then apply the mould to the under side, as much back as the bevel of the pitch—board shews, by being struck on the side of the rail, and then Figure 150, being applied to the outside of the rail, from its first twisting part to 3, will shew how much wood is to be taken off.” In this part Mr. Swan is so unintelligible, that his reader can only guess at his meaning; by the term rail-mould he may either mean the face- mould or the falling—mould; but from the appli- cation which he makes of the said rail-mould, a practical workman only can discover his mean- ing to be that of the face-mould. Figure 15], “ exhibits the square of the rail, with the raking-line of the pitch-board drawn through the middle on the upper side; then draw the depth of the side of the rail parallel to this, and the dotted lines from the diagonal of the rail; these lines shew what quantity of wood will be wanting on the upper and lower sides of the rail. Set your compasses at c, and draw the circular stroke from the raking part of the pitch-board to I); take the distance a b, and transferit from a to I), in Figure 152. The several distances thus found, may be set at any number of places, ranging with the straight part of the rail; and it then forms the width ofthe mould, for the twisting part of the rail. Figure 152, “ shews the sweep of the rail. The rail cannot be fixed less than one-fourth part from the nosing, or front of the step. “ The remaining part of the pitch-board may be JOI divided into any number of parts, as here into four; from these divisions drawlines across the pitch-board to the raking-line, then take the dis- tances from the ground-line of the pitch-board to the plan of the rail, and set them perpendicular from the raking-line of the pitch-board; so shall these divisions, when the rail is in its proper posi— tion,li.e directly over the divisions on the ground- plan. “ In this Figure, I, m, and 72, rise as much above 0, as the dotted line in Figure 15], does above the width of the rail; and they sink as much below 0, as the other dotted line in Figure 151, falls below the width of the rail; the same thicknesses must be glued upon 0, though the greatest part will come off in squaring. The reason of placing the letters, I, m, n, where you see them, is, that they might not obstruct the small divisions of the rail- mould.” This is hardly intelligible to any but Mr. Abra- ham Swan himself. _ Figure 153, “ shews how to find the rail, when it takes more than one step. The remaining part of the pitch-board is divided into four parts, as before in Figure 152, and it takes in two such parts of the next step. Draw lines from these divisions to the diagonal of the pitch-board, as in Figure 150., then take the distance, a I), and set it from c to d, and so proceed with the other divisions. “ Here is also shewn another way to find the out- side of the rail—mould. Draw all the divisions across the plan of the rail; then take the distance from the ground-line of the pitch-board to 4, transfer it from the diagonal of. the pitch-board to 4- on the rail; and so proceed with the other distances. Then, when the rail is put in its pro- per position, c will be perpendicular to b, and all the divisions, as 1, Q, 3, 4, Ste. in the rail, will be perpendicularly over 1, 2, 3, 4, SLC. in the ground-plan.” This method of laying down the face-mould is simple, and easily comprehended by every one who understands any thing of the nature of a prismatic section. Figure 154,“ shews the plan of a rail of five steps. “ Tofind the Tail.—-S€t five divisions, as from e to 11, which is the height of the five steps; draw the diagonal from h, to the plan of the rail; then take the distance e f, and transfer it from g to It, and proceed in the same manner with the other seven distances.” JOI‘ 1'90 .101 w “ To find the width qf the rail-mould.——-Draw the lines across the plan of the rail, as at h, set that distance from the diagonal to i; and so proceed with the rest, as was shewn in Figure 153. “ Having formed the sides of the rail, perpendi- cular to its ground-plan, and having squared the the lower end of the rail, then take a thin lath, and bend itwithin the rail, as is represented by m, in Figure 155.” The general practice of forming the pitching- triangle is by the number of treads, and the rise in the same number of steps. This is not, however, to be understood ofa winding-stair, but of aflight of steps. “ This is the readiest method for squaring a solid rail; but if the rail be bent in the thickness, the nosing of the steps must be drawn upon a cy- linder, or some other solid body of a sufficient width, to contain the width of the rail, or string- board. " “ r represents the depth of the rail, touching the nose of each step. You are to take a sufficient number of thicknesses of this width, to make the thickness ofyour rail; glue them altogether upon your cylinder, or templet, confine them till they are dry, then the rail taken off is ready squared. Proceed in the same manner with the architrave marked it.” His method for gluing a rail in thicknesses is the same as Salmon’s, but his diagram is better con- structed. Mr. Abraham Swan has also applied the develope- ment of a conic frustum to the formation of mouldings upon the spring, round a cylinder, as follows. Figure 156, “ shews the method of bending a cor- nice round any circular body. When you have found the spring of your cornice, which is shewn at the right—hand, let the dotted lines be drawn parallel to the spring, and where they intersect the centre, or middle of this body, as in c, you will have the radius to strike the curve of your cornice. This principle is as correct as the nature of wood will admit of, and the thinner the wood is, the more exactly will it apply. Besides this, there is another method of forming an annular moulding on a cylinder by thicknesses. Mr. William Pain has also contributed to the practice of joinery; and though he has not in- vented any new methods, the plates of his books exhibit the various elevations of stairs, or sec- tions, as they are called, in greater perfection than is to be found in any prior publication: by this means he ascertains the lengths of the rough strings, and the framing of the carriages. He has also shewn the stretch-out or developement of the rail, and its connection with the string- board, in a more obvious manner to the student, than any of his predecessors. In his Builder’s Pocket Treasury and Practical Builder, be de- scribes the scroll in the same manner as is to be found in the British Carpenter, by Price; his text is, however, very unintelligible. In Plate 93, of his Golden Rule, third edition, is the following description, engraved on the plate, for finding the face-mould of a hand-rail upon a cir- cular or elliptic plan :———“ The method for tracing the raking-moulds for stairs, or any kind of moulding on a cylinder, (see Figure 157).—The mould a on an ellipsis, and the mould b on a circle- Stretch the rise and tread of one quar- ter, as a b, or c d, and trace the moulds a and b, from the plan, as 1, 2, 3, 4-, 5, 6, 7, 8, 8L0. which is plain to inspection.” It is not so very plain, nor is there any connection by which its evidence appears. He does not even shew how the outer edge of the face-mould ‘is to be obtained: in the diagram it is quite erroneous, its breadth being equal throughout the length of the curve. He tells us to stretch out the rise and tread of one quarter, as a b, or c d,- but on inspecting the diagram, we find that “ a b, or c d,” is the hy- pothenuse of a right-angled triangle, whose base is the tread, and its height the rise of the steps in one quarter: this method is not regulated by principle, but by whim or trial, and is there- fore erroneous. ln Plate 67, of his Practical House Carpenter, sixth edition, is a semicircular stair, with winders in the semicircle, and flyers adjoining to the winders, where they begin and end, (see Figure 158.) As is usual with Mr. Pain, there is no description of letter-press, and the ex— planation is contained on the plate, as follows: “ A staircase on a circular plan, drawn half an inch to a foot, with falling-moulds and face-mould stretched out, with all the parts figured for prac~ tice, the ramps may be traced by the intersection of lines. “ A. Depth of the block for the circular part. “ B. The thickness of ditto.” Figure 161, shews the rail stretched out for the out- side fallingmoulds, shewiug the thickness of stuff. JOIN E RY. PLATE 6. i" 1:117. 158. .9 3601.- ' ”0.”.de 0;! maid {I IIJIIIIA awn/Md 19‘; 92:1: ”nj my ”Wm-{C7 ” ”I”? 1.7131“ [“7 [mm] "Ll F131. 159. fur? Mop/4’ E - ., ‘x‘ - “3i; : “5 . g ‘43 E; c [211.14, 0‘ ‘_ -. ~ / g \4 £151.14. 6 ._ J t‘ 3 7‘ . / $ . ‘ \p a k W. .5466 E 5 t x \i E s. 5‘ . I a y .r .k , ~: '2 Tread or two \: 1 ‘ ‘ quarter; u "— E = 3 § 2 ~ 2 ‘3 z = k * '3 3 § s .K ' E K § ‘: ~ \. a \ § 3 a a‘ §~ Draw” [11/ J]. (I. .Vzflmla'vn. [mu/on, [hit/[Jim] 1'.” I.) J’d‘hv/Jun X‘ J. Emmi-(14], ”hrdvur J'trn-L 1.914. Engraved [by J. 11.7%!!!“ ,.A.,n\ Lu. . V fl 301 191 .701 ‘W Figure 160, the rail stretched out for the inside falling-mould; and Figure 161, the method of getting out the face-mould. In the construction of the face-mould, instead of the rise and tread of the steps, as he writes, on the lines of the figure, we find, by the. said diagram, that the diameter and rise of the steps in the semicircum- ference are used. Such contradictions entirely confound his readers; and though the latter is nearer to the truth than the rise and treads of the steps, as he writes, the face-mould is far from the pitch, except the wreath were formed for a whole semicircle, as we shall hereafter shew; nor can the thickness of stuff be obtained from the stretch-out ofthe outside falling-mould, as exhibited in Figure 159. In the said figure, the reader may also notice the inconsistency of shewing the scroll in per- spective, while the rail itself is stretched out. In Plate 68, of the said Practical House Car- penter, is shewn the plan of the rail ofa semicir- cular stair, upon a level landing, see Figure 162. He writes thus upon the Plate: “ Face-mould for a continued rail on a landing, without winders.” In this diagram he uses the diameter and height of one step, which is quite analogous to the me- thod used in the preceding example. In Plate 70, of the said “ Practical House Carpenter,” he shews another stair, upon the same plan as in the first example, (see Figure 163;) above is shewn an elevation of the rail at e, in order to get the thickness of stuff. This dia- gram certainly shews some idea of the principle, but he has failed in not giving the true delinea- tion with regard to the thickness and depth, and in drawing the two lines which ought to contain the thickness of stuff, to touch the sections at each end, without cutting into them; but to be correct, they should touch the extreme parts. The method of tracing the face-mould is shewn in Figure 164. It is quite analogous to the two preceding examples. He shews the face-mould in all these examples for the wreath of a whole semivcircumference, which is twice the extent that it ought to be: for though it is not impossible to execute the whole wreath for a semicircle, yet such execution is attended with a prodigious waste of stuff and time; besides the impossibility of matching the grain of the wood. He writes thus upon the Plate: “ B. The'string-board stretched out for the circu- lar part (Figure 165.) “ d f The hand-rail stretched out. “ e. The section of the circular rail, shewing the thickness of stuff. “ c. The face-mould traced from the plan A, for a solid rail. “ If the rail is bentin thicknesses, d and f, Figures 165, 166, represent the mould drawn a quarter of an inch to a foot.” In Figure 167, is his erroneous method of drawing the circular cap with compasses, which has no relation to any principle. In Plate 76, of the said Practical House Carpenter, see Figure 168, is also shewn a stair upon the same plan as in the first example: the method of finding the face-mould is analogous to the first, viz. the diameter of the plan of the rail, and the rise of the steps round the semi-circum- ference, he forms a mould for the whole semi. circumference as before. The elevation of the rail is shewn above, see Figure 169. In Figure 170, also in the said Plate 76, is shewn a stair with winders in the quadrantal turnings, and flyersjoining the winders. In find- ing the face-mould, Figure 171, the radius of the rail, and the height of the steps in the quadrantal are are used, and the face-mould is traced as in the former examples, and is exactly one-half. Besides the waste of stuff attending this method, it is impossible to match the grain; for if the fibres match the straight rail at one end, they will stand at right angles to those of the straight rail at the other end, in such a stair as the present; and in semicircular turnings the fibres of the wreathed piece would be at right angles to both of the straight parts of the rail. These are not the only disadvantages which ac- company this method: as it is evident, that a rail thus got out must be much weaker than one where the fibres run parallel with the chord of the face-mould, neither can it be well secured by bolts at the joints. In Mr. Pain’s works, he does not shew the application of the face to the plank. However, upon the whole, though he has little or no invention in respect of hand-railing, he has as much originality to claim as any of his pre- decessors, Price excepted. His orthographical elevations of stairs, though very useful, are very ill projected. In his display of dog-legged stair- cases, his elevations are tolerably well drawn, see Figure 172. He has also been useful in shew- ing the constructions of carriages for geometrical \ M ‘JOI * stairs, as they were produced in his time. Though his plates abound in contradictions and false schemes, they shew his intention more clearly than some of the preceding authors. Although the principles of cylindric soffits in an oblique straight wall, where the axis of the cylinder is parallel to the horizon, may be gathered from Price; Pain has exhibited the first example: but the constructions which he gives in his British Palladio, and in his Practical House Carpenter, are wrong, as we shall shew under the article SOFFIT; and yet,in the British Palladio, in a similar case, in the covering of polygonal domes, Plate 39, Figures A, B, C, D, he is right. It is something singular that the construction which he gives for a circular wall is correct, as shewn in his Golden Rule, in his Practical Builder, in his British Palladio, and in his Practical House Carpenter. The method of constructing and gluing up columns is shewn in Plate 18, of the Prac- tical House Carpenter. He shews the methods for gluing on the blocks for carving the leaves in the Ionic and Corinthian capitals, Plates 34- and 35, Practical House Carpenter. In Plate 63, of the same work, he attempts the construction of raking mouldings, but fails, as Langley had done before. He also shews in the same work, how the proportions of the heights of the members of cornices upon a diminished scale are obtained, but neglects to shew the projections in the same ratio. In Plate 99, of The Golden Rule, third edition, he shews the constructions of mouldings bent round a cylinder in thicknesses upon the spring, see Figure 173; on which he thus writes: “ Of gluing circular mouldings on the spring, and bending circular dado, which may be grooved or saw-kerfed, as the workman may think best. Raking dado for stairs to be grooved or saw-kerfed by the pitch, on a circular plan.” This is cer- tainly not shewn to the best advantage. The figures of the brackets are shewn at Figures 17-1, where he thus writes between them: “ The shaded part on the faceof the moulding shews themethod for rebating down to the square, and metting ot'the mouldings for the sticking of them; e represents a hook to be made for the springing of the mould- ings.” This would require a little more explana- tion than he has been pleased to give. In Plate 95, first edition, of The Golden Rule, he 192 JOI I‘— attempts the construction of the moulds for a stone pediment in a circular wall, and says, “the same may also be applied to the mouldings of a wooden pediment in a circular wall,” see Figure 175. He writes thus on the Plate: “ Figure A represents a circular bow with a door or window, whose width is equal to a b, and it is required to have a pitch-pediment in stone, or wood; to find the side, or raking curve, that shall fit the bow when set to the pitch, draw the chord-line of the open- ing, as ce, then take one—fourth part of that chord- line, and set it from the chord at c to d on the centre line c f; then draw the pitch-line d e on the pitch-board commonly called, then divide the chord-line c e into a number of equal parts, and draw them from the arch of the wall to the pitch- board; then draw the ordinate lines square from ‘the pitch-board; then take the ordinates from the plan of the wall to the chord-line, as 1 1, 2 Q, 3 3, 4 4, 5 5, 6 6, and set them on ordinates of the pitch—board, as 1 l, 9. 2, 3 3, 4 4, 5 5, 6 6, then tack in nails at the points 1, 2, 3, 4, 5, 6, and bend a thin slip, and mark as that curve directs, that will be the mould required. Suppose Figure B to be a stone plinth or moulding, or wood if required, which mould is found in the same manner as that in Figure A, which is plain to inspection, and will be the side curve to one- fourth part of the whole circle. Note. This method will give the raking-mould in any case required on a circular or elliptical plan; for whatever it rises more or less, draw the pitch asfg, in Figure B, or c :l in Figure A, and trace the lines as above directed, which will complete the work.” This is so little to the purpose, that the work could not be carried into execution by these moulds alone, so that it is veryimperfect, the most essential ones being wanting. We are certainly obliged to him, however, for the attempt he has made, as it may be a stimulus to some other to give a more perfect construction. In summing up the whole, we shall omit the seve- ral schemes which have failed; and the various authors, with their inventions and improvements, will stand as follow: Price first shewed a method for constructing hand-rails, and applied the same to the wreath part of a scroll and to the qua- drantal rail on a landing: he also spoke of its application to continued winding stairs, but gave no example. We shall afterwards notice the disadvantages attending his method. This JOI 193 W author also gave the first construction of raking- monldings, in the Art quand-railing, and Salmon, following Price’s principle, gave an example ofa continued winding-stair. Langley, in his first ex- ample, varied this construction, by applying or- dinates dividing the plan and the section into a like number of equal parts, and making the or- dinates of the section equal to the corresponding ordinates of the plan; and in this Langley gave the first introduction to ordinates in hand-railing, though ordinates were used by Price in other prismatic constructions. - Swan connected the face-mould with the plan, by placing the pitch-board between them, and so «drew ordinates perpendicular to the base of the pitch-board, which he carried up to the hypothe- nusal line, used as a base to the prismatic section, and then drawing ordinates to such base, made the corresponding ordinates of the section equal to those of the plan, and thus completed the face- mould. This was certainly an improvement upon Langley’s first method, as by this means it became more evident to the reader. The methods, how- ever, shewn by Langley and Swan, were in effect the same as Price’s; that is, they would give the same moulds, under the same data or circum— stances, and consequently would partake of the same advantages or disadvantages; as we shall exemplify at the end of this article. The application of the surface of the frustum of a cone was first applied by Swan, to mouldings bent to the spring round a cylindric body. Pain followed the scheme of ordinates laid down by Swan, and constructed his falling-moulds in a more eligible manner than any of the preceding authors; but he is very inconsistent in a disagree- ment between his text and his diagrams, as well as in shewing his moulds for the formation of rails, anwering to a complete semicircular plan. There are several particulars, with respect to hand-railing, to be observed, on the whole; in all the wreaths hitherto constructed, the joints are always made at the spring, viz. at the divid- ing surface, between the straight and circular parts, and the fibres of the wood will always run perpendicular to those of the straight rail, at one end at least; by this means, the fibres, or grain, as they are called, are ill-matched, and the wreath becomes extremely weak at the joint. In none of these methods shewn by Langley and Swan, which in efi‘ectare Price's, will the section coincide VOL.IL JOI # in any more than one point on the top of the lower extremity of the wreath, and this circum- stance therefore occasions a vast waste of stuff, as we shall presently prove. Pain alto shewed the method of constructing columns; forming and gluing up capitals, in order to be carved; with the formation of a cylindro-cylindric soflit, when the axis of the cylindric opening was in a plane perpendicular to the axis of the cylindric wall. The construction of a pediment in a circular wall was also tried by this author, and, so far as he proceeded, he was correct, but was deficient in not giving the whole of the requisite moulds and instructions, which rendered what he had done of no value. _ We have now noticed all the methods that may be considered either as inventions or improve- ments in the art of joinery, and we trust that the account is impartial, and what every one inclined to do justice, will find to be the case; and if any thing has been mistaken, it is occasioned by the disagreement between their text and diagrams, and not from any intention to lessen their merit, or the value of their works. The Author has the satisfaction to inform his readers, that his own methods, as detailed in the articles CARPENTRY and JorNERY, and in his numerous publications, have been in constant practice for upwards of twenty years, and have been found to answer the purpose which he origi- nally anticipated, to the utmost extent of his ex- pectations. He has invented the method for the developement ofa conic soflit in a circular wall, or of a conic surface terminated by a-plan-e, or by a cylindric surface. And though the cuneoidal surface is not developpable,he has shewn how it may be unfold- ed, so as to terminate upon a plane or cylindric surface, by a method which comes very near to the truth. He has discovered an entire new principle of squat: ing the wreath of a hand-rail, by which the face- mould may touch the tops of two vertical sections at each end, either in one of its angular points or in its whole breadth, supposing both the wreath and the mould to be set up to the true pitch. He has invented amethod of tracing the mitre-cap for the hand-rail, as used in dog-legged stair- cases, from a given section of the rail. He has invented a method of gradating the steps, so as to form a regular surface upon the soflit at . 2 c 301 194 JOI thejunction of the flyers and winders; this not only gives an easy turn to the skirting, but per- mits the rail to be kept at an uniform distance from the nosing! of the steps. He was the first that shewed a developement of the plank, in order to apply the face-mould, and -to range the two sides in the cylindric or pris- matic surfaces, according to the plan of the rail. In the articleHAN D-RAILING,he has shewn a more regular method of describing the Spiral lines of the scroll, by finding the centres in a fret or right- angled guilloche; so that the difference of any two adjoining sides of the fret will be always the same. In order to describe the scroll with com- passes, he also invented the method of regulating the difference of radii of a scroll by a line of sines; as had formerly been done by a line of tangents, in order to trace the scroll by hand. He was the inventor, and the first that shewed the method of getting the scroll out of the solid, without gluing any part. The method of capping an iron rail was never practised with certainty until his invention ap- peared in the Carpenter’s Guide. No better me- thod has ever yet been practised for this purpose. He was the inventor of the method of springing the plank, by making its plane of inclination to rest upon three vertical sections of the wreath, viz. one at each end, and one in the middle, be ing obtained by three heights taken from the falling-mould. By this means the thickness of the rail is ascertained with certainty, and will never exceed 2% inches where the rail is intended to be 2 inches deep, and 2,1, inches broad ; where- as, by former methods, the plank would require to be 6 or 8, or even 10 inches thick. . No author before him ever regulated the pitch of the plank by the falling-mould, but by the height . of the steps only; by this he obtained an im- mense saving of stuff. It is hardly necessary to 'inform the reader, that his methods, as laid down . in the Principles of Architecture, have been in practice upwards of twenty years, and have super- seded every other. He also invented the method of cutting the veneers in thickness, so. that the rail may come off squared from the cylinder. . He was the first author that shewed the method of scribing down the skirting upon stairs, how- ever irregular the steps might be in respect of .each other. He also invented a method for squaring the bars for the head of a sash in a circular wall; no me- thod had been ever shewn before by which such work might be executed. He invented, and was the first to shew, a method for the formation of a circular architrave in a circular wall. Besides Price’s method of raking mouldings, he added that for the angle-bars of a polygonal win- dow, such as are used in shop fronts. He improved the method of proportioning mould- ings, by shewing how the projections were to be found in the same ratio with the heights, which had been neglected by other writers. He was the first that treated upon hinging, and the hanging of doors and shutters, and the various kinds of foldingjoints. In Figure 176, No. 1, A B C D EF G HI is half the ground plan of a continued rail, viz. where the risers are equal to each other, as are likewise the heads. Figure 177 shews the falling-mould, and the de- velopement below it, to the quadrant E F G H I; and because the risers and treads are all equal, the edges of the falling-mould will be straight lines parallel to each other: efg k i, No.2, is an ortho- graphic projection of the quarter of the rail, cor- responding to E F G H I, No.1; in No. Q, draw L V parallel to A I, No. 1; make the angle V L M, No. 2, equal to the angle which the edge of the falling-mould makes with the base of the de- velopement in Figure 177 ; through idraw K N parallel to L M; through N draw N M perpendi- cular to L 1\I; through L draw L K parallel to lVI N; then M N or LK will be the thickness of stuff necessary, according to the method given by Price and Swan. a b c d efg k i, No. 3, is a projection of the rail to the whole semicircumference. ‘Ve shall now shew the thickness of stuff according to Pain. It will be recollected, that he finds the pitch of the rail by the diameter or semidiameter, and the rise of the steps in the semicircumference or quarter accordingly: suppose then there are eight steps in the semicircle, now 2.2) y is the diameter, andgr the rise of eight steps; thereforejoiu Tt‘ .r, and you have the line of section of the cutting plane: through a draw R S parallel to w .z‘, and through idraw Q T, also parallel to tax: draw T S and Q R perpendicular to war,- then the breadth Q R or T S, and the length Q T or R S of the rect- JéfifiNIERY. “awn by .1]. (1. .1fl-fiulmn. Lam/(w,full/Aria! l/‘z/ l.’ JVA'IM/A'fl/I X' J. [fulfiP/a’, l/Vun/mu- (Hive/I z/fu. L PIA TE 1). EH, y / / X/ Flying. Flu/ml w’a’ Mr J. b’. 7%]! In): ” 301 195 JOI WW angle Q R S T, will be respectively the thickness ‘ and length of the stuff. The projection of the upper half of No. 3 is equal and similar, and similarly situated to No. 2; the lower half of No. 3 is equal and similar to the upper part when reversed, the lower part at a b c d shewing the soffit, and the upper, fg k i, the back or top of the rail. Figure 178 shews the projection for a quarter of the rail, upon a plane parallel to one of the radii: this shews an equal thickness to that shewn at No. 3, Figure 176, the pitch being obtained from the radius, and the height of the steps in a quar- ter of the circumference. Figure 179 shews the method of finding the face- mould, according to the first invention of the Author of this Work, shewn in the Carpenter’s New Guide, where the cutting plane of the cylin- der is perpendicular to the plane of the chord of the rail, and passes through the upper corners of the sections at each end. Figure 180 shews the projection upon a plane parallel to the chord of the plan, agreeable to the face-mould, Figure 179. All these projections are made agreeable to one pitch-board, Figure 177. We shall now shew the quantity of stuff accord- ing to each method. Figure 181 is a develope- ment of the plank, shewing the application of the _ face-mould according to Price, together with the thickness, the length, and breadth of the plank. The particular measures are to be taken from the subjoined scale. Ft. In. The length } 1 5 { which reduced to measures inches, gives 17. The breadth O 8% The thickness 0 6 By these measures we obtain 867 solid inches in the quantity of stuff required by Price’s method. Figure 182 is a developement of the plank accord- in g to the pitch and face-mould required by Pain’s method, for a whole semicircumference. Ft. In. The length } Q 10 {which reduced to measures inches, gives 34. The breadth O 8% as in Price’s. The thickness 0 4% By these measures we obtain 1.300% solid inches in the quantity of stufl' for a whole semicircnm- ference, as required by Pain’s method. Figure 183 is a developement of the plank for a uarter of the circumference as re uired b Pain’s q 2 y method. Ft. In. The length } l 8 } which reduced to measures inches, gives 20. The breadth O 85%} h f The thickness 0 4% as e ore. By these measures we obtain 765 solid inches required by Pain for one quarter of the circum- ference. Figure 184 is a developement of the plank, shew- ing the quantity of stuff according to the method used by the Author. Ft. In. ‘ The length } 1 8% { which reduced to measures " inches, gives 20%, The breadth O 4 The thickness 0 3 By these measures we obtain 246 solid inches for the quantity of stuff, by the method invented by the Author. From these calculations, it appears that if the quantity of stuff which the Author’s method re- quires, be called unity, or one, Pain’s method will require three times as much, and that invented, or first presented by Price, three and a half times as much. In these we have only compared the numbers answering to the solidity of one quarter of the circumference, as the formation of a rail for the whole semicircumference would be ridiculous, not only on account of the quantity of stuff, but the impossibility of being able to match the fibres at thejoint, as has been before observed. It may, however, be observed, in Pain’s method, that though the quantity of stuff required for one quarter of the circumference be much greater than the necessary quantity, yet the thickness and breadth for a whole semicircumference does not appear extra for such a large portion of the rail. It may also be observed, that none of the preced- ing authors ever followed a falling-mould, nor has only one of them brought the solid of the wreath into the straight of the rail. If these had been done, the thickness of stufl’ required would have been much greater than that required for the quadrantal part of the circumference only. ' ’ It is remarkable that they should have made the sections of the prism for the face-mould upon a plane perpendicular to one of the radii, and con. sequently parallel to the other radius of the. qua- drantal plan, as the rail requires much thicker stufi' * 2 c 2 301 196 JUM M in this position than any other they could have chosen. Figure 185 shews the several inclinations accord- ing to the plane of section: A B C is the inclina- tion according to Price and his followers; A B E is that according to Pain; and A B D that prac- tised by the Author; which indeed is the only inclination founded upon principle, and is nearly an arithmetical mean between the other two; that used by Pain being too high, and that by Price too low. It has already been observed, that the method of preparing the scroll, by gluing blocks side by side, was very incorrect, being founded only in whim: and though gluing up scrolls in parallel blocks is not an approved method, nor ought to be so, yet it may not be amiss to shew the true principle. Let Figure 185 be the plan of the scroll, the shank being formed by the parallel blocks K B, E C, FD, glued to the block or cen- tral part, which forms the eye. Figure 186, the falling—mould, the heights k l, a m, b n, c o, d p, irq, are those upon the points A, B, C, D, on the plan, and the height h 1‘ that upon F or H. Fi- gure 187 is an elevation or projection of the blocks, shewing the method of gluing them to- gether; the heights kl, a m, b n, c o, d p, are re- spectively equal to the corresponding heights in Figure 186. This Figure, viz. 187, shews how the blocks are to be formed before they are put to- gether. JOINT, the surface of separation of two bodies brought into contact, and held firmly together either by a glutinous liquid, or by opposite pres- sures, o-r by the weight of one body lying upon the other. A joint is, however, not the mere con- tact of surfaces, but the nearer they approach ‘ the more perfect is the joint. Perhaps two pieces of wood adhering together by means of glue, or other such tenacious liquid, between two plane surfaces, is the most perfect. In masonry, the distances of the planes. intended to form a joint are very considerable, owing to the coarse- ness of the particles which enter the composition of the cement. JOINTER, in joinery, the largest plane used by the joiner to straighten the face or edge of the stuff which he is preparing. JOINTER, in bricklaying, a crooked piece of iron, forming two curves of contrary flexure by its edges on each side, used for drawing the coursing and vertical joints by the edge of the jointing rule. JOINTING RULE, a straight edge used by brick- layers for regulating the direction or course of the jointer, in the horizontal and vertical joints of the brickwork. J OISTS, one or more horizontal rows of parallel equidistant timbers in a floor, on which the floor- ing is laid. There are three kinds of joists, viz. binding joists, bridgingjoists, and ceiling joists. JONES, INIGO, a celebrated architect, born in London about 1572. He was bred a joiner, but his skill in drawing recommended him to the notice of the earl of Pembroke; who sent him to Italy, where he acquired a complete knowledge of architecture. James I. made him surveyor—general of his works, which oflice he discharged with great fidelity. He continued in the same post under Charles I. and had the superintendencc of the building of St. Paul’s, Covent—Garden; with the management of the masques and interludes for the entertainment of the court. This brought him into a squabble with Ben Jonson, his coad- jutor, who ridiculed him in his comedy of Bar- tholomewfair, under the name of Lantern Leatlzer- head. He suffered considerably during the time of Cromwell, so that grief, misfortunes, and age, brought him to his grave in July, 165]. In 1655, appeared his Discourse on Stonehenge, in which he attempts to prove it to have been a Roman temple. As an architect, Inigo generally, but not always, shines to great advantage. He designed the palace of 'Whitehall and the Banqueting— house, the church and piazza of Covent-Garden,. Coleshill, in Berkshire, Cobham-hall,in Kent, and various other buildings, public and private. The principal of his designs were published in folio, in 1727, and some in 1744. JUFFERS, stuff about four or five inches square, of any length. This term is not now in use, though frequently found in old books. JUMP, in masonry, one among the very numerous appellations given to the dislocations of the strata, by practical miners of different districts. JUMPER, a long iron tool, with a steel chisel— like point, used in quarries and mines for drilling or boring. shot-holes in rocks, which require to be blasted with gunpowder. Drill, neger, and gall, are other terms by which this tool is called. “hum 4 §\\\ u W\ \ \\ \ \N\\\\\\ \ \ L 197 KEY. KAABA, see CAABA. KEEP TOWER, the middle, or principal tower in a castle. See CASTLE. KEEPING, in painting, a technical term, which signifies the peculiar management of those parts of the art, colouring and chiaro-scuro, which pro- duces the proper degree of relievo in objects ad- mitted into a composition; according to their re- lative positions in the imagined scene, and the degree of importance the artist attaches to them. KENILVVORTH CASTLE, is famed in the annals of VVarwickshire for its antiquity. “ This ancient castle,” says Dugdale, “ was the glory of all these parts, and for many respects may be ranked, in a third place at the least, with the most stately castles of England.” This fortress was built by Geofli'y de Clinton, in the time of Henry I. He was Chamberlain and treasurer to that monarch. By subsequent kings and occupiers it was greatly enlarged and strengthened at different times: and ‘ in the various civil and domestic wars of Eng- 1 land, it was frequently the object of contention with different monarchs and nobles. What re— mains of the buildings shews that the whole was = an immense and spacious pile; consisting of an outer wall with bastion towers, a tilt-yard, with towers at each end; and several buildings within 1 The area within the 3‘ There were four i gatehouses, and the walls were from ten to fifteen “ At a short distance from the ‘ the ballium, or base-court. walls consists of seven acres. feet in thickness. castle was a priory for Black Canons; of which ; buildings, parts of the gateway and chapel re- 5 main. Near these is the parish church, the west- ern door-way of which is a curious specimen of ancient architecture. KERF, the way made by a saw through a piece of timber, by displacing the wood with the teeth of the saw. KEY-STONE, of an arch or vault, the last stone placed on the top thereof; which, being wider and fuller at the top than the bottom, wedges as a it were, and binds in all the rest. M. Belidor makes the thickness of the arch-stones of a bridge, one twenty-fourth part of the width KIL of the arch; but Mr. Gautier, another experi- enced engineer, makes their length, in an arch twenty-four feet wide, two feet ; in arches, forty- five, sixty, seventy-five, ninety wide, three, four, five, six feet, respectively ; and it is observed by Mr. Muller, that the thickness allowed by Belidor is not sufficient to prevent the weight of the arches from crushing the key-stones to pieces by their pressure against one another. The name key-stones, or arch-stones, is sometimes also given to all the stones which form the sweep of an arch, or vault, answering to what the French more distinctly call voussoirs. KEY, an instrument for locking and unlocking doors; see LOCK. KEY, of a floor, the last board that is laid. KEYED DADO, that which is secured from warp- ing by bars grooved into the back; see the fol- lowing article. KEYS, in naked flooring, pieces of timber framed in between every two joists, by mortise and tenon; and when driven fast between each pair, with their ends butting against the grain of the joists, are called strutting pieces. KEYS, in joinery, pieces of timber let, trans- verse to the fibres, into the back of a board, made of one, or several breadths of timber, either by a dove-tailing, or by first making a groove equal to the width of the keys, and then cutting nar- row grooves in the sides of the first-made groove, close to the bottom, preserving a sufficient sub- stance at the top of each. Keys are used for the purpose of preventing boards from warping. Dado, when made of broad boards, glued to. gether, should always be keyed. See DADO. KILDERKIN, a liquid measure, which contains two firkins, or eighteen gallons, beer measure; and sixteen ale measure. Two kilderkins make a barrel, and four an hogshead. KILN, a kind of oven, or stove, for admit- ting heat, in order to dry substances of va- rious kinds, as corn, malt, hops, Ste. It also signifies a fabric or building constructed for the purpose of burning lime-stone, chalk, and other KIL 198 KIL calcareous stories, into lime. ' Kilns are of differ- ent kinds, and formed in different ways, accord- ing to the purposes for which they are designed. KILN, Brick, see Baron. KILN, Hop, a stove or kiln for the purpose of drying or stoving hops. KI LN, Lime, a sort of kiln constructed for the pur- pose of burning various kinds of calcareous sub- stances, such as lime-stone, chalk, shells, Ste. into lime. They are built of different forms or shapes, according to the manner in which they are to be wrought, and the kinds of fuel to be em- ployed. It has been remarked, in a work on landed property, that, in places where materials are dear, from their being fetched from a distance, and where the fuel is coals, and also expensive, the form of a kiln is mostly that of an inverted cone, a form which has its inconveniences; but in districts where the art of burning lime is prac- tised with superior attention and correctness, the form has of late years been. gradually changing from conical to elliptical. But, in his opinion, “ the best form of a lime furnace, in the esta- blished practice of the present day, is that of the egg placed upon its narrower end, having part of its broader end struck ofi“, and its sides somewhat compressed, especially towards the lower extre- mity; the ground plot or bottom of the kiln be- ing nearly an oval, with an eye, or draft-hole, to- ward each end of it.” It is supposed that “two advantages are gained by this form, over that of the cone. By the upper part of the kiln being contracted, the heat does not fly off so freely as it does out of a spreading cone. On the contrary, it thereby receives a degree of reverberation, which adds to its intensity.” But the other, and still more valuable effect, is this: “ when the cooled lime is drawn out at the bottom of the furnace, the ignited mass, in the upper parts of it, settles down, freely and evenly, into the central parts of the kiln; whereas, in a conical furnace, the regular contraction of its width, in the upper as well as the lower parts of it, prevents the burn- ing materialsfrom settling uniformly, and level- ling downward. They ‘hang’ upon the sides of the kiln, and either form a dome at the bottom of the burning mass, with a void space beneath it, thereby endangering the structure, if not the workmen employed; or, breaking down in the centre, form a funnel, down which the under- burnt stones find their way to the draft-holes.” And “the contraction of the lower part of the kiln has not the same effect; for, after the fuel is exhausted, the adhesion ceases, the mass loosens, and, as the lime cools, the less room it requires. It therefore runs down freely to the draft-holes, notwithstanding the quick contraction of the bot- tom of the kiln or furnace.” And, lastly, that, “ with respect to the lime- furnace (which is, he thinks, entitled to the most sedulous attention of agricultural chemistry), the fire requires to be furnished with a regular supply ofair. When a kiln is first lighted, the draft- holes afford the required supply. But after the fire becomes stationary in the middle, or towards the upper part of the kiln (especially of a tall kiln), while the space below is occupied by burnt lime, the supply from ordinary draft-holes be- comes insufficient. If the walls of the kiln have been carried up dry or without mortar, the air finds its way through them to the fire. In large deep kilns that are built with air-tight walls, it is common to form air-holes in their sides, especi- ally in front, over the draft-holes. But these con- vey the air, in partial currents, to one side of the kiln only, whereas that which is admitted at the draft-holes passes regularly upward to the centre, as well as to every side of the burning mass; and, moreover, tends to cool the burnt lime in its pas- sage downward, thereby contributing to the ease and health of the workmen. Hence he is of opi- nion, that the size of the draught-holes ought to be proportionate to that of the kiln and the size of the stones taken jointly (air passing more freely among large than among small stones), and that the required supply of air should be wholly ad- mitted at the draft-holes. By a sliding or a shift- ing valve, the supply might be regulated, and the degree of heat be increased or diminished, at pleasure,” according to circumstances. . The most ancient kind of lime-kiln is probably that which is made by excavating the earth in the form. of a cone, of such a size as may be ne- cessary; and afterwards building up the sides, or not, according to the circumstances of the case: the materials being then laid in, in alternate layers of fuel and stone, properly broken, until the whole is filled up. The top is then covered with sods, in order that the heat may be prevented from . escaping: and the fire lighted at the bottom, and the whole of the contentsburnt, in a greater or less space of time, in proportion to the nature KIL 1'99 KIL of the stone, and the quantity that is contained in the kiln. From the circumstance of the top parts of these kilns, in some districts, being covered over, and the sides sometimes built up with sods, they are termed sod-kilns, in order to distinguish them from the other sorts. When the whole of the contents of such kilns are grown cold, they . are drawn or taken out from the bottom; and the kiln again filled, if necessary. These kilns are obviously intended for burning only one kiln-full at a time. But as the burning of lime in this way is tedious and uneconomical, other methods and forms of kilns have been had recourse to. Where lime is much wanted, either for building or other purposes, they therefore use perpetual kilns, or what are more generally known by the name of draw-kilns. These, as all lime-kilns ought to be, are, the author of Modern Agriculture says, situ- ated by the side of a rising bank, or sheltered by an artificial mound of earth. They are generally built either of stone or brick; but the latter, as being better adapted to stand excessive degrees of heat, is considered as preferable. The outside form of such kilns is sometimes cylindrical, but more generally square. The inside should be formed in the shape of a hogshead, or an egg, opened a little at both ends, and set on the small- est; being small in circumference at the bottom, gradually wider towards the middle, and then contracting again towards the top. In kilns con- structed in this way, it is observed, fewer coals are necessary, in consequence of the great degree of reverberation which is created, above that which takes place in kilns formed in the shape of a sugar-loaf reversed. Near the bottom, in large kilns, two or more apertures are made: these are small at the inside of the kiln, but are sloped wider, both at the sides and the top, as they ex- tend towards the outside of the building. The uses of these apertures are for admitting the air necessary for supplying the fire, and also for per- mitting the labourers to approach with-a drag and shovel, to draw out the calcined lime. From the bottom of the kiln within, in some cases, a small building, called a horse, is raised in the form of a wedge, and so constructed as to acceé lerate the operation of drawing out the burned lime-stone, by forcing it to fall into the apertures which have been mentioned above. In other kilns of this kind, in place of this building, there is an iron grate near the bottom, which comes close to the inside wall, except at the apertures, where the lime is drawn out. When the kiln is to be filled, a parcel of furze or faggots is laid at the bottom; over this a layer of coals; then a layer of lime-stone, which is previously broken into pieces, about the size of a man’s fist; and so on alternately; ending with a layer of coals, which is sometimes, though seldom, covered with sods or turf, in order to keep the heat as intense as possible. The fire is then lighted in the aper. tures; and when the lime-stone towards the bot- tom is completely calcined, the fuel being con- siderably exhausted, the lime-stone at the top subsides. The labourers then put in an addition of lime-stone and coal at top, and draw out at bottom as much as they find thoroughly burn- ed; and thus go on, till any quantity required be calcined. When lime-stone is burned with coals, from two and a half to three and a half bushels, on a medium, three bushels of calcined lime-stone are produced for every bushel of coals used in the process. A lime-kiln of this sort is described in Count Rumford’s Essays, in the possession of the Dublin Society, as well as the principal objects that ought to be had in view in constructing the’kiln pointed out: the first of which is, “ to cause the fuel to burn in such a manner as to consume the smoke, which has here been done by obliging the smoke to descend and pass through the fire, in order that as much heat as possible might be generated. Secondly, to cause the flame and hot vapour, which rise from the fire, to come in contact with the lime-stone by a very large surface, in order to economize the heat, and prevent its going off into the atmosphere; which was done by making the body of the kiln in the form of a hollow truncated cone, and very high in proportion to its diameter; and by filling it quite up to the top with lime-stone, the fire being made to enter near the bottom of the cone. “ Thirdly, to make the process of burning lime perpetual, in order to prevent the waste of heat which unavoidably attends the cooling of the kiln, in emptying and filling it, when, to per- form that operation, it is necessary to put out the fire. “ And, fourthly, to contrive matters so, that the lime in which the process of burning is just finish- ed, and which of course is still intensely hot, may, in cOoling, be made to give off its heat in ll KIL ._- n- such a manner, as to assist in heating the fresh quantity of cold lime-stone with which the kiln is replenished, as often as a portion of lime is taken out of it. “ To effectuate these purposes, the fuel is not mixed with the lime-stone, but is burned in a close fire-place, which opens into one side of the kiln, some distance above the bottom of it. For large lime-kilns on these principles, there may be several fire-places all opening into the same cone, and situated on different sides of it: which fire-places may be constructed and regu- lated like the fire-places of the furnaces used for burning porcelain. ‘ “ At the bottom of the kiln there is a door, which is occasionally opened to take out the lime. “ When, in consequence of a portion oflime be- ing drawn out of the kiln, its contents settle doWn or subside, the empty space in the upper part of the kiln, which is occasioned by this sub- traction of the burned lime, is immediately filled up with fresh lime-stone. “ As soon as a portion of lime is taken away, the door by which it is removed must be immediately shut, and the joinings well closed with moist clay, to prevent a draught of cold air through the kiln. A small opening, however, must be left, for rea- sons which are explained below. “ As the fire enters the kiln at some distance from the bottom of it, and as the flame rises as soon as it comes into this cavity, the lower part of the kiln (that below the level of the bottom of the fire-place) is occupied by lime already burned; and as this lime is intensely hot, when, on a portion of lime from below being removed, it descends into this part of the kiln, and as the air in the kiln, to which it communicates its heat, must arise upwards in consequence of its being heated, and pass off through the top of the kiln, this lime, in cooling, is by this contrivance made to assist in heating the fresh portion of cold lime- stone, with which the kiln is charged. To faci- litate this communication of heat from the red- hot lime just burned to the lime-stone above in the upper part of the kiln, a gentle draught of air through the kiln, from the bottom to the top of it, must be established, by leaving an opening in the door below, by which the cold air from without may be suffered to enter the kiln. This opening (which should be furnished with some kind of a register) must be very small, otherwise 200 KIL m r 4 , __... it will occasion too strong a draft of cold into the kiln, and do more harm than good; and it will probably be found best to close it entirely, after the lime in the lower part of the kiln has parted with a certain proportion of its heat.” It is acommon practice to burn lime-stone with furze in some places. The kilns which are made use of in these cases are commonly known by the denomination of flame-kilns, and are built of brick ; the walls from four to five feet thick, when they are not supported by a bank or mound of earth. The inside is nearly square, being twelve feet by thirteen, and eleven or twelve feet high. In the front wall there are three arches, each about one foot ten inches wide, by three feet nine inches in height. When the kiln is to be filled, three arches are formed of the largest pieces of lime-stone, the whole breadth of the kiln, and opposite to the arches in the front wall. When these arches are formed, the lime-stone is thrown promiscuously into the kiln to the height of seven or eight feet, over which are frequently laid fif— teen or twenty thousand bricks, which are burned at the same time with the lime-stone. When the filling of the kiln is completed, the three arches in the front wall are filled up with bricks almost to the top, room being left in each sufficient only for putting in the furze, which is done in small quantities, the object being to keep upa constant and regular flame. In the space of thirty-six or forty hours, the whole lime-stone, about one hun- dred and twenty, or one hundred and thirty quar- ters, together with fifteen or twenty thousand bricks, are thoroughly calcined. Kilns constructv ed in this way may be seen near \Vellingborcugh, in Northamptonshire, and other places in the northern parts of the kingdom. And in many of the northern counties of Scotland, which are situated at a great distance from coal, it is also a common practice to burn lime-stone with peat; and, considering the rude ill-constructed kilns which are used for the purpose, it is astonishing with what success the operations are performed. In some of these districts, it is stated that lime- stone is sufficiently calcined with peats, laid stra- tum super stratum, in kilns formed of turf; but, owing to the quantity of ashes which fall from the peat, the quality of the lime is considerably injured; and, from the open and exposed situa- tion of many of these kilns, the waste of fuel is immense. But the most common method of KIL 201 a” burning lime-stone with peat, is in kilns con- structed somewhat similar to those in the dis- tricts where furze is used as the only fuel. There are in general only two arches, or fire-places, and the peats are thrown into the bottom of these arches, the fronts of which are seldom closed up, by which means the wind has often great influence in retardingthe operation, and frequently pre- vents the complete calcination of the lime-stone. An improvement might, it is supposed, be made on these kilns at a very trifling expense: if an iron grate were laid across the bottom of the arch, with a place below for the ashes to fall down, and the front of the arch closed up by a door made of cast-metal, one-third of the fuel might be saved, and the operation performed in a shorter time, and with a much greater'certainty, than by the me- thod now practised in such kilns. - In the communications to the Board of Agricul- ture, l\'Ir. Rawson asserts, that he has produced a considerable saving in the burning of lime, by constructing his kiln in the following manner: “ It is made twenty feet in height; at the bot- tom a metal plate is placed, one foot in height, in— tended to give air to the fire; over this plate runs the shovel that draws the lime. The sloped sides are six feet in height, the breadth at the top of the slope is eight feet; the sides are carried up perpendicular fourteen feet, so that every part of the inside, for fourteen feet, to the mouth, is exactly of the same dimensions. On the mouth of the kiln a cap is placed, built of long stones, and expeditiously contracted, about seven or eight feet high. In the building of thecap, on one side of the slope, the mason is over the centre of the kiln, so that any thing dropping down will fall perpendicularly to the eye beneath. He is here to place an iron door, eighteen inches square, and the remainder of the building of the cap is to be carried up, until the hole at the top be con- tracted to fourteen inches. The kiln is to be fed through the iron door, and when filled, the door close shut. The outside wall must be three feet at the bottom to batter up to two feet at top, and made at such a distance from the inside wall of the kiln, that two feet of yellow clay may be well packed in between the walls, as every kiln built without this precaution will certainly split, and the strength of the fire be thereby exhausted. At eight feet high from the eye of the kiln, two flues should be carried through the front wall, through VOL. 11. 'KIL the packed clay, and to the opposite sides of the kiln, to give power to the fire.” It is observed, that with this kiln, he has produced one-third more lime from a given quantity of fuel; and stones of bad quality will be here reduced into powder, and may be put into the kiln without the necessity of being broken so small as is usual. As many situations will not admit of building a kiln twenty feet high, while other situations may allow of its being built thirty, or even forty feet, (for it cannot be made too high), the diameter of the kiln should be proportioned to the height to which it is carried up. ‘ And it is farther stated, as another application of this sort of contrivance, that “ for several years he has made use of a small kiln in an outside kitchen, the height nine feet, the diameter three feet and a half. In the side of the kiln next the’ fire, he had three square boilers placed, one of them large, containing half a barrel, with a cock, which supplied the family with constant boiling water; for the two others, he had tin vessels made to fit the inside with close covers, in which meat and vegetables with water were placed, and put into the two smaller boilers, which ”never had any water, but had close covers. The tin boilers were heated sooner than on the strongest fire, and when the meat, Ste. were sufliciently dressed, the whole was taken out of the metal boilers. At one side he had an oven placed for roasting and boiling meat; the bottom was metal of twenty-six'inches diameter, and one inch and a half thick, a fine from the fire went underneath. Even with the bottom of the oven, a grating nine inches square was placed, which opened a communication be- tween the oven and the hot fire of the kiln. The height of the oven was fourteen inches, shut close by a metal door of eighteen inches square, and the top, level with the mouth of the kiln, was co— vered by another metal plate of half an inch thick, on which was placed a second oven; the heat which escaped through the half-inch plate, though not near the fire, was sufficient to do all small puddings, pies, breakfast-cakes, &c. Ste. The meat in the large oven was placed on an iron frame, which turned on a pivot, and stood on a drippingopan, and was turned by the cook every half hour. And over the kiln he had a tiled stage for drying corn, and a chimney at one side, with a can] on the top, which carried ofi“ all steam and sulphur: a large granary was attached to the ‘ 2 D KIT 20% KNU ! I! 22:: “W. building.” It is added, that the lime, if sold, would more than pay for fuel and attendance; and he has frequently had dinner dressed for fifty men, without interfering with his family business in any great degree. KING—POST, or CROWN-POST, see CROWN- Posr. , KIRB-PLATE, see CURB-PLATE. KIRB-ROOF, see CURB-ROOF. KITCHEN (Welsh, kegz'n) an apartment used for the preparation of food, and furnished with suit- able accommodations and utensils for that pur- pose, of which the following are some of the principal. A range of grating; a smoak-jack in the chimney, to turn the spits for roasting; a large screen to stand before the fire, to keep off the cold air from the articles roasting, by which means the operation is considerably accelerated; an oven, as also a copper boiler, should be constructed on one side of the fire-place, and on the other side, a large cast-iron plate, fixed horizontally, on which to keep sauce and stew pans continually boiling with an uniform degree of heat; several preserving stoves should be fitted up, according to the number of the family; a table as large as the kitchen will admit of, should be constructed, with a chopping-block at one end. It would be impossible to enumerate the whole of the articles for culinary purposes; but, besides the above, the kitchen should also be furnished with dres- sers, having drawers or cupboards under them, put up in every vacant part; it should also have shelves fitted up round the sides, in order to set stew pans, sauce pans, 8L0. out of the way. Ad- joining to the kitchen, ought to be a large coal- cellar, for the convenient supply of the fire. The water ought to be conducted to the kitchen by * means of pipes, to be drawn off by one or more cocks, as may be wanted. The screen should be made of wood, and lined with tin, and fitted up with shelves, so as to hold the dishes and plates to be made hot for dinner. The copper-boiler is sometimes made double, or divided, and both parts heated by the same fire; each part should be furnished with a water-cock. The kitchen table should not be less than three inches thick. If the windows do not afford a very good light, a sky-light should be placed over the table, with a moveable cap, so as to admit any quantity of air at pleasure. ‘ KNEE, a piece of timber cut at an angle, or having grooves to an angle. KNEE, in hand-railing, a part of the back with a convex curvature: it is the reverse of a ramp, which is hollow on the back. KNIFE, Drawing, see DRAWING KNIFE. KNOTTING, a process in painting, for preventing the knots from appearing in the finish. Knotting is a composition of strong size, mixed with red-lead, for the first knotting,which prevents the gum from coming through. The second knot- ting is a composition of white-lead, red~lead, and oil; but in principal rooms, where the knots hap- pen to be very bad, they are often silvered: which is done by laying on a coat of gold size, and, when properly dry, a silver leaf is placed on them, which is sure to prevent the knots appearing. The operation of knotting is the first process in painting. KNUCKLE, of a hinge, the cylindrical part, where the one strap is indented into the other, and revolves upon a pin fixed as an axis, in that of the cylinder. See HINemG. 203 L. LAB LABEL, an ornament placed over an aperture, in the castellated style of building, consisting of a: horizontal part over the head, with two parts re- turning downwards at a right angle, one on each side of the aperture : sometimes these are termi- nated at the bottom with a bead, but most fre- quently return again at a right angle outwards, and, consequently, parallel to the part over the head. LABOUR, in measuring, the value put on a piece of work, in consideration only of the time required to perform it. LABYRIN TH (Greek, AaCuéneoc) among the an- cients, a large and intricate edifice cut into various isles and meanders, running into each other, so as to render it difficult to get out. There is mention made of four celebrated laby~ rinths among the ancients, ranked by Pliny in the number of the wonders of the world; viz. the Cre- tan, the Egyptian, the Lemnian, and the Italian. That of Crete is the most famed; it was built, as Diodorus Siculus conjectures, and Pliny posi- tively asserts, by Dadalus, by command of king Minos, who kept the Minotaur shut up in it, on the model of that of Egypt, but on a less scale: but both affirm, that in their time it no longer existed, having been either destroyed by time, or purposely demolished. It was hence that Theseus is said to have made his escape by means of Ariadne's clue. Diodorus Siculus and Pliny represent this laby- rinth as having been a large edifice; while others have considered it. as merely a cavern hollowed in the rock, and full of winding passages. “ If the labyrinth of Crete,” says the Abbé Barthelemi, “ had been constructed by Daedalus under the order of Minos, whence is it that we find no men- tion ofit, either by Homer, who more than once [ speaks of that prince, and of Crete, or by Hero- dotus, who describes that of Egypt, after having said that the monuments of the Egyptians are much superior to those of the Greeks; or by the more ancient geographers; or by any of the writers of the ages in which Greece flourished? This work was attributed to Daedalus, whose name,” LAB says our author, “is sufficient to discredita tradi- tion. His name, like that of Hercules, had be- conie'the’ resource of ignorance, whenever it turn. ed its eyes on the early ages. All great labours, all works which required more stréngth than in- genuity, were attributed to Hercules; and all those which had relation to the arts, and required a certain degree of intelligence in the execution, were ascribed to Daedalus.” According to Diodo- ms and Pliny, no traces of the labyrinth of Crete existed in their time, and the date of its destruc- tion had been forgotten. Yet it is said to have been visited by the disciples of Apollonius of Tyana, who was contemporary with those two authors. The Cretans, therefore, believed that they possessed the labyrinth. “ At Nauplia, near the ancient Argos,” says Strabo, “ are still to be seen vast caverns, in which are constructed laby- rinths, that are believed to be the work of the Cy- clops;” the meaning of which, as Barthelemi understands him, is, that the labours of men had opened in the rock passages which crossed and returned upon themselves, as in quarries. Such, he says, is the idea we ought to form of the laby- rinth of Crete. He then suggests an inquiry, whether there were several labyrinths in that island? Ancient authors speak only of one, which most of them place at Cnossus, and some few at Gortyna. Belon and Tournefort describe 3. ca- vern situated at the foot of mount Ida, on the south side of the mountain, at a small distance from Gortyna: which, according to the former, was a quarry, and according to the latter, the an- cient labyrinth. Besides this, another is sup- posed to have been situated at Cnossus, and, in proof of the fact, it is alleged, that the coins of that city represent the plan of it. The place where the labyrinth of Crete was situated, accord- ing to Tourneforl, was, as Barthelemi supposes, one league distant from Gortyna; and, according to Strabo, it was distant from Cnossus six or seven leagues; with respect to which our author concludes, that the territory of thelatter city ex. tended to the vicinity of the former. In reply to the inquiry, what was the use of the caverns, de» 2 D 2 LAB 204 LAB nominatedilabyrinths, Barthelemi imagines, that they were first excavated in part by nature; that in some places stones were extracted from them for. building cities, and that, in more ancient times, they served for an habitation or asylum to the in- habitants of a district exposed to frequent incur- ‘ sions. According to .Diodorus Sieulus, the most ancient Cretans dwelt in the caves. of mount Ida. The people, when inquiries were made on the spot, said, that their labyrinth was originally a prison. It might indeed have'been applied to this use; but it is scarcely credible that, for pre- venting the escape of a few unhappy wretches, such immense labours would have been under- taken. The labyrinth of Egypt, according to Pliny, was the oldest of all ; and was subsisting 1n his time, after having stood, according to tradition, as he says, 4600 years. He says it was. built by king Petesucus, or Titho'és; but Herodotus makes it the work of several kings : it stood on the south- ern bank of thelake Moeris, near the town of Cro- codiles, or Arsinoe, and consisted of twelve large contiguous palaces, in which the twelve kings of Egypt assembled to transact afl'ai1s of state Dand religion, containing 3000 apartments, 1500 of which were under g10u11d. This st11.1ctu1e seems to have been designed as a pantheon, or universal temple of all the Egyptian deities, which were separately worshipped in, the provinces. It was also the place of the general assembly of the magistracy of the whole nation ; for those of all the provinces or nomes met here to feast and sacrifice, and to judge causes of great consequence. For this reason, every nome had a hall or palace appropriated to it; the whole edi- fice containing, according to Herodotus, twelve; Egypt being then divided into so many king- 'doms. Pliny makes the numbei of these palaces sixteen, and Strabo makes them twenty -seven. All the halls were vaulted, and had an equal num- ber of doors opposite to one another, six opening to the north, and six to the south, all encom- passed by the same wall. The exits, by various passages and innumerable returns, aflbrded to Herodotus a thousand occasions of wonder. The roofs and walls within were encrusted with mar— ble, and adorned with sculptured figures. The halls were surrounded with pillars of white stone finely polished; and at the angle, where the laby- rinth ended, stood the pyramid, which Strabo as- serts to be the sepulchre of the prince who built the labyrinth. According to the description of Pliny and Strabo, this edifice stood in the midst of an immense square, surrounded with buildings at a great distance. The porch was of Parian marble, and all the other pillars of marble of Sy- ,, ene; within were the temples of their several deities, and galleries, to whichwas an ascent of ninety steps, adorned with many columns of por- phyry, images of their gods, and statues of theii kings, of a bcolossal size: the whole edifice was constructed of stone, the floors being laid with vast flags, and the roof appearing like a canopy of stone: the passages met, and crossed each other with such intricacy, that it was impossible for a stranger to find his way, either in or out, without a guide; and several of the apartments were so contrived, that on opening of the doors, there was heard within a terrible noise ofthundet. Although the Arabs, since the days of Pliny, helped to ruin this structure, yet a considerable part of it is still standing. The people of the country call it the palace of Cha1on. Strabo, D10do1 us Siculus, Pliny, and bIela speak of this monument with the same admiration. as Herodotus; but not one of them says it was con-» structed to bewilder those who attempted to pass through it; though it is manifest, that, without a guide, they would have been in danger of losing their way. The Abbé Barthelemi suggests, that this danger introduced a new term. into the Greek language. The word labyrinth, taken in the lite» ral sense, signifies a circumscribed space, inter- sected by a number of passages, some of which cross each other in every direction, like those in quarries and mines, and others make larger or smaller circuits round the place from which they depart, like the spiral lines that are visible on certain shells. Hence it has been applied, in a figurative sense, to obsculea 1nd captious ques- tions, to indirect and ambiguous answe1s, and to those discussions, which, after long digressions, bring us back to the point from which we set out. The labyrinth of Lemnos was supported by co- lumns of wonderful beauty; there were some re- mains of it at the time when Pliny wrote. That of Italy was built by Porsenna, king of Etruria, for his tomb. LABYRINTH FRET, a fret with many turnings, in. the form of a labyrinth; one of the most ancient ornaments in the world. LA on i205 LAN W LACUNARIS, or LACUNARS, in a1chitectu1e, the panels or coflers. formed on the ceilings of apa1tme11ts, and sometimes on the soffits of the corona of the Ionic, Corinthian, and Composite orders. In the temple of Minerva at Athens, the lacunars are placed immediately above the frieze within the portico, and formed with a single recess, having an ovolo at the top, which moulding terminates the vertical plane sides, and the horizontal heads - of the lacunars. The lacunars are not square, but longer in the longitudinal than in the transverse direction of the building. In this they are formed in one recess, with an ovolo at the top of the recess, or the farthest ex- tremity of the sides. The lacunars are longer from front to rear of the portico, than in the trans- verse direction of the building. In the temple of Theseus at Athens, the lacunars are formed above the frieze, in two rows, between large beams which reach from the rear to the front of the pronaos: their figures are of a square horizontal section, and have only a single recess upwards, with an ovolo above it. The side of the square of each cofi'er is about one-fifth part of the diameter of the column, and their re- cess upwards half the side of their square. The distance between the beams is equal to the breadth of the antaa at the bottom, or nearly equal to the diameter of the columns. The beams are not re- gulated by the columns, but placed at equidis- tant intervals, to receive the two rows of lacunars, or coffers. Within the temple or cella, the beams reach transversely from side to side; but without, and under the soflit of the pronaos, they extend longitudinally from the front to the rear of the pronaos, and the lacunars in the same direc- tion. In the soflit of the temple of Pandrosus at Athens, the lacunars are formed immediately above the architrave, each into three recesses, with an ovolo at the bottom of each, nearly as broad as the perpendicular surface. The whole depth of the recess is nearly half the side of the square of its lower part. Each part diminishes gradu- ally in breadth in a sloping straight line, till the side of the square of the upper part is so contracted as to be only half that of the lower. Each succeeding third part diminishes regula1ly in altitude, so that, accounting the bottom the first, the alt1tude of the second, or the one next above, is something less, and the third about the same quantity less than the second. Each ovolo is something less in height than the vertical sur- face below it, and has the same ratio to its re— spective surface. Thecella of the temple of Vesta at Rome is sur— rounded with a circular colonnade. The ceiling of the portico has a double row of lacunars, be— ing two in the breadth of the portico. The lacu- nars approach as nearly to a square as is consis- tent with their diminution, formed by radiations towards the centre of the building, and are con- structed in two recesses. The greatest breadth of the outside lacunar is about nine-thirteenths of the diameter of the columns. The Whole depth of the recess upwards is about one—seventh of a diameter. The radiating sides are in vertical planes, and the other two sides of each are ver- tical cylindric concentricsurfaces. The greatest breadth of the upper recess is about two-thirds of the lower. The hollow of this recess is occupied by a rose ofa circular form. The recess or cradle vaults of the temple of Peace at Rome are arched and enriched with octagonal lacunars, each form- ed in three recesses, which diminish in their margins as they recede upwards. Between the octagonal lacunars are others of a square form in a diagonal position. The ceiling of the middle of the chapel of the said temple is comparted with hexagonal and rhdmboidal lacunars. The lacunars of the arch of Titus at Rome are square, the side of each being about three- quarters of the diameter of the column. ‘ LADY-CHAPEL, a name invented by modern ar— chitects and virtuosi to signify the chapel which is generally found in our ancient cathedrals be- bind the skreen of the high altar. It is so deno» minated from its being generally dedicated to the Virgin Mary, called Our Lady. LANCE-T ARCH, the same as pointed arch. LANCET WINDOW, that of which the head is a laneet a1ch; but the term is more generally ap- plied to those windows which are long and nar- row,w with lancet a1ches. LANDING, the first part of a floor at the head of a stair. LANTERN, in a1chitect11re, a tunet raised above the roof with windows round the sides, in order to light the apartment below. Lanterns are much more convenient than skylights; for as the surface of the glass stands vertical, they are not so liable LAT 206 to be broken, nor so subject to the rattling noise of heavy rains and hail. LANTERN is also used for a square cage of timber, with glass in it, placed over the ridge of a cor- ridor, or a gallery between two rows of shops, to illuminate them. - ‘LAP, the junction of two bodies where they mutu- ally cover each other. LARDER, or SAFE, a place in which undressed meat is kept for the use ofa family. ' It ought to be so .large, as to hold a quantity pro- portioned to the number of the family, and should be well ventilated through the roof, so as to keep a continued Circulation of air; the light must be from windows in the wall, which ought to have a northern aspect. The roof ought to be double, so as to contain a cavity for air, in order to pre- clude the heat of the sun, and the whole building constructed of wood. The windows should be wired, rather than glazed, and the interstices be- tween the wires so small as not to admit of any files. In order to prevent the sun from getting in, the exterior roof should over-hang the safe, so as to keep off the sun’s rays, which will only be in the morning and afternoon of the day. If a northern aspect cannot be obtained for light, other means must be employed to preclude the sun’s rays. The floor should be elevated above the ground, to prevent dampness, say two or three feet, as may be found convenient; and the safe here spoken of should not adjoin any other building, since its use is to keep the meat cool. The safe should be fitted up with a row of shelves and several rows of hooks, in the manner that butchers hang up joints of meat, 8L0. The shelves are necessary to lay the meat on when wanted. The hooks must be fastened to beams, and not to the sides of the safe; and the beams should be placed so high as to keep the meat above the head of any person. LARMIER (from the French) signifying tears; the word is of the same import as CORONA, which see. LATCH, the catch for holding a door fast. LATH, a slip of wood .used in plastering, tiling, and slating. These are what Festus calls am- brz'ces; in other Latin writers they are denomi- nated templa; and by Gregory of Tours, liga- tum. In plastering, the narrower the laths are, the better they are for the purpose, so as they are of sufficient breadth to hold the nails, as the more the LAT W number of interstices is increased, the more readily will the lime or stuffhang; and the thicker they are, the better will they be adapted to resist violence; but then they would be much more expensive. The laths are generally made of fir, in three, four, and five feet lengths, but may be reduced to the standard of five feet. Laths are single or double; the latter are generally about three-eighths of an inch thick, and the former barely one quarter, and about an inch broad. Laths are sold in bun- dles ; the three feet, are eight score to the bundle, four feet, six score, and the five feet, five score. The lath for plain tiling is the same as that used in plastering. Laths are also distinguished into heart and sap laths,- the former should always be used in plain tiling, and the latter, of an in- ferior quality, are most frequently used by the plas- terer. Heart-of-oak laths, by the statute Ed w. l I I . should be one inch in breadth, and half an inch in thickness ; but now, though their breadth be an inch, their thickness is seldom more than one quarter of an inch ; so that two, as they are now made, are but equal to one. According to the said statute, pantile laths are nine or ten feet long, three-quarters of an inch thick, and one andahalf inch broad, and should be made of the best yellow deal: the bundle consists of twelve such laths. A square of plain tiling will require a bundle of laths, more or less, according to the pitch. The distance of laying laths one from another is various, difl'ering more in some places than in others; but three and a half, or four inches, are usual distances, with a counter- lath between rafter and rafter; but if the rafters stand at wide intervals, two counter-laths will be necessary. Laths are employed for various other purposes besides plastering and tiling, as in filleting for sustaining the ends of boards; in naked flooring and roofing, for furring up the surfaces; and in every kind of small work, where the dimensions of the parts do not exceed the scantling of laths. In lathing for plastering, it is too frequent a custom to lap the ends of the laths upon each other, where they terminate upon a quarter or batten, to save the trouble of cutting them; but though this practice saves a row of nails, it leaves only a quarter of an inch for plaster, and if the laths are very crooked, as they frequently are, there will be no space whatever left to IJAU 907 LAW M straighten the plaster: the finished surface must, therefore, be rounded, contrary to the intention and to the good effect of the work; but if the ends are to be laid upon each other, they should be thinned at the lapping out to nothing at the extremity, or otherwise they should be cut to exact lengths. Laths should be as evenly split as possible; those that are very crooked should not be used, or the crooked part should be cut out; and such as have a short concavity on the one side, and a convexity on the other, not very prominent, should be placed with the concave side outwards. The following is the method of splitting laths: the lath cleavers having cut their timber into lengths, they cleave each piece with wedges into eight, twelve, or sixteen pieces, according to the scantling of the timber: the pieces thus cloven are called bolts ; then, in the direction of the felt- grain, with their dowl—ax, into sizes for the breadth of the laths: this operation they call felting; and, lastly, with their chit, they cleave them into thicknesses by the quarter-grain. LATH BRICKS, are bricks made much longer than the ordinary sort, and used instead of laths for drying malt upon; for which purpose they are extremely convenient, as not being liable to catch fire, and retaining the heat much longer than those made of wood, so that a very small fire is sufficient after they are once heated. LAUNDRY, a large room, wherein linen after washing is mangled and ironed (and sometimes dried, if there is not a drying room for the pur- pose.) The chief and most important utensil in a laundry, is a good stove to heat the irons, likewise, dry the linen, besides which, there should also be a large range of grating to air the linen after being ironed or mangled. The stove ought to stand nearly in the middle of the room, and have a long iron pipe for the smoke to ascend, which should be carried several times back- ward and forward, and at length terminate in the flue of the chimney near the ceiling, by which 'means it will throw a considerable heat into the room. As it is a known property of heat to ascend, large racks or horses are made so as to be drawn up by pulleys horizontally to the ceiling, where the linen will dry very soon. There should be a mangle, a mangling table, and a large board or dresser fixed to the window side of the room, which ought to be fitted up underneath with large drawers and cupboards for holding linen in after finished. There should be an adjoining room for the laundry-maids to sleep in. There ought to be a place to hold a suificient quantity of coals to serve for a day or two, which is filled from the coal-house, near the wash-house; there ought also to be a place fitted up for the maids to wash their hands. LAWN, an open space of short grass-ground, in the front of a residence, or in a garden, park, or other pleasure-ground. These, when extended in the principal fronts of habitations, add consider- ably to the neatness and grandeur of their ap- pearance, by laying them open, and admitting more extensive prospects. Where there is a sufficient scope of ground, they should be as llarge as the nature of the situation will admit, always being planned in the most conspicuous parts immediately joining the houses, and extende ed outward as far as convenient, allowing width in proportion; having each side or verge bounded by elegant shrubbery compartments in a varied order, separated in some parts by intervening spaces of grass-ground, of varied dimensions, and serpentine gravel-walks, gently winding be- tween and through the plantations, for occasional shady, sheltered, and private walking: or similar walks carried along the fronts of the boundary plantations, and immediately joining the lawns, for more open and airy walking in; and in some concave sweeps of the plantations there may be recesses and open spaces both of grass and grave], of different forms and dimensions, made as places of retirement, shade, Ste. Though the usual situations of lawns are those just mentioned; yet if the nature of the ground admit, or in cases where there is a good scope of ground, they may be continued more or less each way; but always the most considerable on the principal fronts, which, if they be to the south, or any of the southerly points, they are the most desirable for the purpose. ’ With respect to the dimensions, they may be from a quarter of an acre, or less, to six or eight acres, or more, according to the extent and situa- tion of the ground. Sometimes lawns are ex- tended over Ila-has, to ten, twenty, or even to fifty or sixty acres, or more. But in these cases they are not kept mown, but eaten down by live stock. The form must be directed by the nature of the LAW 208 W LAZ situation; but it is commonly oblong, square, oval, or circular. ‘But in whatever figure they are designed, they should widen gradually from the house outward to the/farthest extremity, to have the greater advantage of prospect; and by having that part of them within the limits of the pleasure- ground, bounded on each side by plantations of ornamental trees and shrubs, they may be con- tinued gradually near towards each wing of the habitation, in order to be sooner in the walks of the plantations, under shade, shelter, and retire- ment. The terminations at the farther ends may be either by ha-has to extend the prospect, or by a shrubbery or plantation of stately trees, arranged in sweeps and concave curves. But where they extend towards any great road, or distant agree- able prospect, it is more in character to have the utmost verge open, so as to admit of a grand View from and to the main residence. Butthe side-boundary verges should have the plantations rurally formed, airy and elegant, by being planted with different sorts of the most ornamental trees and shrubs, not in one con- tinued close plantation, but in distinct separated compartments and clumps, varied largeror smaller, and differently formed, in a somewhat natural imitation, being sometimes separated and de- tached less or more, by intervening breaks, and open spaces of short grass, communicating both with the lawns and interior districts; and gene- rally varied in moderate sweeps and curves, especially towards the lawns, to avoid stiff, formal appearances, both in the figure of the lawns and plantations. In planting the trees and shrubs, which should be both of the deciduous and ever— green kinds, where intended to plant in distinct clumps, either introduce the deciduous and ever- greens alternately in separate parts, or have some of both interspersed in assemblage; in either method, placing the lower growth of shrubs towards the front, and the taller backwards, in proportion to their several statutes, so as to ex- hibit a regular gradation of height, that the dif- ferent sorts may appear conspicuous from the main lawns. They may be continued backwards to a considerable depth, being backed with trees and shrubs of more lofty growth. The internal parts of the plantations may have gravel or sand walks, some shady, others open; with here and there some spacious short grass openings of dif- ferent dimensions and forms. It is seldom that extensive» lawns in parks or paddocks, Sec. have any boundary plantations close to what may be considered as a continuation of them beyond the pleasure-ground, but are sometimes dotted with noble trees, dispersed in various parts, at great distances, so as not to obstruct the View; some placed singly, others in groups, by twos, threes, fives, 8tc. and some placed irregularly, in triangles, sweeps, straight lines, and other different figures, to cause the greater variety and effect, each group being diversified with different sorts of trees, all suf- fered to take their natural growth. Where small, these kinds of openings should always be kept 'perfectly neat, by being often poled, rolled, and mown, but where they are of larger extent, this is scarcely ever the case. * LAYER, see COURSE. LAZARETTO or, LAZAR-HOUSE, a public build— ing, in manner of an hospital, for the reception of poor sick: or in some countries, an edifice appointed for persons coming from places sus- pected of the plague, to perform quarantine. This is usually a large building, at a distance from any city, whose apartments stand detached from each other, See. where ships are unladcn, and their crew is laid up for forty days, more or less, according to the time and place of their departure. \Ve are indebted to John Howard, Esq. the most distinguished philanthropist, who has ap- peared in this or any other country, and whose services in the cause of humanity can never be forgotten, for a particular account of all the prin- cipal lazarettos in Europe, with plans of the build— ings, a detail of their chief regulations, and very important and useful hints for their improvement. With this view he determined, towards the end of the year 1785, notwithstanding the expense and danger which he thus incurred, to visit them in person. Accordingly, the first lazaretto which he inspected was that at Marseilles, which is situated on an elevated rock near the city, at the end of the bay, fronting the south-west, and corn— manding the entrance of the harbour. This is a spacious building, and its situation renders it very commodious for the great trade which the French curry on in the Levant. Within the lazaretto is the governor’s house, a chapel, in which divine service is regularly performed, and a tavern, from which persons under quarantine may be supplied with necessaries. In order to LAZ 209 LL LEA __ ’- prevent any communication, that is not allowed by the regulations of the establishment, there is a double wall round the lazaretto; and at the gate there is a bell for calling any person within this enclosure; and by the number and other modifications of the strokes, every individual knows when he is called. At Genoa, whither Mr. Howard next proceeded, the lazaretto is situated on the sea-shore, near the city, detached from other buildings, and encompassed by a double wall. Another lazaretto, belonging to the Genoese, stands on a rising ground at Varignano, near the gulf or noble port of Specia. At Leg- horn there are three lazarettos; one of which is new, having been erected in the year 1778. The lazaretto at Naples is very small; that at Messina lies on an island near the city. At Naples there are two kinds of quarantine performed; one by ships with clean bills of health, and the other by ships with foul bills. The first, called the petty quarantine, lasts 18 days, and the ships which perform it lie at the entrance of the port near the health-office. The other, called the great quaran- tine, is performed at a lazaretto, situated on a peninsula near the city. The health-office at Zante is in the city at the water side. The old lazaretto is distant about half a mile from the city, and situated on a rising ground near the sea. There is another, called the new lazaretto, which is appropriated to a numerous body of peasants, who pass over to‘ the Morea to work in harvest time; on their return, they perform here a seven days’ quarantine; and other persons perform fourteen days’ quarantine in the old lazaretto. The lazaretto at Corfu is finely situated on a rock surrounded with water, about a league‘from the city. Thelazaretto of Castel-Nuovo,in Dalmatia, is on the shore, aborit two miles from the city; at the back of it there is a delightful hill, which belongs to a convent of friars. Persons in qua- rantine, after a few days, are allowed to walk there, and divert themselves with shooting, Ste. In order to obtain the most complete and satisfactory information by performing the strictest quaran- tine, our author determined to go to Smyrna, and there to take his passage to Venice in a ship with a foul bill. He was thus enabled to give a par- ticular account of his reception and accommoda- tion in the new lazaretto of this city, which is chiefly assigned to Turks and soldiers, and the crews of those ships which have the plague on VOL. 11. board; and this he thought to be the more ne- cessary, as the rules and tariffs of the other laza— ’ rettos in Europe have been evidently formed from those established at Venice. The city of Venice has two lazarettos, appropriated to the ex- purgation of merchandize susceptible of infection, coming from suspected parts, and for the accom- modation of passengers in performing quarantine; as also for the reception of persons and effects infected in the unhappy times of pestilence. The old lazaretto is two miles, and the new about five miles distant from the city, both on little islands, separated from all communication, not only by broad canals surrounding them, but also by high walls; they are of large extent, being about 400 geometrical paces in circumference. Of these Mr. Howard has given a particular description, with an account of the regulations, and mode of government to which they are subject, and a plan of the old lazaretto. At Trieste there are two lazarettos; one new, but both clean, and a com trast to those which our author had seen at Venice. Of the new one he has given a plan. It is surrounded, at the distance of about 20 yards, by a double wall, within which are separate bury- ing places for Roman Catholics, Greeks, and Protestants. Mr. Howard closes his account of the principal lazarettos in Europe, with the out- lines of a proper lazaretto, and an engraved sketch of a plan for its construction. He has also subjoined, in minute detail, various pertinent remarks respecting quarantines and lazarettos in general; together with observations on the im- portance of a lazaretto in England, in its con- nection with the advantages which our commerce might derive from it. LEAD (from the Saxon Iced) The colour of lead is of a bluish-white; when tarnished, it becomes yellowish-white, then bluish, and at last bluish-black. Lustre, when untarnished, 3; hardness, 5; and specific gravity somewhere be- tween 11 and 12. According to Brisson, it was 11.352; and a specimen tried by Gellert, which was found at Freyburgh, was estimated at 11.445. Next to gold, platina, and mercury, it is the heaviest metal, being upwards of eleven times heavier than an equal bulk of water. The heaviest is reckoned the best. It stains paper and the fingers. Next to tin, it is the most fusible of all the metals. It is soluble in most of the acids, though more readily so in the nitrous diluted than 2 E M-__s.-._- .._.,., .. LED 210 LEV ‘ 2W _‘ the others. By exposure to the moist atmosphere, it rusts, or oxides. It is malleable and unelastic, and its oxide is easily fusible into a transparent yellow glass. Lead is much used in building, particularly for coverings, gutters, pipes, and in glass windows. For which uses, it is either cast into sheets in a mould, or milled; which last, some have pre- tended, is the least serviceable, not only on ac- count of its thinness, but also because it is so exceedingly stretched in milling, and rendered so porous and spongy, that when it comes to lie in the hot sun, it is apt to shrink and crack, and consequently will not keep outthe water. Others have preferred the milled lead, or flatted metal, to the cast, because it is more equal, smooth, and solid. The lead used by glaziers is first cast into slender rods, twelve or fourteen inches long, called canes; and these, being afterwards drawn through their vice, come to have a groove on either side for the panes of glass; and this they call turned lead. The method of paling or soldering lead for fitting on of embossed figures, Ste. is by laying the part whereon the figure is to be paled horizon- tally, and strewing on it some pulverized resin; under this they place a chafing-dish of coals till such time as the resin becomes reddish, and rises in pimples; then the figure is applied, and some soft solder rubbed into thejointing; when this is done, the figure will be paled on, and as firm as if it had been cast on. For other uses in building, see the article SHEET LEAD. LEAN-TO, a small building, with a shed roof attached to a larger one. LEAVER, see LEVER. LEAVER BOARDS, see LEVER BOARDS. LEAVES, a representation in marble, stone, brass, wood, or other material, of natural leaves. See ORNAMENT. LEDGE, a surface on which to support a body in motion, or to support a body at rest. The ledges of a door are the narrow surfaces wrought upon the jambs and 50th parallel to the wall in order to stop the door, so that when the door is shut, the ledges coincide with the surface of the door. The ledges of a door are, therefore, one of the sides of the rebate, each rebate having only two sides. In temporary works the ledges of doors are formed by fillets. LEDGEMENT, the developement of a surface, or the surface of a body stretched out on a plane, so that the dimensions of the different sides may easily be ascertained. LEDGERS, in scaffolding for brick buildings, the horizontal pieces of timber parallel to the wall, fastened to the standards by cords, in order to support the put-logs, on which are laid the boards for working upon. LEGAL COLUMN, see COLUMN. LEGS, of a right-angled triangle, the two perpendi- cular sides. LEGS, of an hyperbola, the two parts on each side of the vertex. LENGTH (from the Saxon leng) the greatest ex— tension of a body. In a right prism, the length is the distance between the ends: in a right pyramid, or cone, the length is the distance be- tween the vertex and the base. LENGTHENING, of timber, is the method of joining several beams, so as to form along beam of any given length. LESBIUM MARMOR, a name given by the an- cients to a species ofmarble ofa bluish white, some— times used for vases and other ornamental works, but principally in the walls of public buildings. LEV EL, a mathematical instrument, used for draw- ing a line parallel to the horizon and continuing it out at pleasure, and by this means, for finding the true level, or the difference of ascent or descent between any two places, for conveying water, levelling the surface of floors, and for various other purposes in architecture, hydraulics, surveying, 8w. LEVEL, Carpenter’s, consists of a long rule, straight on its lower edge, about ten or twelve feet in length, with an upright piece fixed to its upper edge, perpendicular to, and in the middle of the length, having its sides in the same plane with those of the rule, and a straight line drawn on one of its sides perpendicular to the straight edge of the rule. This standing piece is generally mortised into the other, and firmly braced on each side, in order to secure it from accidents, and has its upper end kerfed in three places, viz. through the perpendicular line, and on each side. The straight edge of the transverse piece has a hole or notch cut out on the under side, equal on each side of the perpendicular line. A plummet is suspended by a string from the middle kerf at the top of the standing piece, *LEV *2 I1 LEV WM so that when hanging at full length, it may vibrate freely in the hole or notch. When the straight edge of the level is applied to two dis- tant points, with its two sides placed vertically, if the plummet hangs freely, and coincides with the straight line on the standing piece, the two points are level; but if not, suppose one of the points to be at the given height, the other point must be lowered or heightened, as the case may require, until the thread is brought to a coincidence with the perpendicular line. By two points, is meant two surfaces of contact, as two blocks of wood, or chips, or the upper edges of two distant beams. The use of the level in carpentry, is to lay the upper edges of joists in naked flooring horizontal, by first levelling two beams as remote from each other as the length of the level will allow; the plummet may then be taken off, and the level be used as a straight edge. In the levelling of joists, it is best to make two remote joists first level in themselves, that is, each throughout . its own length, then the two level with each other; after this, bring one end of the interme- diatejoists straight with the two which have been levelled; then the other end, in the same manner; then try the straight edge longitudinally on each intermediate joist, and such as are found to be hollow, must be furred up straight. To adjust the level—Place it in its vertical situa- tion upon two pins or blocks of wood; then, if the plummet, hanging freely, settle upon the line on the standing piece, or if not, one end being raised, or the other end lowered, to make it do so, turn the level, end for end, and if the plummet fall upon the line, the level is just; but if not, the bottom edge must be shot straight, and as much taken off the one end as you may think necessary; then trying the level first one way and then the other, as before, if a coincidence takes place between the thread and the line, the level is adjusted; but if not, the operation must be repeated till it come true. The most convenient class of levels is the spirit level, called also the air level, which is more accurate than any other kind, and is most ex- tensively used. The invention of this instrument has been ascribed to M. Thevenot. Others have attributed this application of a bubble of air to Dr. Hooke. The instrument consists of a cylin- drical glass tube filled with spirits of wine, except leaving in it a small bubble ofair; its ends being hermetically sealed to keep in the fluid. This bubble, being the lightest of the contents of the tube, will, by the laws of hydrostatics, always run towards that end of the tube which is most elevated; but when the tube is perfectly hori- zontal, the bubble will have no tendency towards either end. The tube is not strickly cylindrical withinside, though it bears that appearance, but is slightly curved, the convex side being upwards, and by this means the bubble will rest in the middle of the tube when it is horizontal, but approaches either end if elevated above the other. The simplest form of a spirit level for fixing any plane truly horizontal, consists of a glass tube of the above description, called a bubble tulle, fixed into a block of wood, as at A B, Figure 1. The lower surface, D E, of the block is made flat; and when the bubble, C, stands be- tween two scratches marked on the glass at a b, the line D E is horizontal. The method of making it correct is this; the tube is first fitted into the block, the lower edge, D E, of which is placed on a bench or table as nearly horizontal as can be determined, so that the bubble stands between the scratches a b. The level is now reversed, that is, the end D is put where E was at first. In this position, if the bubble stands in the middle, it proves the level to be correct, and the table horizontal; but if it runs to either end of the tube, it shews that end to be too much elevated: suppose it B, for instance; this end of the tube must therefore be let deeper into the wood, or the surface DE rectified to produce the same effect: one-half the error must be com- pensated by this means, and the other half by rectifying the table or support; for D E, the level, must 110w be reversed again to verify these correc- tions; and when they are so made that the hub- ble stands at a I), either way, the level is correct. To illustrate this more plainly, see Figure 2, which represents a section of a bubble tube; but, for elucidation, is shewn as if curved much more than they are ever made. Suppose the convex or upper surface of the tube to be a segment ofa large circle, B C D; from the laws of hydrostatics, it is plain, that the bubble of air, being the lightest body in the tube, will certainly occupy the highest point of the circle at C; and the two points, B, I), being equally distant therefrom, will be in the same horizontal line B E D. The > ‘2 E 2 LEV 212 "fi. - ..._...__ 47 larger the radius of the circle DB, so will the ,level be the more sensible of any deviation from the horizontal, because the bubble will have to traverse a greater distance along the tube, in proportion to any partial elevation of either end. .LEVELLING, the art or act of finding a line parallel to the horizon, at one or more stations, in order to determine the height of one place with respect to another; for the laying grounds even, regulating descents, draining morasses, conducting waters, for the irrigation of land, Ste. LEVER, or LEAVER, (from the French levier, ' formed of the verb lever, derived from the Latin, levare, “ to raise”) in mechanics, an inflexible straight bar, supported, in a single point, on a fulcrum, or prop, and used for the raising of weights. The lever is the first of those called mechanical powers, or simple machines, as being, of all others, the most simple; and is chiefly applied to the raising of weights to small heights. In a lever three things are to be considered: the weight to be raised, or upheld; the power by which it is to be raised, or sustained; and the fulcrum, or prop, by which the lever is supported, or rather on which it moves round, the fulcrum remaining fixed. Levers are of three kinds: sometimes, the fulcrum, or centre of motion, is placed between the weight and the power. This is called a lever of tkefirst kind, or eectis heterodromus; to which may be reduced scissars, pincers, snuffers, 8tc.: sometimes the weight is between the fulcrum and the power, which is called a lever of the second kind ,- such are the cars and rudder of a boat, the masts of ships, cutting knives fixed at one end, and doors whose hinges are as the fixed point: and sometimes the power acts between the weight and the fulcrum, which is the lever of the tkird kind; such is a ladder lifted by the middle to rear it up against a wall: these two are called vectes komodromi. In this last, the power must exceed the weight in proportion as its distance from the centre of motion is less than the distance of the centre from the weight. And as the first two kinds of lever serve for producing a slow motion by a swift one, so the last serves for producing a swift motion of the weight by a slow motion of the power. It LEV is by this kind of lever that the muscular motions of animals are performed, the muscles being in- serted much nearer to the centre of motion than the point where the centre of gravity of the weight to be raised is applied; so that the power of the muscle is many times greater than the weight which it is able to sustain. Though this may appear at first a disadvantage to animals, because it makes their strength less; it is, however, the effect of excellent contrivance; for if the power were, in this case, applied at a greater distance than the weight, the figure of animals would be not only awkward and ugly, but altogether unfit for motion; as Borelli has shewn in his treatise De Motu Animalium. The knowledge of the properties of the lever is of the utmost use in ascertaining the laws of the resistance of timber; we shall therefore begin with the first principles of motion, from which the properties of the lever are obtained; and also the principles of the centre of gravity of one, or of a system of bodies. 1. Force is the power exerted on a body to move it. 2. Direction of motion or tendency, is the effort which one body makes to move another towards a given point. 3. Line of direction is the straight line in which a body moves, or has a tendency to move, with- out having any regard to the point to which it tends. 4. Angle of direction is the angle contained between two lines of direction. 5. When two or more bodies act against each other without any of them being overcome by the rest, this state of quiescence is called equilibrium . 6. Opposite directions, or opposite tendencies, are when each of two bodies move, or have a ten- dency to move, to a different point in the same line of direction. 7. Opposite forces are those that act upon each other in the same line of direction, but have a tendency to contrary points in the line, by which tendency an equilibrium is produced, or otherwise a change of motion. 8. Contrary directions are when two bodies move, or have a tendency to move, in lines parallel to two opposite planes. Axiom L—Every body endeavours to preserve its present state, whether of rest or of moving MEN 2! uniformly in a right line, till it is compelled to change that state by some external force. Axiom 2.—-—The alteration of motion either gene- rated or destroyed in a body, is proportional to the force applied, and is made in the direction of that right line in which the force acts. Axiom 3.—-Action and reaction are equal between two bodies and opposite directions. Axiom 4.—-—Two equal forces acting against each other, or against a body, in Opposite directions, destroy each other’s effect. Axiom 5.—If a body is acted upon by two forces in opposite directions, it is the same thing as if it were only acted upon by one force equal to their difference, in the direction of the greater force. Axiom 6.—~If a body is kept in equilibrio by three or more forces, the sums of the contrary force, when reduced to parallel directions, are equaL Axiom 7.——VVhen a right line is drawn in a direc- tion of its length by two forces acting at its ex— tremities, the line may either be flexible or in- flexible. Axiom 8.——VVhen a right line is pressed or pushed by two forces in a direction of its length, and , retains its straightness, the right line is inflex- ible. Axiom 9.— Vhen a right line is stretched by two forces, the right line draws each of the forces with the same intensity that the forces stretch the line; because action and reaction are equal and contrary. Axiom 10.——When a right line is pressed by any two forces at its extremities in the direction of the line, it repels the force with the same inten- sity with which it is pressed by the forces. Axiom 11.——If two forces act upon a body and keep it in equilibrio, their lines of direction are in the same right line, and the two forces are equal, and have opposite tendencies. Axiom 12.—A force pulling by a string or flexible I line upon one side of a body, has the same effect in moving or in keeping it in equilibrio, as an equal force pushing or pressing on the same line of direction on the other side. Axiom 13.—-—A force acting upon a body has the same power in whatever point of the line of direction it is applied. Axiom 14.-—-If a line be pressed or drawn by two opposite forces, in the direction of the line, LEV all its parts will be equally stretched or com- pressed. Postulate.—Grant that the intensities of forces may be represented by right lines, as well as their directions. Proposition l.-—Plate I. Figure 1.——If any body, A, be moved by any impulse which would cause it to describe the right line A B, uniformly in a given time; and if the same body, A, be moved by another impulse, which would cause it to describe the right line A D, uniformly in an equal time : these two impulses, acting at the same in- stant, would carry the body through the diagonal, A C, of a parallelogram A B C D. For the impulse which is given in the direction AB, will not prevent the body from coming to D C, by the action of theimpulse in the direction AD, in an equal time to that in which AD would have been described by the separate im- pulse: for the same reason the impulse which is given in the direction AD, will not prevent the body from coming to B C, by the action of the impulse in the direction A B, in an equal time to that in which AB would have been described by the separate impulse: therefore, as the body will meet the lines DC and B C at the same time, it will meet in the intersection C; but because the lines AB and AD, are uniformly described in‘the same time, any two parts, AE and AF, taken from these lines in the ratio of the lines themselves, will also be described in equal times; and because BC is equal to A D, and E G equal to AF; ABzB C :: AE : EG; therefore the body moves in a straight line which is the diagonal of the parallelogram. Corollary 1.—-Hence, if the direction, intensity, and tendency, of any two forces acting upon a solid are given, a single force may be found, which shall be equivalent to the two. Corollary 2.—-Any single force, whose quantity and line of direction are given, may be resolved into two forces, which shall act at a given point in that line, in two given directions. Proposition II.——Given, the tracts, intensities, and tendencies of two forces making any angle with each other, to find a single force equivalent to them. Case I. Figure 2.——When each of the two given forces have a tendency, from the points A“ and C towards B, or from B towards A and C. Com- plete the parallelogram A B CD, and draw the LEV 214i M diagonal BD, and it will represent the quantity and direction of the third force, that will be equivalent to A B and C B ; and its tendency will be from B towards D, when the extreme forces tend towards B ; but towards B when the ex- treme forces have a tendency from B. Case II. Figure 3.—-—-When the two given forces tend to two different points. Let A B and B C be the two given forces, let the tendency of A B be from B towards A, and that of B C from C towards B; produce either, as A B, to E: make B E equal to A B, and complete the parallelogram BC DE; draw the diagonal B D, and it will be equivalent to BC and BE, or because BE is equal to BA, and both in the same straight line : and since both forces tend to the same point, A, the force B D is equivalent to B A and B C. It is evident, that though the angles and direc- tions given were the same in both cases, yet the tendency and quantity would be different in each. Proposition [IL—To resolve any force into two others, in any given directions, which shall act against any point of the line of direction of the given force. Figure 4. Let B E be the line of direction of the given force, B the given point, from which the required intensities are to act, and B F, B G their directions. Make B D equal to the intensity of the given force; complete the parallelogram ABC D ; then B A is the force acting in the line B F ; B C that in the line B G; and their tendencies are contrary to the middle force. Proposition IV.-—-If any two forces keep a third in equilibrio, the direction of the third has the same point of concourse, and is in the same plane with the other two, and all the three forces are to each other as the sides and diagonal of a parallelogram formed on their lines of direction, Figure 5. Let A B, B C, be the two forces; complete the parallelogram A BC D; then the force DB is equivalent to A B and B C; but if any force be in equilibrio with D B,it must be equal and oppo- site ; therefore, make B, E equal and opposite, and the two forces B D and B E are in equilibrio: take away the force D B, and let its equivalent forces A B and BC counteract BE, then the three forces A B, C B, and B E, are also in equi- librio: because BD and BE are in a straight line, the direction of E B passes through the point B, and is in the same plane with AB and LEV WM BC; for D B is in that plane: and because B E is equal to B D, the three forces A B, C B, E B, are expressed by the two sides AB and BC, and the diagonal DB of the parallelogram AB C D, formed on their lines of direction. Corollary 1.——Hence, if any three forces be in equilibrio with each other, they are as the sides of a triangle drawn parallel to their directions. Corollary2.———If the directions of any three forces, acting against the same point, keeping it in equilibrio, be given, and one of the intensities; the intensities of the other two may be found. Proposition V.-—-The lines of direction of three forces keeping each other in equilibrio, or a solid, and the intensity and tendency of one of them being given; to find the intensity and tendency of the other two. Case I. Figure 4.——VVhen two of the angles formed by the three lines of direction are less than two right angles. Let the three directions be B F, B E, B G, and let the given intensity be in the line B E, and let its tendency be from E towards B. Make BD equal to the given in- tensity, and complete the parallelogram A B C D. A B is the intensity in its own line of direction B F, its tendency being from B towards F; and B C is the intensity of the force in its line of direc- tion BG, its tendency being from B towards G: for, produce E B to H, since the force acting in the line EB presses the point B, then, by Axiom 12, it is the same thing, whether the force in the line EB press the point B, or an equal force on the other side of B: in EH draw the point B, and instead of the force pressing the point B by a force at E, let the point B be drawn by a force at H; thus the point B will be drawn by three forces, which are in equilibrio by the last Proposition. Or if the point B had been drawn by a force acting at E, the two forces acting in the lines B F and B G would have pressed these lines, and consequently three forces acting at F, G, H, would be all pressing the point B; it therefore appears, when three forces keep each other in equilibrio, and their lines of direction make two angles less than two right angles, that the force acting in the intermediate line will be contrary to those in the two extreme lines. Though this example only shews how to find the two extreme forces when the intermediate force is given; yet the intermediate force and one of the extreme forces may as readily be found ”by LEV 215 LEV M having the other extreme force given: because ‘ when one of the angles of a parallelogram is given, and the position of a diagonal passing through that angle, it may be described ’as readily by having either of the sides as the diagonal. Case II. Figure 5.—When any two angles of direction are greater than two right angles. Let AB, EB, CB, be the three directions, ‘ whereof any two angles made by these lines are greater than two right angles, and consequently the remaining one less than two right angles. Let the given force act in EB; produce E B through the opposite angle to D, so as to divide it into two angles ; make B D to represent the intensity in EB, then by completing the paral- lelogram A B C D, as before, B A will represent the intensity in BA, and B C in B C; and as the forces are supposed to act at the points A, E, C, they are either all drawing the point B, or all pressing ‘it. Proposition VI.——Given, the directions of four forces in the same plane, keeping a solid in equilibrio, and one of the intensities, to find the intensities of the other three. Produce any two directions till they meet each other; also produce the other two directions till they meet each other; join the two angular points; then, by means of the given force, find the other two at the same point: then, because two forces ‘ acting at each point of concourse in the same right line must be equal, and have opposite ten- dencies, the force in this line acting at the other point of concourse will now be given: therefore find the two remaining intensities in the same manner as at the first point of concourse. Example I. Figure 6.—Let EA, F B, G C, H D, be the direction of the forces that support the body AB C D, and let the given force be in BA. Pro- duce EA, F B, till they meet in I; also produce G C, H D, till they meet in Q. Join I Q, and produce it to P; then let IK represent the given force, and complete the parallelogram IK LM. Make Q P equal to I L, and complete the paral- lelogram O P QR; then will I M represent the intensity in FB, 0Q in G C, and RQ in H D. Example II. Figure 7.—Let A B D be a lever with three arms, A C, B C, D C, revolvable about C, as a fulcrum, supported in the direction C O ; and let forces act at the extremities A, B, D, in given directions, A K, D E, E B, and keep it equilibrio: it is required to find the proportion of the forces. Produce two of the directions till they meet; also produce the other direction, and that of the prop till they meet; join the two angular points, and proceed as in Example I. and find the parallelograms H E F G, and K LM N : then LK is the force acting at A, and M K that in the direction of the prop, H E, the force acting at B, and FE that at D. The tendencies of these forces are thus distinguished : let the point B be drawn towards B, then the line EB is in a state of tension; and because the angles H E G and G EF, are less than two right angles, the force in the direction E D will also be in a state of ten- sion, and the middle one, E K, in a state of compression. Again, because the angles L KM and. M K N are less than two right angles, and because EK is in a state of compression, KA is likewise in a state of compression, and the middle one C K, is in a state of tension; or the post, CO, on the opposite side, is in a state of compression, acting on the other side of G. It must be observed, when any force acts upon any point of a solid body, that to draw on one side of the point is the same as to press upon the other side, or to press upon one side is the same, as to draw upon the opposite; there- fore, as the point C is drawn by the force M K, the prop, C O, is compressed by the fulcrum at C. The arms CA, C B, CD, are supposed to be void of weight. Ifthe forces acting at A, B, D, be weights, P, Q,R, going over the pulleys S,T, U, all the lines, AS, B T, D U, will be in a state of tension. Proposition VII.-—Given, the direction of five forces in one plane, keeping a solid in equili- brio, and the intensities and tendencies of two of them, to find the intensities and tendencies of the rest. Find a force equivalent to the two given forces, then unite this given force, with the three re- maining ones, and the directions of four forces, with the intensity of one of them, will be given to find the rest, which may be found by the last Problem. Let A B C D F be a lever, with four arms, FA, FB, F C, F D, revolvable about E, and let it be acted upon by five forces, four of which act upon the arms at the points A, B, C, D, in lines of direction A Q, B S, C K, D I and the other upon the centre at F, in the line of direction FP; then the intensities and tendencies of the two forces LEV 216 W acting in the directions CK, and DI, are given; the one from C to K, and the other from I to D. Produce the two directions C K and D I to meet each other at G, and complete the parallelogram - G K I H, as in Case 2, Problem II. and G H will _ be the direction and quantity of the force equi- valent to GI and G K : then proceed, as in , Problem VI. with the given force G H now found, and the three remaining directions A Q, B S, P F, and complete the parallelograms MN OP and Q R S T; then N P is the quantity that supports the point or axis F in the direction N F, and S R that which supports B in the direction BR. From this example it appears, that when the direction of any number of forces is given, and all the intensities and tendencies but three, the intensities and directions of these three may be found by compounding any two of the given forces, then uniting the force found with an- other of the given forces, and again compound- ing these, and so on until all the given forces are compounded; then proceeding with the last com- pounded force and the three remaining directions, as in Problem. Proposition VIII.——If there be two straight lines, AB, BC, Figure 9, making any angle, AB C, 4 with each other, and if two forces, equal and LEV opposite in the directions A X, C Y, in the same straight line he applied,and three others in the directions AW, BZ, C J, then if the whole be in equilibrio, the directions Z B, A W, C J, will have the same point of concourse, or other- wise they will be parallel. Join A C, cutting Z B produced in T ; take any distance, A D, and complete the parallelogram AG D F; make B H equal to AF, and complete the parallelogram B H I K; make C L equal toBK and C E equalto A D, and complete the parallelogram CM EL; then all the points A, B, C, are in equilibrio by forces pr0portional to, and in the directions of the sides and diagonals of the respective paral- lelograms at these points: now there can be no equilibrium unless C J coincide with C M, for no other force but CM, both in direction and quantity, will balance the two given forces CL and CE; suppose therefore that CJ coincides with CM, produce the directions A W and CJ to meet Z B producedz; then if A W and CJ do not meet itin the same point, they will meet it in two different points, U and V; for draw 0 F, R L, N G, S M, parallel to BV, cutting AC at O, R, N, S; also draw H P, K Q, parallel to A C, cutting BV at P and Q; then will AO:HP :K Q:C R and therefore AN :8 C; now the triangles ABT and A F0 are similar, therefore . . . likewise the triangles C T B and C R L therefore .TA:TB::OA:OF .TBzTszRLzRC TA:TC::RL:OF but because LB 15 equal to SM, and OF to NG . . TA: TC :: SM: NG then again, by similar t11angles, AUT and AGN . . . TU : TA :: NG : NA and it has been proved that . also by the similar triangles T C V and SCM the1efore but because S C and N A are equal; TU 1s equal to TV, therefore the points U andV coincide; consequently the three directions meet in the same point. Corollary ].—FO+L R is equal to B I; for the triangle AFO is equal and similar to the tri- angle H B P equal and similar to the triangle K QI ; and the triangle C LR is equal and simi- lar to the triangle K B Q. Corollary 2.——If V a be made equal to AG, and V C to C M, and the parallelogramV a b c, be com- pleted, the forces in the directions A W, ZB, and CJ, are as Va, V b, and V c, viz. the three parts of a parallelogram in these directions : for draw a d, TA:TC::SM:NG TC:TV::SC:SM TUzTV::SC:NA and c e parallel to AC, meeting VB in c and a’, then will deG N:OF:B P, and dsze: l\I S=R L=B QzPI, therefore B P +P I:V d+ d b; but B P+I P is the force in the direction ZB, consequently the three forces Va, V 1), V0, are equal to those that act in A W, ZB and C J. Corollary 3.—-If the points A and C are joined by an inflexible line, AC, it is evident that the equilibrium will still be maintained, for this line (by the last Proposition) acts the same as the two opposite forces in A X and C Y. Corollary 4.—~—VVhen A‘V, B Z, and C J, are parallel, FD will coincide with F 0, GA with GN, LE with LR, andflC M with SM: now / 7/4 I [IIIIIIIIIlllIllllllllllIIIIIIIIIIIIIIIIIIIiEWI " hl/ /{.\’/.l'/Ifl/:)'l.7ll. / ) i ’7 ll" ., ' , 1’ 1, ,. ,' , 7 ‘ Elli/Imw/ 51/ 11117017,“, ,1 m on ,7 I a null/I {1/ /.J//>’/m.uw X-./. Bfl/V/f/ll [Min/mu-dfivrl, 13113. " " I , LEV ‘ 2 W LR :O F: :TA : :TC; itwill therefore be C M: A G : : T A : T C ; consequently, the force A G: force. C M: force B I. Corollary 5.—Hence, if the directions of three forces acting in the plane of a triangle, at the angles, be in equilibrio, the three intensities are as the parts of a parallelogram formed on their lines of direction. Proposition IX.—If three forces acting against the same point he in equilibrio with each other, . and if any point,-F, Figures 10 and 1), taken in the. line of direction of any one of the forces, the other two forces are to each other reciprocally as the distances of their lines of direction from that point. Let the lines of direction of the three forces be A D, B D, and C 1). CASE I. Figure 10.——-VVhen the point, F,is taken in the line of direction of the middle force. Complete the parallelogram D E F G; draw FH perpendicular to A D, and F1 to C D. Then because the opposite angles D E F and D G F of the parallelogram are equal, the angles H EF and 1 G F are equal; and because EHF and G I F are right angles, the triangles EH F and G I F are similar; therefore 'FG : FE : : FI : .F H; but E D is equal to FG, and GD is equal to FE, therefore ED : GD :: FI : FH;that is, the force acting at A is to the force acting at C, as F1 to F H. CASE II. Figure 11.-——VVhen the point, F, is taken in one of the extreme lines of the direction, A D. On D F, as a diagonal, complete the paral- lelogram DEFG; draw FH perpendicular to DB, and F1 to DC: then because GFH and E F l are right angles, and the angle IFH is common, the remaining angles IFG and H FE are equal; and because the angles FI G and F H E are right angles, the triangles GI F and E H F are similar; therefore FG : FF :: FI : F H; that is, the forces at B and C are reciprocally as ' the distances of their lines of direction taken from any point in the lines of direction of the other force. Therefore, universally, if any three forces be in equilibrio, any two of them are reciprocally as the distances of their lines of direction, taken from any point in the line of direction of the other force. Proposition X. Figures 19. and 13.—If a solid, A B C, be supported by three forces in the lines of direction Z B, A W, C J, these three lines will VOL. II. LEV have the same point of concourse, or be parallel to each other. . Join AB, BC, CA; now the triangle ABC cannot be in equilibrio, unless the directions have the same point of concourse, or be parallel, and also in the plane of the triangle: other- wise the forces at the two points in each of the sides of the triangle would not be equal in opposite directions; therefore the equilibrium of the triangle would be destroyed, as has been shewn by Proposition VIII.and consequently that of the solid would also be destroyed. Corollary ].-——The intensities of any three forces keeping a solid in equilibrio, will be as the parts of a parallelogram formed on their lines of direction. Corollary 2.—Likewise the intensities of any two forces are reciprocally as the distances of their lines of direction from any point .in the line of the other force, whether their directions meet or are parallel to each other. Corollary 3.——Hence, in three forces acting upon a prismatic solid, or lever, in parallel directions, any two forces will be to each other in the reciprocal ratio of the distances of their lines of direction, on the opposite side of the solid, to the direction of the other force. Proposition XI.—Ifa solid be in equilibrio by three forces, and if any point be taken in the line of direction of any one of them: the products of each of the other’two, by the distance of their respectivelines of direction from that point, will be equal. Figure 14. Let A, B, C, represent the intensities at A, B, C, in the directions EA, G B, F C. Take any point, D, in the middle line of direction, and draw D E, D F perpendicular to the other two lines of direction: then (Corollary ‘2, last Problem) A : C ::’DF : DE; therefore ADE=C X D F. Again, from any point, F, in one of the extreme lines of direction, draw FG and FH perpendicu- lar to the other two, then A : B : : FG : FH; therefore A X F H :13 x FG. Corollary 4.——Hence, if three forces act perpendi- cular to a prismatic rod, or beam, the products of any two, each by its distance on the beam from the third, are equal. Corollary 5,—Hence, if three forces act perpen- dicular to a prismatic rod, or beam, the products of any two of their distances from the third, in the direction of the beam, are equal; for in this case all thelines, FD, D E, F G, FH,coincide in 9F W LEV 2 l 1 V L EV I» .— one straightline, and become parallel to the beam, and the segments intercepted by the directions are equal to those on the beam. LEVER BOARDS, a set of boards so fastened together that they may be turned at any angle to admit of more or less air or light, or to lap upon each other, so as to exclude all air or light, through apertures. LIBRARY, an edifice or apartment destined for holdinga considerable number of books placed regularly on shelves; or the books themselves lodged in it. Some authors refer the origin of libraries to the Hebrews; and observe, that the care those people took for the preservation of their sacred books, and the memory of what concerned the actions of their ancestors, became an example to other nations, particularly to the Egyptians. Osimandyas, king of Egypt, is said to have taken the hint first; and, according to Diodorus, had a library built in his palace, with this inscription over the door, ‘Y'I‘XHZ IATPEION. Nor were the Ptolemies, who reigned in the same country, less curious and magnificent in their books. The scripture also speaks of a library of the kings of Persia, Ezra v. l7.vi. 1. which some imagine to have consisted of the historians of that nation, and of memoirs of the affairs of state; but, in effect, it appears rather to have been a repository of laws, charters, and ordinances of the kings. The Hebrew text calls it the house of treasures, and afterwards the house of the rolls, where the treasures were laid up. We may, with more justice, call that a library, mentioned in the second of Esdras to have been built by Nehemiah, and in which were preserved the books of the prophets, and of David, and the letters of their kings. The first who erected a library at Athens was the tyrant Pisistratus: and yet Strabo refers the honour of it to Aristotle. That of Pisistratus was transported by Xerxes into Persia, and was afterwards brought back by Seleucus Nicanor to Athens. Long after, it was plundered by Sylla, and re-established by Adrian. Plutarch says, that under Eumenes there was a library at Pergamus, containing 200,000 books. Tyran- nion, a celebrated grammarian, contemporary with Pompey, had a library of 30,000 volumes. That of Ptolemy Philadelphus, according to A. Gallius, contained 700,000, rolls, which were . burnt by Caesar’s soldiers. M Constantine, and his successors, erected a magni- ficent library at Constantinople; which in the eighth century contained 300,000 volumes, all burnt by order of Leo Isaurus; and, among the rest,a copy of the Iliad and Odyssey, written in letters of gold, on the entrails of a serpent. The most celebrated libraries of ancient Rome, were the Ulpian, and the Palatine. They also boast much of the libraries of Paulus jEmilius, who conquered Perseus; of Lucilius Lucullus, of Assinius Pollio, Atticus, Julius Severus, Dorniti'us Serenus, Pamphilius Martyr, and the emperors Gordian and Trajan. Anciently, every large church had its library; as appears by the writings of St. Jerome, Anasta« sius, and others. Pope Nicholas laid the first foundation of that of the Vatican, in 1450. The Bodleian library at Oxford, built on the foundation of that of Duke Humphrey, exceeds that of any university in Europe, and even those of all the sovereigns of Europe, except the emperor’s and the late French king’s, which are each of them older by a hundred years. It was first opened in 1602, and has since found a great number of benefactors; particularly Sir Robert Cotton, Sir H. Savil, Archbishop Laud, Sir Kenelm Digby, Mr. Allen, Dr. Pococke, Mr. Selden, and others. The Vatican, the Medicean, that of Bessarion at Venice, and thosejust men- tioned, exceed the Bodleian in Greek manu- scripts; which yet outdoes them all in Oriental manuscripts. As to printed books, the Ambrosian at Milan, and that of VVolfenbuttle, are two of the most remarkable, and yet both inferior to the Bodleian. The principal public libraries in London, beside that of the Museum, are those of the College of Heralds, of the College of Physicians, and of Doctors’ Commons, to which latter every bishop, at the time of his consecration, gives at least £20, sometimes £50, for the purchase of books; those of Gray’s Inn, Lincoln’s Inn, inner Temple, and Middle Temple; that of Lambeth, founded by archbishop Bancroft, in 1610, for the use of succeeding archbishops of Canterbury. and increased by the benefactions of archbishops Abbot, Sheldon, and Tennison, and said to con- sist of at least 15,000 printed books, and (317 vo- lumes in manuscript; that of Red-cross-street, founded by Dr. Daniel W'illiams, a presbyterian divine, and since enriched by many private benc— LIB 219 factions; that of-the Royal Society, called the Arundelian or Norfolk library, because the prin- cipal part of the collection formerly belonged to the family of Arundel, and was given to the society by Henry Howard, afterwards duke of Norfolk, in 1666, which library has been in- creased by the valuable collection of Francis Aston, Esq. in 1715, and is continually increasing by the numerous benefactions of the works of its learned members, and others: those of St. Paul’s and of Sion college; the Queen’s library, erected by queen Caroline in 1737; and the Surgeons’ library, kept in their hall in Lincoln’s Inn fields. In order to give some idea of the construction of a library, it will be necessary to know the different sizes of paper, and for this purpose the following table will be found useful: 1' FOOISC‘JP " ' " 13% by 16% inches 9.. Crown — — - - - 15 ~20 3. Dcmy- - - - - 17% _.29 4. Medium - - - - 18 _ 93 5. Royal- - — - - 1941 __ Q4 6. Super-royal - - - 19; —.Q7 7. Elephant - - - - 93 figs 8. Imperial — - - ~ ‘22 —— 30 9. Colombier - - - 23% __ 3 10. Atlas - — — - - 96% __ 34% 11. lr-l Double Elephant, or Grand Eagle - - i 2 2 —40 The dimensions of the shelves, and their distances from each other will therefore be determined by the kind of books intended to be deposited on them. L1 BRA RY, The King’s, at St. James’s, was founded by Henry, eldest son of James I. and made up partly of books, and partly of manuscripts, with many other curiosities, for the advancement of learning. It has received many additions from the libraries of Isaac Casaubon and others. LiBnARY, Cottonimz, originally consisted of 958 volumes of original charters, grants, instruments, letters of sovereign princes, transactions between this and other kingdoms and states,~genealogies, histories, registers of monasteries, remains of Saxon laws, the book of Genesis, thought to be the most ancient Greek copy extant, and said to have been written by Origen in the second century, and the curious Alexandrian copy or manuscript in Greek capitals. This library is kept in the British Museum, with the large valu- able library of Sir Hans Sloane, amounting to LIB" upwards of 42,000 volumes, Sac. There are many public libraries belonging to the several colleges at Oxford and Cambridge, and the Universities of North Britain. , LIGHTHOUSE, a marine building, erected for the purpose of exhibiting a light to warn seamen in the night of their approach to any sand, pro— montory, or insulated rock: as those on the South Foreland,Flamborough head, the Eddystone, See; or a building erected at the entrance of a harbour, to direct the ingress and egress of vessels during the night, as at Ramsgate, and other places. The latter kind are generally smaller than the former, and are called harbour lights. Lighthouses consist of circular towers from fifty to one hundred feet in height, arched over at the top, with a projecting platform surrounded by an iron railing. On this platform a framing of stone is fixed higher than the railing, containing an excavation for the reception of the bottom of the lantern; the space between this frame and the railing, is called the gallery, Where the light- keepers get up to clean the outside of the glass. When lighthouses are erected on the main land, there is nothing peculiar in their construction; there are, however, some instances of their being required in situations diflicult of access, and ex- posed to the accumulated fury of winds and waves; and to erect a permanent building on a spot of this description, requires uncommon resources, and necessarily brings every energy of the architect into action. The most celebrated antique building of this description was the Pharos of Alexandria, in Egypt, the work of Sostratus of Cnidus, under the patronage of Ptolemy Lagus, and his suc- cessor Philadelphus, about 283 years before the Christian aera; it is ascertained to have existed for a period of about 1600 years, and is supposed to have been thrown down by an earthquake. This lighthouse obtained its name from the island of Pharos, on which it stood; and from its great celebrity, other structures of a similar kind have generally obtained the same name; as the Faro (ll Messina, and others; but among the modems, the most remarkable are the Tour de Corduan, off the French coast, and the Eddystone Lighthouse, near the coast of Cornwall. The former of these, begun in the reign of Henry II. and finished under Henry IV. in 1610, stands upon a. small island near the mouth of the Garonne, in the ‘2 r 2 O L1G 220 L1G bay of Biscay, and was the work of Louis de Foix, a celebrated French architect. But the object more immediately in view in the present article, is the Eddystone lighthouse, as it now stands, begun in 1756, and completed in 1759, by Mr. John Smeaton: a building which has . been very justly considered as the chefd’aeuvre of this species of architecture. The peculiarly exposed situation of the Eddy- stone rocks, with the disappointment of former endeavours to erect a permanent structure upon them, have been related under the head EDDY- STONE, we shall therefore confine this article to a description of the constructive process of the lighthouse, extracted from Mr. Smeaton’s Nar— rative. v Mr. Smeaton begins his account with a general description of the Eddystone rocks, the course of the tides, their situation, component matter, and the proper season for visiting them. He then takes an ample view of Mr. VVinstanley’s edifice, to whom he ascribes great praise for having undertaken and achieved what had been generally deemed impracticable; and after deploring that gentleman’s disaster, goes on to describe the second lighthouse, built by Mr. Rudyerd, as a most complete edifice of the kind,being of tim- ber, in the course of which he details the best methods of fixing iron chains, and securing timber work to rocks, which we shall give in his own words. “ As nothing would stand upon the sloping sur— face of the rock without artificial means to stay it, Mr. Rudyerd judiciously concluded, that if the rock was reduced to level bearings, the heavy bodies to be placed upon it, would then have no tendency to slide; and this would be the case, even though but imperfectly executed; for the sliding tendency being taken away from those parts that were reduced to a level, the whole would be much more securely retained by the iron bolts or branches, than if, for the retention of the whole, they had depended entirely upon the iron—work; as manifestly appears to have been the case with the building of Mr. VVin- stanley. According to Mr. Rudyerd’s print, the inclined surface of the rock was intended to have been reduced to a set of regular steps, which would have been attended with the same good efi‘ect, as if the whole could have been reduced to one level; but in reality, from the hardness of J ‘— the rock, the shortness and uncertainty of the intervals in which this part of the work must have been performed; and the great tendency of the laminae whereof the rock is composed to rise in spawls, according to the inclined surface, when worked upon by tools, urged with sufficient force to make an impression; this part of the work, that is, the stepping of the rock, had been but imperfectly performed, though in a degree that sufliced. “ The holes .made to receive the iron branches, appear to have been drilled into the rock by jumpers, making holes of about 2% inches diame- ter; the extremities of the two holes forming the breadth for the branch, at the surface of the rock, were about 7 i inches; and these holes were di- rected so that at their bottoms they should be separated somewhat better than an inch more, that is, so as to be full 8% inches. In the inter- mediate space, a third hole was bored between the two former; and then if the three holes were broke into one, by square-faced pummels, this would make the holes sufficiently smooth and re- gular. By this means he obtained holes of a dove-tail shape, being Q; inches wide, 7% broad at top, 8% at bottom, and 15 and 16 inches deep; and, as these could not be made all alike, every branch was forged to fit its respective hole. The main pieces of each branch were about 4% inches broad at the surface of the rock, and 6% at the bottom; and this being first put down into the hole, the space left for a key would be 3 inches at top, and 2 inches at bottom, which would ad- mit it to be driven in so as to render the whole firm, and the main branch fixed like a dove-tail or lewis. “ The holes being each finished, and fitted with their respective branches, and cleared of water, a considerable quantity of melted tallow was poured into each hole: the branch and key being then heated to about a blue heat, and put down into the tallow, and the key firmly driven, all the space unfilled by the iron, would become full of tallow, and the overplus made to run over: when this was done, all remaining hot, a quantity of coarse pewter, being made red-hot in a ladle, and run into the chinks, as being the heaviest body, would drive out the superfluous melted tallow: and so effectually had this operation succeeded, that in those branches which were cut out in 1756, and had remained fast, the whole cavity LlG 9 had continued so thoroughly full, that not only the pewter, but even, in general, the tallow re- mained apparently fresh: and when the pewter was melted from the irons, the scale appeared upon the iron, as if it had come from the smith’s forge, without the least rust upon it. “All the iron branches, which are shewn, as I found them, in Plate; 1, having been fixed in the manner above—mentioned, they next proceed- ed to lay a course of squared oak balks, length- wise upon the lowest stcp, and of a size to reach up to the level of the step above. Then a set of short balks were laid crosswise of the former, and upon the next step compoundedly, so as to make good up to the surface of the third step. The third stratum was therefore again laid length- wise, and the fourth crosswise, 8w. till a base- ment of solid wood was raised, two complete courses higher than the highest part of the rock; the whole being fitted together, and to the rock, as close as possible, and the balks, in all their intersections with each other, trenailed together. They were also fitted to the iron branches where they happened to fall in; for the branches do not seem to have been placed with any complete re- gularity or order, but rather where the strength and firmness of the rock pointed out the pro- perest places for fixing them; they were however to appearance disposed, so as to form a double circle, one about a foot within the circumference of the basement, and the other about three feet within the former; besides which, there were two large branches fixed near the centre, for taking hold of the two sides of a large upright piece of timber, which was called the mast; by which two branches it was strongly fixed down ; and being set perpendicular, it served as a centre for guiding all the rest of the succeeding work. “ The branches were perforated, in their respective upper parts, some with three, and some with four holes; so that, in every pair (collectively called a branch) there would be at a medium seven holes; and as there were at least thirty-six original branches, there would be 252 holes, which were about seven-eighths of an inch in diameter; and, consequently, were capable of receiving as many large-bearded spikes, or jag-bolts, which being driven through the branches into the solid timber, would undoubtedly hold the whole mass firmly down; and the great multiplicity of trenails in 21 LI G the inter-sections, would confine all the strata closely and compactly together. “ I cannot omit here to remark, that though. the instrument we now call the lezm'shis of an old date, yet, so far as appears, this particular application of that idea, which Mr. Rudyerd employed in fixing his iron branches firmly to the rock, was made use of for the first time in this work: for though Mr. Winstanley mentions his having made twelve holes, and fixed twelve great irons in the rock, in his first year’s work, yet he gives no intimation of any particular mode of fixing them, but the common way with lead: and the stump of one of the great irons of Mr. VVinstan- ley’s, that was cut out in the course of the work of the summer 1756, was fixed in that manner; but we remarked, that the low end of this bar or stanchion, was a little club-ended, and that the hole was somewhat under-cut; so that, when the lead was poured in, the whole together would make a sort of dovetail engraftment: however, when these irons, by great agitations became loose, and the lead yielded in a certain degree, they would be liable to be drawn out; as the orifice by which they entered must have been large enough to receive the iron club. Mr. Rud- yerd’s method, therefore, of keying and securing, must be considered as a material accession to the practical part of engineery; as it furnishes a secure method of ’fixing ring-bolts and eye-bolts, stanchions, 810. not only into rocks of any known hardness; but into piers, moles, 8w. that have already been constructed, for the safe mooring of ships; or fixing additional works, whether of stone or wood. “ In this way, by building stratum super stratum, of solid squared oak timber, which was of the best quality, Mr. Rudyerd was enabled to make a solid basement of what height he thought pro- per: but, in addition to the above methods, he judiciously laid hold of the great principle of en- gineery, that weight is the most naturally and effectually resisted by weight. He considered, that all his joints being pervious to water, and that though a great part of the ground joint of the whole mass was in contact with the rock, yet many parts of it could not be accurately so; and therefore, that whatever parts of the ground joint were not in perfect contact, so as to ex- clude the water therefrom, though the separation was only by the thickness of a piece of post- 'LlG 22 2 LIG‘ paper, yet if capable of receiving water in a fluid state, the action of a wave upon it edge- wise, would, upon the principles of hydrostatics, produce an equal effect towards lifting it up- wards, as if it acted immediately upon so much area of the bottom as was not in close contact. “ The more effectually therefore to counteract every tendency of the seas to move the building, in any direction, he determined to interpose strata of Cornish moor-stone between those of wood; and accordingly having raised his foundation solid, two courses above the top of the rock, he then put on five courses, of one foot thick each, of the moor-stone. These courses were as well jointed as the workmen of the country could do it, to introduce as much weight as possible into the space to contain them': they were however laid without any cement; but it appears that iron cramps were used, to retain the stones of each course together, and also upright ones to confine down the outside stones. “ When five feet of moor-stone were laid on, which, according to the dimensions, would weigh 120 tons; he then interpbsed a couple of courses of solid timber, as before; the use of which was‘ plainly for the more effectual and read y fastening of the outside uprights to the solid, by means of jag-bolts, or screw-bolts; and that these bolts might the more effectually hold in the wood, in every part of the circle (which could not be the case with timbers lying parallel to each other, because in two points of the circle, opposite to each other, the timbers would present their ends towards the bolt) he encompassed those two courses with circular, or whatare technically called compass timbers, properly scarfed together, and breakingjoint one course upon the other. “7e must not however suppose, that these courses were composed wholly of circular timbers to the centre, but that the circles of compass timbers on the outside were filled up with parallel pieces within; and that the compass timbers were, in the most favourable points, jag-bolted to the in- terior parallel pieces. “ The two uppermost courses, after clearing the rock, and before the five moor-stone courses came on, were furnished with compass timbers, as well as some others below. “ The two courses of wood above the moor-stone courses terminated the entire solid of the base- ment; fora well-hole was begun to be left upon these courses for stairs in the centre, of 6 feet 9 inches in the square; and hereupon was fixed the entry door, or rather, one course lower, making a step up, just within the door; in consequence of this, the entire solid terminated about nine feet above the higher side of the base, and 19 feet above the lower side thereof. “ In Mr. \Vinstanley’s house, the entry was from the rock into an internal staircase, formed in the casing upon the south-east side; he therefore needed only a few external steps. But Mr. Rudyerd’s entry door, being full eight feet above the highest part of the rock, would consequently need a ladder. This he made of iron, of great strength; and being open, when-ever the seas broke upon this side of the house, they readily found their passage through, without making any violent agitation upon it. “ The two compass courses terminating the en- tire solid, having been established, as already mentioned, he again proceeded with five moor- stone courses; nearly the same as the former; allowing for the necessary difference resulting from there now being.a central well-hole for the stairs, and a passage from the entry door, as de- cribed, to the well-hole; this passage was 2 feet 11 inches wide, and, as it appears, took up the whole height of the five courses. The weight of these five courses, according to the dimensions, amounted to 86 tons. “ He then again proceeded with two compass courses, covering the door-head and passage, so as now to leave no other vacuity than the well- hole; and upon these he laid four moor-stone courses, the weight of which amounted to sixty- seven tons. He then proceeded with two com- pass courses, aud after that, with beds of timber, cross and cross, and compass courses interpos- ing; and, last of all, with one compass course, upon which he laid a floor over all, of oak plank three inches thick, which made the floor of the store-room. “ The height of this floor above the bottom of the well, was near 18 feet; above the foot of the mast 33 feet; above the rock on the higher side 27 feet; and above the foot of the building on the lower side 37 feet. In all this height, no cavity of any kind was intended for any purpose of depositing stores, &’c. From the rock to the bottom of the well, all was solid, as we have shewn; but as the building increased in height, L1G 223 LlG W .1 I and consequently was more out of the heavy stroke of the sea, a less degree of strength and solidity would be equivalent to the former, and therefore admit of the convenience of a staircase within the building, with a passage into it: which last, being made upon the east side, Would be withdrawn from the heavy shock of the seas from the south-west quarter, and the rock being there highest, the ascent by the iron stair upon the outside, would be the least; the whole there- fore, to the height of the store-room floor, as above-mentioned, having been made with allpos— sible solidity, was denominated the solid. , “ The height of Mr. Rudyerd’s store-room floor was fixed as high as the floor of Mr. Winstanley’s state-room, which was over his store-room; and as many were doubtless still living, who had seen and examined Mr. Winstanley’s lighthouse, during the four years that it stood in a finished state; and as in that time there would be an op- portunity of knowing from experience, to what height the unbroken water of the waves mounted in bad weather, we may very well suppose that Mr. Rudyerd regulated the height of his solid from that information. We have already seen, that the two compass courses of wood, which capped the first bed of moor-stone, and terminated the entire solid, were forcibly screwed down by ten large iron bars or bolts, to the beds of timber below the moor-stone, and these by the trenails and branches to the rock. We must suppose this precaution to have been taken, to prevent any derangement from the heavy strokes of the sea in storms and hard gales, which were liable to happen inthe very finest part' of the season, before there was any proper opportunity of connecting the upper part of the work with the lower, by means of the upright timbers, that were to form the outside case; be- cause, till the work was brought to that height, there could be no proper means of beginning to fix them: and as we do not find any traces or men- tion of binding the upper courses with the lower, after the staircase was set forward, we must sup- pose that the outside casing had been then begun from the rock, and carried on progressively, so as to become a bond of the upright kind: for, all such timbers as were high enough, having been screwed fast to the compass courses, would be thereby secured to the lower courses; otherwise, from what I have myself experienced of the situ- ation, I should have expected, that whenever the two courses of compass timber were put upon the second bed of moor-stone, if a hard gale should have come on at south-west, it would not only have lifted up and carried away the timber beds, but possibly would have deranged the moor-stone courses, notwithstanding the upright cramps to the outside stones. “ The solid being in this manner completed, the upper part of the building, comprehending four rooms, one above another, was chiefly formed by the outside upright timbers; having one kirb or circle of compass timber at each floor, to which the upright timbers were screwed and connected; and upon which the floor timbers were rested. The uprights were 'also jag-bolted and trenailed to one another, and, in this manner, the work was carried on to the height of 34 feet above the store-room floor; and there terminated by a plank— ing of three inches thick, which composed the roof of the main column, as well as served for the floor of the lantern, and of the balcony round it. - “ Thus the main column of this building consisted of one simple figure, being an elegant frustum of a cone, unbroken by any projecting ornament, or any thing whereon the violence of the storms could lay hold; being, exclusive of its sloping foundation, 22 feet 8 inches upon its largest circu- lar base; 6] feet high above that circular base; and 14 feet 3 inches in diameter at the top: so that the circular base was somewhat greater than one- third of the total height, and the diameter at top was somewhat less than two-thirds of the base at the greatest circle. “ The junction of the upright timbers upon each other, was by means of scmfs, as they are techni- cally called in ship-building and carpentry; that is, the joining of timbers end to end by over- lappinrr. The timbers were of different lengths, from 10 to 20 feet, and so suited, that no two joinings or scarfs of the uprights might fall to- gether. The number of uprights composing the circle was the same from top to bottom; and their number being seventy-one, the breadth at the bottom would be 1 foot nearly; their thick- ness there was 9 inches; and, as they diminished in breadth towards the tOp, they also diminished in thickness. The whole of the outside seams was well caulked with oakum, in the same man— ner as in ships; and the whole payed over with L1G t pitch, consequently, upon a near view, the seams running straight from top to bottom, in some measure resembled the flutings of columns; which, in so simple a figure, could not fail to catch the attention of the beholder, and prove an agreeable engagement of the eye. “ The whole of the building was indeed a piece of shipwrightry: for it is plain, from the preced- ing account, that the interposed beds of moor- stone had nothing to do with the frame of the building, it being entire and complete exclusive thereof: the beds of moorstone could therefore only be considered in the nature of ballust, and amounted, from what has been before stated, in the whole, to the weight of above two hundred and seventy tons. ’ “ All the windows, shutters, and doors, were com- posed of double plank, cross and cross, and clink- ed together; which falling into a rebate, when shut, their outside formed a part of the general surface, like the port-holes in a ship’s—side; with- out making any unevenness or projection in the surface. There were, however, two projecting parts terminating this frustum; one at the top, and the other at thejoining with the rock; the utility of which seems to render them indispen- sable. They had each a projection of about 9 in- ches. The top projection, which is in the nature of a cornice, consisted of a simple bevel, and the use of it was very great; for in time of storms and hard gales of wind, when, acc'ording to the accounts of Mr. Winstanley’s building, the broken sea rises to a far greater height than the whole structure, it would be likely to break the windows of the lantern, unless there was some- thing to throw it off, as their use does not admit of any defence by shutters. Therefore Mr. Rud- yerd applied this simple cornice, judging it suf- ficient to have the effect of throwing off the sea in time of storms; and yet not of so much pro- jection, as that the sea at the height of 7] feet above the foot of the building, could have power enough to derange it. “ The bottom projection, which has been called the kant, and which fills up the angle formed be- tween the uprights and the sloping surface of the rock, so as to guard the foot of the uprights from ' that violence of action which the waves naturally exert when driven into a corner, was certainly a very useful application: but I am inclined to think it was not there upon the first completion. .224 —’7 LIG “ Upon the flat room of the main column, as a platform, Mr. Rudyard fixed his lantern, which was an octagon of 10 feet 6 inches diameter ex- ternally. The mean height of the window frames of the lantern above the balcony floor, was nearly 9 feet, so that the elevation of the centre of the light above the highest side of the base was 70 feet; that is, lower than the centre of Mr. VVin- stanley’s second lantern by 7 feet; but higher than that of his first by 9.4- feet. The width of Mr. Rudyerd’s lantern was however nearly the same as that of Mr. VVinstanley’s second: but, instead of the towering ornaments of iron work, and a vane that rose above the top of the cupcla no less than 2] feet, Mr. Rudyerd judiciously contented himself with finishing his building with a round ball, of 2 feet 3 inches diameter, which terminated at 3 feet above the top of his cupola. The whole height of Mr. Rudyerd’s lantern, in- cluding the ball, was no more than ‘21 feet above his balcony floor; whereas that of Mr. VVinstan- ley’s, including the iron ornaments, Was above 40. “ The whole height then of Mr. Rudyerd’s light- house, from the lowest side to the tOp of the ball, was 92 feet, upon a base of 93 feet 4 inches, taken at a medium between the highest and lowest part of the rock that it covered. “ I have endeavoured to describe this building with all possible minuteness, because it affords a great, and very useful lesson to future engineers. ‘Ve are sure that a building such as Mr. \Vin- stanley’s was not capable of resisting the utmost fury of the sea, because, in four years after its completion, it was totally demolished thereby: but Mr. Rudyerd’s building having sustained the repeated attacks of that element, in all its fury, for upwards of forty—six years after its comple- tion; and then being destroyed, not by water, but by fire: we must conclude, it was of a con- struction. capable of withstanding the greatest violence of the sea in that situation. And b withstanding it there, this lighthouse proves the practicability of a similar erection in any like ex posure in the known world. “ I have seen a paper in the hands of one of the present proprietors, upon which were put down the quantities of materials said to have been ex- pended in the construction of this building: viz. 500 tons of stone, 1200 tons of timber, 80 tons of iron, and 35 tons of lead; and of trenails, screws, and rack—bolts, 2500 each.” LIG IO U: LIG Mr. Smeaton then proceeds to detail the means by which the erection of the new lighthouse fell into his hands, his several interviews with the proprietors, and various other preliminary occur— rences, among which the following remarks on the difference in structure of stone and wood, and on the bond of the stones to the rock and to each other, are particularly worthy of notice. “ In reflecting upon the late structure, it appear- ed most evidently, that had it_not been for the moorstone courses, inlaid into the frame of the building, and acting therein like the ballast of a ship, it had long ago been overset, notwithstand- ing all the branches and iron-work contrived to retain it: and that in reality the violent agitation, rocking, or vibration, which the late building was described to be subject to, must have been owing to the narrowness of the base on which it rested; and which, the quantity of vibration it had been constantly subject to, had rendered, in regard to its seat, in some degree rounding, like the rockers of a cradle. It seemed therefore a 'primary point of improvement, to procure, if possible, an enlargement of the base, which, from the models before me, appeared to be practica- ble. It also seemed equally desirable, not to in- crease the size of the present building in its waist; by which I mean that part of the building between the top of the rock and the top of the solid. If therefore ‘I still kept strictly to the conical form, a necessary consequence would be, that the diameter of every part being propor- tionably increased by an enlargement of the base, the action of the sea upon the building would be greater in the same proportion ; but as [the strength increases in proportion to the increased weight of the materials, the total absolute strength to resist that action of the sea, would be greater by a proportional enlargement of every part, but would require a greater quantity of materials: on the other hand, if we could cn- large the base, and at the same time rather dimi- nish than increase the size of the waist and upper works; as great a strength and stiffness would arise from a larger base, accompanied with a less resistance to the acting power, though consisting of a less quantity of materials, as if a similar co- nical figure had been preserved. “ On this-occasion, the natural figure of the waist or bole of a large spreading oak, presented itself to my imagination. Let us for a moment consi- VOL. 11. der this tree: suppose at 12 or 15 feet above its base, it branches out in every direction, and forms a large bushy top, as we often observe. This top, when full of leaves, is subject to a very great impulse from the agitation of violent winds; yet, partly by its elasticity, and partly by the natural strength arising from its figure, it resists them all, even for ages, till the gradual decay of the material diminishes the coherence of the parts, and they suffer piecemeal by the violence; but it is very rare that we hear of such a tree be- ing torn up by the roots. Let us now consider its particular figure—Connected with its roots, which lie hid below ground, it risesfrom the sur- face thereof with a large swelling base, which at the height of onediameter is generally reduced by an elegant curve, concave to the eye, to a diameter less by at least one—third, and sometimes to half of its original base. ~From thence its taper diminishing more slowly, its sides by degrees come into a perpendicular, and for some height form a cylinder. After that a preparation of more circumference becomes necessary, for the strong insertion and establishment of the principal boughs, which produces a swelling of its dia- meter. Now we can hardly doubt but that every section of the tree is nearly of an equal strength in proportion to what it has to resist: and were we to lop off its principal boughs, and expose it in that state to a rapid current of water, we _ should find it as much capable of resisting the action of the heavier fluid, when divested of the greatest part of its clothing, as it was that of the lighter when all its spreading ornaments were exposed to the fury of the wind: and hence we may derive an idea of what the proper shape of a column of the greatest stability ought to be, to resist the action of external violence, when the quantity of matter is given whereof it is to be composed. “In Plate V. Fig-are l, is a sketch, represent- ing the idea which I formed of this subject. It is farther observable, in the insertions of the boughs of trees into the hole, or of the branches into the boughs, (which is generally at an oblique angle) that those insertions are made by a swell- ing curve, of the name nature as that wherewith the tree rises out of the ground; and that the greatest rake or sweep of this curve is that which fills up the obtuse angle; while the acute angle is filled up with a much quicker curve, or sweep 9.. G LIG 226 ~¥ ~ — m — of a less radius: and Figure 2, of the same Plate, represents my conception of this matter. In this view of the subject, I immediately rough— turned a piece of wood, with a small degree of tapering above; and leaving matter enough he- . low, I fitted it to the oblique surface of a block of wood, somewhat resembling the sloping surface of the Eddystone rock; and soon found, that by re- conciling curves, I could adOpt every part of the base upon the rock to the regularly turned taper- ing body, and so as to make a figure not ungrace— ful; and at the same time carrying the idea of great firmness and solidity. “ The next thing was to consider how the blocks of stone could be bonded to the rock, and to one another, in so firm a manner, as that, not only the whole together, but every individual piece, when connected with what preceded, should be proof against the greatest violence of the sea. “ Cramping, as generally performed, amounts to no more than a bond upon the upper surface of a course of stone, without having any direct power to hold a stone down, in case of its being lifted upward by an action greater than its own weight; as might be expected frequently to hap- pen at the Eddystone, whenever the mortar of ‘ the ground bed it was set upon was washed out of the joint, when attacked by the sea before it had time to harden; and though upright cramps, to confine the stones down to the course below, might in some degree answer this end, yet, as this must be done to each individual stone, the quantity of iron, and the great trouble and loss of time that would necessarily attend this me- thod, would in reality render it impracticable; for it appeared, that Mr. VVinstanley had found the fixing twelve great irons, and Mr. Rudyerd thirty-five, attended with such a consumption of time (which arose in a great measure from the dif- ficulty of getting and keeping the holes dry, so as to admit of the pouring in of melted lead) that any method which required still much more, in putting the work together upon the rock, would inevitably, and to a very great degree, procrastinate the completion of the building. It therefore seemed of the utmost consequence to avoid this, even by any quantity of time and mo- derate expense, that might be necessary for its performance on shore; provided it prevented hinderance of business upon the rock: because of time upon the rock, there was likely to be a great — - f scarcity, but on the shore a very sufficient plenty. This made me turn my thoughts to what could be done in the way of dovetailing. In speaking however of this as a term of art, I must observe, that it had been principally applied to works of carpentry: its application in the ma- sonry way had been but very slight and sparing; for in regard to the small pieces of stone that had been let in with a double dovetail, across the joint of larger pieces, and generally to save iron, it was a kind of work even more objectionable than cramping; for though it would not require melted lead, yet being only a superficial bond, and consisting of far more brittle materials than iron, it was not likely to answer our end at all. Somewhat more to my purpose I had occasionally observed, in many places in the streets of Lon- , don, that, in fixing the kirbs of the walking paths, the long pieces, or stretchers, were retain- ed between two headers, or bond pieces; whose heads "being cut dovetail-wise, adapted them- selves to and confined in the stretchers: which expedient, though chiefly intended to save iron and lead, nevertheless appeared to me capable of more firmness than any superficial fastening could be; as the tye was as good at the bottom as at the top, which was the very thing I wanted; and therefore if the tail of the header was made to have an adequate bond with the interior parts, the work would in itself be perfect. ‘Vhat I mean will be rendered obvious by the inspection of Figure 3, in PLATE V. Something of this kind I also remembered to have seen in Be- lidor’s description of the stone floor of the great sluice atCherburgh, where the tails of the up- right headers are cut into dovetails, for their in— sertion into the mass of rough masonry below. From these beginnings I was readily led to think, that if the blocks themselves were, both inside and out, all formed into large dovetails, they might be managed so as mutually to lock one another together; being primarily engrafted into the rock: and in the round and entire courses, above the top of the rock, they might all proceed from, and be locked to one large centre stone. After some trials in the rough, I produced a complete design, of which Figure 5, PLATE V, is the exact copy; the dotted lines repre- senting the course next above or below, which in the original was drawn from the same centre, on the other side of the paper; so that looking on MG )9 ‘1 L1G each side separately, each course was seen dis- tinctly; or, looking through the paper, the rela- tion of the two courses, shewing how they mu- tually broke joint upon one another, was clearly pointed out: and this method of representation was pursued throughout; but not being practi- cable in copper-plate work, Iam under the neces- sity of introducing the method by dotted lines, "though attended with some degree of confusion of the main design. “ It is obvious, that in this method of dovetail- ing, while the slope of the rock was making good ; by cutting the steps (formed by Mr. Rud- yerd) also into dovetails, it might be said, that the foundation stones of every course were en- grafted into, or rather rooted in the rock; which would not only keep all the stones in one course together, but prevent the courses themselves (as one stone) from moving or sliding upon each other. But after losing hold of the rock, by get- ting above it; then, though every stone in the same course would be bonded in the strongest manner with every other, and might be consider- ed as consisting of a single stone, which would weigh a considerable number of tons, and would be farther retained to the floor below by the ce- ment, so that, when completed, the sea would have no action upon it but edgeways; yet, as a force, if sufficiently great, might move it, not- withstanding its weight, and the small hold of the sea upon it, and break the cement before time had given it that hardness which it might be expected to acquire afterwards; I had formed more expedients than one for fixing the courses to one another, so as absolutely to prevent their shift- ing; but I shall not trouble my reader with a re- cital of those expedients at present, as they will more properly come in along with the reasons of my choice, in the detail of the actual proceed— ings.” Mr. Smeaton made his first voyage to the Eddy- stone on the 2d of April, 1756, but was prevent- ed from landing by the weather; but on the 5th of the same month he was more successful, and staid upon the rock about two hours and a half, during which time he observed, “ such traces of the situations of the irons fixed by Mr. Winstan- ley, as that it would not be difficult to make out his plan, and the position of the edifice; from whence it appeared very probable that Mr. VVin- stanley’s building was oversct all together; and that it had torn up a portion of the rock itself" with it, as far as the irons had been fastened in it.” He also “perceived that Mr. Rudyerd’s iron branches, as then called, were much smaller and shorter than he had described them to be at the bottom of his print; that many of them were loose, and some broken and bent: and that in regard to the steps, described to be cut upon the rock, there were only five of them, of which the traces were remaining: so that there was but one flat or tread of a step above the centre of the house; and the upper part of the surface of the rock above that was a sloping plain, as it had been at first. Three steps, of the five now remaining, seemed to have been but faintly cut, and the uppermost but one was so imperfect, that he sup- posed a large spawl or splinter had come from it; and this appeared the more probable, as the uppermost step was so shaken, that another large spawl might have been easily raised from it, by a slight action of a wedge. Above the upper- most step the rock seemed to be ofasofter nature, was cracked in many places, and probably had received some damage from the fire. None of the steps appeared to have been cut with much regu- larity, either as to level or square; but to have all the marks of hurry upon them. In the centre of the house a slight footing was cut for the mast, suitable to 'a square of 18 inches, with large iron branches, answerable to two of its sides, and a small hole bored in the centre, of about 1% inch diameter, being 6 inches deep. By consulting Plate 1. many of the above matters will be made apparent to the eye. “ I then,” says Mr. Smeaton, “proceeded to try the degree in which the rock was workable, and found that from a flat surface, indifferently taken, ‘ I could, with a pick sink a hollow at the rate of five cubic inches per minute; and could cut or drilla hole with a jumper of 1%, inch diameter, at the rate of one inch deep in five minutes. I also tried a method of forcing two holes into one, by a square flat-faced bruiser, or pummel; so that, if there should be occasion, 1 might be able: to make acontinued groove; or let in an iron branch, in the manner of Mr. Rudyerd,and I had the satisfaction to find that the whole sues . ceeded to my wishes.” In the choice of materials, Mr. Smeaton was deter— mined in favour of moorstone, or granite, for the outside work, and Portland stone for the inside. 2 G 2 LIG 2 8 L1G The latter was not eligible for the outer surface, on account of its liability to be destroyed by a marine insect; and the moorstone was too hard and expensive in the working to admit of its being used throughout the building. By the 15th of May, Mr. Smeaton had made ten voyages of observation to the Eddystone, and then returned to London, where having settled with the proprietors, he received his commission to proceed on the work. He then went back to Plymouth, and, on the 3d of August, landed with the first company of workmen on the rock, where he began to fix the centre and lines of the work. After describing the difficulties under which he laboured from the uncertainty of the weather, and the necessity in which the work- men were placed, of returning to shore every tide, till a vessel fit for their reception could be pro- perly moored ofi“ the rock, Mr. S. observes upon his preference of the use of picks and wedges for operating upon the rock, that “it might seem, at first sight, that a greater dispatch would have been by the use of gunpowder, in blasting the rock, in the same manner as is usual in mines, and in procuring limestone from the marble rocks in the neighbourhood of Plymouth : but though this is a very ready method of work— ing hard and close rocks, in proportion to the dispatch that could be made by picks and wedges ; yet, as a rock always yields to gunpow- der in the weakest part, and it is not always easy to know which part is weakest; it might often have happened, if that method had been pursued, that, instead of forming a dovetail recess, such as was required, the very points of confinement would have been lost. Besides, the great and sudden concussion of gunpowder might possibly loosen some parts that it was more suitable to the general scheme should remain fast. For these reasons, I had previously determined to make no use of gunpowder for this purpose. “ On the 7th of September,” says Mr. Smeaton, “ I sent to Portland the draughts for the six foundation courses, that were to be employed in bringing the rock to a level; which, with the draughts for eight that I had before dispatched, completed the order for the whole quantity of Portland stone to be used in the solid up to the entry door; being all that we could expect to set in place the next season. The rock was not in- deed yet ready for completing the exact moulds for those stones that were to fit into the dove- tails made in it; but, by ordering the stones large enough, and being scappelled something near their proper form, it would prevent loss of time in waiting to get the true figure from the rock, as well as unnecessary waste. “ Nothing happened to prevent the companies from working every tide from the 27th of August till the 14th of September, in which time they had worked one hundred and seventy-seven hours upon the rock. In this interval, having procured a carpenter to be applied to that purpose, I be- gan to make the moulds for the exact cutting of the stones to their intended shapes. This was done by laying down, in chalk lines upon the floor of a chamber, the proposed size and figure of each stone, being a portion of the plan at large of the intended course; and the carpen- ter having prepared a quantity of battens, or slips of deal board, about three inches broad, and one inch thick, shot straight upon the edges by a plane; those battens being cut to lengths, and their edges adapted to the lines upon the floor, and properly fitted together, became the exact representatives of the pieces of stone whose figure was to be marked from them, when their beds were wrought to the intended parallel distance. “It is obvious that there was no necessity for making moulds for a whole course after the work became regular; as was the 7th course, after the six foundation courses brought the rock to a level; it was sufficient to make one mould to each circle of stones, beginning with the centre stone; but as the six foundation courses were adapted to the particular irregularities of the rock, and consequently could not be strictly re— gular, it was necessary that a separate mould should be made for every separate stone, com- posing that part of the work. “ During this interval, I visited the rock, and on arriving there the 8th of September, was inform- ed by Mr. Jessop, that the preceding evening, there being a very strong tide, and no wind, a VVest—lndiaman, homeward bound, and a man-of- war’s tender, were in great danger of driving upon the north-east rock ; but that he timely per- ceiving their danger, though they themselves were not aware of it, ordered out the seamen and hands, who towed them off. “ On this visit I staid two days; for as the work- ing company had begun to take down the upper LIG £2.29 LIG W part of the rock, it was necessary to concert, and put in practice, the proper means of doing that, without damage to what was destined to remain. l have already mentioned my resolution of not using gunpowder; yet it was necessary, for the sake of dispatch, to employ some means more expeditious than the slow way of crumbling off the matter, by the blunt points of picks. It has been already noticed, that the laminae composing the rock were parallel to the inclined surface: and it was very probable that the chasm, into which NIr. \Vinstanley’s chain had been so fast jambed, that it never could be disengaged, extended far- ther into the rock than the visible disunion of the parts: this made me resolve to try a method sometimes used 111 this country, for the division of hard stones, called the key andfeat/zer, in order to cross cut this upper stratum of the rock. The construction and operation of the key and feather is as followsz—A right line is marked upon the surface of the rock or stone to be cut, in the di- rection in which it is intended to be divided. Holes are then drilled by a. jumper, at the dis- tance of six or eight inches, and about one inch and a quarter in diameter, to the depth of about eight or nine inches; the distances, how- ever, of the holes, and their diameters, as well as their depth, are to be greater or less, according to the strength of the stone, in the estimation of the artist directing the work. The above dimen- sions were what we used on this occasion. The key is along tapering wedge, of somewhat less breadth than the diameter of the holes, and so as to go easily into them; the length being three or four inches more than the depth of the holes. The feathers are pieces of iron, also of a wedge- like shape; the side to be applied to the key be- ing flat, but the other side a segment ofa circle, answerable to that of the holes; so that the two flat sides of two feathers being applied to the two flat sides of the key, and the thick end of the feathers to the thin end of the key, they all together compose a cylindric, or rather oval kind of body; which in this position of parts is too big to go into the holes by at least one-eighth of an inch; that is, in the direction of a diameter passing through the three parts; but, in the other direction, is no broader than to go with ease into the holes. A key and a pair of feathers is made use of in each hole; and the feathers being first dropped in, with the thick ends downward, the _ keys are then entered between them; the flat sides of all the keys and the feathers being set parallel to that line in which the holes are dis- posed: ' the keys are then driven by a sledge hammer, proceeding from one to another, and being forced gradually, as in splitting of mom- stone, the strongest stones are unable, to 1esist theirjoint effort; and the stone is split according to the direction of the original line, as effectually, and much more regularly and certainly, than could be done with gunpowder, and without any concussion of the parts. Had our rock been en- tirely solid, this way of working might not have been applicable, on account of the crack’s going too deep; but here, when it arrived at the joint where the chain was lodged, the split part be- came entirely disengaged from the rest; and in this way we were enabled to bring off the quan- tity of several cubic feet at a time: and thus the chain was released, after a confinement of above fifty years. The impossibility of disengaging it before now appeared very evident; for the pres- sure had been so great by the 1'ock’s closing upon it, as bef01e suggested, that the links in tl1ei1 1n- teisections we1e pressed into each other, as com- pletely as if they had been made of lead; though the bolt iron composing the chain had been at least five- eighths of an inch in diameter. “ On Thu1sday, the 16th, I again went off to the rock, and found the wo1k in the following situa- tion. The lowest new step (the. most difficult to work upon, because the lowest) with its dove- tails quite completed. The second step rough bedded, and all its dovetails scappelled out. The third step (being the lowest in Mr. Rudyerd’s work) smooth bedded; and all the dovetails roughed out. The fourth in the like state. The fifth rough bedded, and dovetails scappelled out: and the sixth smooth bedded, and all the dovetails roughed out. Lastly, the top of the rock, the great- est part of the bulk whereof had been previously taken down by the key-and-feather method, as low as it could be done with propriety, was now to be reduced to a level with the upper surface of the sixth step; the top of that step being neces- sarily to form apart of the bed for the seventh, or first regular course; so that what now remain- ed, was to bring the top of the rock to a regular floor by picks: and from what now appeared (as all the upper parts, that had been damaged by the fire, were cut off) the new building was likely ”-mm, ......r1.. LIG 230 LlG to rest upon a basis even more solid than the former had done. “ On Thursday, the 30th, I traced the outlines upon the upper part of the rock for the border of the seventh course, all within which was to be sunk to the level of the top of the sixth, and all without to be left standing, as a border for de— fence of the ground joint of the work with the rock; and measuring the height of the top step above the bed of the first, I found it to be eight feet four inches; which would now be the difference of level, between the west orlowest side of the new building, and the east or p 7 highest.” The setting in of the equinoctial winds prevented much farther progress in the work for this sea- son; but on the 7th of November, the weather being somewhat moderate, Mr. Smeaton went off in the Eddystone boat, with battens, and the car- penter, to mould off the dovetails from the rock, when he found “four or five of the dovetails in the upper step wanting some amendment, that would employ as many men at each, for about four orfive hours. The greatest part of the top of the rock was now brought to a regular floor, but some part of the north-east side wanted bringing down to a level.” And here the Operations for the year ended; for, on the 15th of the month, the workmen left the rock, having been able to . make only thirty-eight hours and a half since the 2d of October. Mr. Smeaton occupies the interval between this pe- riod and the next working season with describing the regulations of his mason’s yard, the size of the stones, Ste. among which the following re- marks may be useful to the reader. “ From the beginning I always laid it down as a fundamental maxim, that on account of the pre- cariousness of weather to suit our purposes, (and without its being favourable, I think it has al- ready sufficiently appeared, that nothing is to be done upon the Eddystone) if we could save one hour’s work upon the rock, by that of a week in our work-yard, this would always prove a valu- able purchase; and that therefore every thing ought to be done by way of preparation, which could tend to the putting our work together with expedition and certainty, in the ultimate fixing of it in its proper place; and for this purpose, it was necessary to make use of as large and heavy pieces of stone as, in such a situation as the Ed- r dystone, were likely to be capable of being ma- naged without running too great a risk. . “ The common run of modern buildings, even iof the largest size, are composed of pieces in gene- ral not exceeding five or six hundred weight, except where columns, architraves, cornices, and other parts are to be formed, that indispensablyr require large single pieces; because stones of this size and bulk are capable of being handled without the use of tackles, or purchases, unless where they are to be raised perpendicularly: yet, it appeared to me, that this choice of general magnitude resulted only from the workmen’s not having commonly attained all that expertness in the management of the mechanic powers that they might have; in consequence of which, they avoid, wherever they can, the necessity of em- ploying them. This arises not from the real na- ture of the thing, when properly understood; for a stone of a ton weight is, when hoisted by a proper tackle, and power of labourers, as soon and as easily set in its place, as one of a quarter of that weight; and, in reality, needs much less hewing than is necessary for the preparation of four stones to fill up the same space; nor need this reasoning stop at stones of a ton weight, but it might proceed even to as large sizes as are said to be found in the ruins of Balbec, if there were not inconveniences of other kinds to set on the opposite side of the question, as well as the want ofquarries in this kingdom to produce stones of that magnitude. “ The size of the stones that could be used in the Eddystone lighthouse seemed limited by the practicability of landing them upon the rock: for as nothing but small vessels, that were easily manageable, could possibly deliver their cargoes alongside of the rock, with any reasonable pros- pect of safety; so no small vessels could deliver very large stones, because the sudden rising and falling of the vessels in the gut amounted fre- quently to the difference of three or four feet, even in moderate weather, when it was very prac- ticable for a vessel to lie there; so that in case, after a stone was raised from the floor of the ves- sel, her gunnel should take a swing, so as to hitch under the stone, one of such a magnitude as we are now supposing, on the vessel’s rising, must infallibly sink her; and hence it appeared, that much of the safety in delivering the cargoes would depend upon having the single pieces not L1G 2 31 L1G to exceed such weight as could be expeditiously hoisted, and got out of the way of the vessel, by a moderate number of hands, and by such sort of tackles as could be removed from the rock to the store—vessel each tide: and on a full view of the whole matter, it appeared to me very practicable to land such pieces of stone upon the rock, as in general did not much exceed a ton weight; though occasionally particular pieces might amount to two tons. “ The general size of our building stones being thus determined upon at a ton weight, those would have been far too heavy to be expeditiously transferred and managed, even in the work-yard, unless our machinery rendered that easy, which would otherwise be difficult, without too great an expense of labour: and as the moving and transferring the pieces of stone in the work-yard would be greatly increased in quantity, by the very mode of attaining a certainty in putting the work together upon the rock; this consideration made it still the more necessary, to be able to load upon a carriage, and move the different pieces from one part of the yard to the other, with as much facility (comparatively speaking) as if they had been so many bricks: for, that we might arrive at perfect certainty in putting the work ultimately together in its place upon the rock, it did not appear to be enough, that the stones should all be hewn as exactly as possible to moulds that fitted each other; but it was farther necessary, that the stones in every course should be tried together in their real situation in respect to each other, and so exactly marked, that every stone, after the course was taken asunder, could be replaced in the identical position in which it lay upon the platform, within the fortieth part of an inch. Nor was this alone sufficient; for every course must not only be tried singly together upon the platform, and marked, but it must have the course next above it put upon it, and mark- ed in the same manner, that every two conti- guous courses might fit each other on the outside, and prevent an irregularity in the outline: and this indeed, in effect, amounted to the platform- ing of every course twice: so that, in this way of working, every stone must be no less than six times upon the carriagez—lst. When brought into the yard from the ship, to carry it to the place of deposition, till wanted to be worked.— ley. When taken up and carried to the. shed to be worked.—-3dly. After being wrought, to be returned to its place of deposition.——4thly. When taken up to be carried to the platform.——5thly. When finished on the platform to be returned to its place of deposition.—-6thly. When taken up to be carried to the jetty, to be loaded on board a vessel to go to sea. “ It might, at first sight, appearesuperfluous to try the courses together upon each other, as the under and upper sides of all the courses were planes: and, in case the work could have been put together upon the rock in the same way that common masonry generally is done, it would have been so: that is, if we could have begun our courses by setting the outside pieces first, then it would have been very practicable to have re- gulated the inside pieces thereto ; but as our hepe of expedition depended upon certainty in every part of our progress, this required us to be in a condition to resist a storm at every step: the out- side stones therefore, unconnected with the inner ones, would have scarce any fastening besides their own weight, and would be subject to the most immediate and greatest shock of the sea; and, after completing the outward circle, the inner space would be liable to become a receptacle for water: the necessity therefore of fixing the centre stone first, as least exposed to the stroke of the sea, and of having sure means of attaching all the rest to it, and to one another, rendered it . indispensable that the whole of the two courses should be tried together; that if any defect ap- peared at the outside, by an accumulation of er- rors from the centre, it might be rectified upon the platform. “ The moorstone, though very hard with respect to its component parts, yet being of a friable nature, is extremely difficult to work to an arris (or sharp corner), or even to be preserved, when so wrought by great labour and patience, that is, with sharp tools, and small blows; it therefore soon appeared to me, that we should make very rough and coarse work of it, if the finishing of the pieces were left to the workmen of the coun- try where produced; for, though carefully wrought there in their place, yet in loading and unloading from their carriages, and again putting on board, and unloading from the vessels, the arrises would be very subject to damage. Therefore, to have as much done in the country as possible, and to save weight in carriage (leaving the finishing part ’ LIG Dar _ to be done at home) rough moulds were sent for each size and species of stone, which were to be worked by them to a given parallel thickness, and with length and breadth enough, when so bedded, (as it is called) to be cut round all the sides to the true figure of the finishing mould: but they were to reduce them as near the size as they could safely do it by the hammer; and, that they might not leave on unnecessary waste, they were to be paid no more for either stone or car- riage, than what the mould measured upon the thickness given; and if they were wanting of substance sufficient to make the figure complete, it should be at our option to reject them when they came home.” Our author next proceeds to detail his experi- ments on cements; but as they constitute no part of the building process, the reader is referred to the articles CEMENT and MORTAR, where the subject is duly considered. On the 5th of June, 1757, the operations on the rock were recommenced, and by the 10th all the preliminary matters were settled; so that “on Saturday, the 11th of June, the first course of stone was put on board the Eddystone boat, (see Plate III. Figure 1) with all the necessary stores, tools, and utensils, we landed at eight on Sunday morning, the 12th of June, and be- fore noon had got the first stone into its place, being that upon which the date of the year 1757 is inscribed, in deep characters; and the tide coming upon us, we secured it with chains to the old stancheons, and then quitted the rock till the evening tide, when it was fitted, bedded in mortar, trenailed down, and completely fixed; and all the outward joints coated over with plaster of Paris, to prevent the immediate wash of the sea upon the mortar. This stone, ac- cording to its dimensions, weighed two tons and and a quarter. The weather serving at intervals, it was in the evening of Monday, the 13th, that the first course, consisting of four stones, was finish- ed; and which, as they all presented some part of their faces to the sea, were all of moorstone. “ The next day, Tuesday the 14th, the second course (see Plate 111. Figure ‘2) arrived; and some of it was immediately landed, proceed- ed with, and in part set the same tide: the loose pieces being chained together by strong chains, made on purpose for this use, and those ultimately to the stancheons, or to lewises in the holes of 2.132 LIG the work Course I. that had already been fixed. The sea was uncommonly smooth when we got upon the rock, this evening’s tide, but while we were proceeding with our work, within the space of an hour and a half, the wind sprung up at north-east, and blew so fresh, that the ‘Vcston, lying to deliver the remainder of her cargo, had some difficulty in getting out of the gut; and, had it not been for the transport buoy, to which she had a fastening by a rope, it would probably have proved impracticable to have got her out again. And we soon saw it was necessary to get every thing in the best posture time and circum~ stances would admit, in order to quit the rock with safety to ourselves, and security to what we must necessarily leave behind us. “ The pieces that were fixed and trenailed down, were supposed to bc proof against whatever might happen; but the loose pieces, and those that were simply lowered down into their dovetail recesses, were considered as needing some additional se- curity, to prevent their being carried away by the violence of the sea. Of the thirteen pieces of which Course II. consisted, five only were land- ed: No. 1 was completely set; No. ’2. and 3 were lowered into their places, and secured by chains; and No. 4 and 5, which lay at the top of the rock, were chained together, and also to the slide- ladder, which was very strongly lashed down to the eye-bolts, purposely fixed on the rock for that intent. “ In the evening (of June 15,) we made a short tide upon the rock, and had the satisfaction to find that no material damage had happened to any thing; we therefore proceeded with our work, and completely fixed No. 2 of Course II. On the morning of Friday the 17th we again lauded for a short time; and, notwithstanding we did not meet with any thing amiss on our return to the rock on Wednesday evening, after the hard gale of wind, yet this morning we found a part of the rock in the border of our work, that secured a corner of No. 3, was gone: we therefore, to secure that stone to its neighbour, applied an iron cramp, of which we had some in readiness in case of accident. We were prevented landing in the evening, by a fresh wind and rain at north“ west, but landed again on Saturday morning's tide, the 18th. However, we had not been long there before a great swell arose from the south~ west; and, though there had been no wind appu- LIG 233 , L1G 2% rently to occasion it, yet it came upon us so fast, that we were obliged to quit the rock before we could get our work into so satisfactory a posture of defence as I wished. It was, however, as fol- lows: No. l, 2, 3, 4, and 5, were completely fix- ed as intended; N o. 6 and 7, were fitted, and low- ered upon their mortar beds ; No. 8, was simply got into its place, with a weight of lead of five hundred weight upon it; which, in all such trials as had hitherto been made thereof, had lain quietly. Not having time to get the stone, No. 9, into its place, we chained it upon the top of the rock to the slide-ladder, as we had done before on Tuesday. In this condition we left the rock, having staid till we were all wet from head to foot. “ The storm continued till Tuesday morning; about noon of that day,” says Mr. Smeaton, “ the wind and sea having become still more moderate, I judged it practicable to row a-head against it, so as to get to the westward of the rock, and recon- noitre our damages: accordingly, taking four oars in the light yaw], it being then near low water, I observed, when the sea fell away from the rocks, (every sea then breaking bodily over it) that No. 9, and the slide-ladder to which it was chained, were both gone; that the two pieces of moor- stone, No. 5 and 6, which had only been let down upon their mortar beds, without farther fasten- ing, were also gone; that No. 3 had broke its cramp, and was gone; and that the five hundred weight of lead, that had been laid upon the most projecting part of the piece, No. 8, had, by the force of the sea acting edgewise upon it, been driven to the eastward, till it was stopped by the rise of the third step, against which it seemed abutted; so that having thereby quitted the piece, No. 8, upon which it was laid, that was gone also: we therefore, as it appeared, had lost five pieces of stone; the loss of which was, in the first instance, alleviated by finding that the first course appeared so thoroughly united with the rock, that its surface began to look black, with dark-coloured moss fixing upon it, and giving it the same hue as the rock itself: also, that our shears and Windlass were all standing, without the least derangement. “ I did not wait for the subsiding of the winds and seas, so as to enable us to land, and look out whether or no we could recover any of the lost pieces; 1 immediately made for Plymouth in the V0L.IL light yawl, and landed at Mill Bay, at five o’clock on Tuesday evening, the QISt; and, having col— lected the moulds of the stones we had lost, and chosen proper spare blocks, I set a couple of men to work upon each piece of stone, day and night, till finished. This disaster, though it furnished a few reflections, yet they were not of the un« pleasant kind; for, as every part of the stone- work, that was completed according to its origi- nal intention, appeared to have remained fixed, it demonstrated the practicability of the method chosen; and at the same time shewed the prefer- ence of wedging to cramping, as the cramp had failed: and also the utility of trenails, as a se- curity till the mortar was become hard. “ At four o’clock on Monday morning, the 27th, the weather serving, I went out with Richardson and company, in the Eddystone boat; we got to the buss at ten, and found the Weston at the transport buoy, but could not land till the after~ noon’s tide, being a complete week since we had been last upon the rock. We first replaced the ladder, and afterwards proceeded, without more than usual interruptions, till the 30th in the even- ing, when we closed and completed the Course No.11. and began upon Course III. The exe- cution of these two courses had taken us up from the 12th to the 30th inclusive, and though they consisted of no more than seventeen pieces of stone in the whole, 'yet I found myself no ways disheartened; for, in establishing these two courses, I considered the most difficult and ar- duous part of the work to be already accomplish- ed, as these two courses brought us up to the same level where my predecessor Mr. Rudyerd had begun. “ Friday, July the lst, we were able to land. I observed, that during the last tide, the swell had washed some of the pointing out of the exterior joints, and also some of the grouting out of the uprightjoints; but as a heavy sea seemed likely to come on 'with the tide of flood, Ijudged it to be to no purpose to repair the cement while a violent swell continued; I therefore employed the company in cutting off the iron stancheons belonging to the former building, as they now began to be in our way, and as the hold we got of them ceased to be of use, in proportion as we got more fastening from the lewis holes of our own work. “The weather having become more favourable, 2 n ‘ MG 234 j n— on Sunday morning, the 3d of July, I went on board,~accompanied by Mr. Jessop and his party, to whom, as they had never had the opportunity of setting a stone, it behoved me to attend. We, however, not only met with a repulse this day, but could not make any farther attempt to go out till Tuesday, the 5th; and then the wind,. "though gentle, being contrary, had not the com— pany on board the buss come with their two yawls and towed us thither, in all probability the day would have been spent in fruitless attempts. Our difi‘iculty was considerably increased by the coming on of so thick a fog, that, all our efforts united, we had much ado to regain the buss. Rich- ardson told me they had had such bad weather, that the slide-ladder had again broke its lashings and driven away; that they had however got all the irons cut off close to the rock ; but that the last tide, though there was only a breeze at south- west, the swell was so great, and came on so suddenly, as to put them in great danger of be- ing washed off from the top of the rock, before they could quit it. “ At two o’clock this day we landed, and J essop’s company set six pieces of stone, and effectually repaired the cement; and next day a proportion- able dispatch was made, though the weather was not very mild. “ On Monday, the 11th, I again went out; Course III. consisting of twenty-five pieces, was closed on the following day, and Course IV. begun. “ Thursday, the 14th of July, the company pur- sued the work of Course IV. and now, both com- panies being fully instructed in the method of setting the basement courses, I returned to Ply- mouth; from whence I proposed to visit each company as often as should seem expedient, but always once in each company’s turn, if wind and weather should permit. “ Contrary winds, ground swells, and heavy seas for several days, interrupted the regularity of our proceedings; however, taking such opportunities as we could, the Course No. IV. consisting of twenty-three pieces of stone, was closed in the ~morning’s tide of the Slst of July; (see Plate III.) and in the evening’s tide five pieces of Course V. were set. Our work- went on regularly for some days together; and on visiting the work ' upon the 5th of August, I found the Course, Jim-V. containing twenty-six pieces, closed in; L1G (see Plate III.) but that by some inadvertency in proceeding with the interior part, the masons had been obliged to set tWO of the outside pieces so as to be farther out than they should have been by an inch each. However, as I found the work was sound and firm, I thought it better to cut off the superfluous stone from the outside, than to disturb the work by the violence that must have been used in unsetting the pieces; I therefore determined to let them stand as they were, till the cement was becéme so 'hard as to support the edges of the stone while the faces were working afresh; and which, from the mor- tar of our first and second course, we found was likely to be the case before the close of the sea- son. One of the dovetails had also given way in drivingatrenail, owing to a flaw in the stone; for the remedying whereof we applied a cramp. “ The 8th of August, at noon, the weather being exceeding fine, with a low neap tide, I took the opportunity of drawing a meridian line upon the platform of Course VI. the sea never going over the work during the whole tide, which was the first time it had not washed over all, since we be- gan to build: we therefore took this favourable opportunity of carefully making good all our pointings and groutings, wherever the water had washed during the bad weather that had succeed- ed the last departure of the Eddystone boat; and which was the case with it in places where it had not had time to set before a rough tide came on; but I observed, with much satisfaction, that whatever, not only of the original work, but of the repaired pointing, had once stood a rough tide, without giving way, the same place never after failed. I also observed, that as in mending the pointings we had in some places made trial of Dutch tarras as well as puzzolana, interchange- ably, the puzzolana, for hard service, was evi- dently superior to the tarras; and some particular joints had proved so difficult, that I was obliged to try other expedients; the best of which was to chop oakum very small, and beat it up along with the mortar. This was our last resource, and it never failed us. “ Upon the 11th, I again went out in the vessel that contained the remaining pieces of Course VI. those I saw fixed; and that course, consisting of thirty-two pieces, closed in the same evening. See Plate III. This completing our six basement courses, brought our work upon the same level to LIG 235 M which we had, the preceding season, reduced the top of the rock; and upon this, as a common base, the rest of the structure was to be raised by regular entire courses. The time this part of the work (consisting of one hundred and twenty-three pieces of stone) had taken up, was from the 12th of June to the 11th of August inclusive, being a space of sixty-one days. We now considered our greatest difficulties to be successfully surmount- ed, as every succeeding course had given us more and more time, as well as more and more room; and this will appear from our proceed- ings; for it has already been noticed that the two first courses, consisting of nineteen pieces of stone only, had cost us seventeen days. “ Having now got the work to this desirable situ- ation, I apprehend it will be agreeable to my reader, to be more particularly acquainted with the method in which the stones were set and fix- ed. I have intimated, that when each separate piece, of which a course was to consist, was se- parately wrought, they were all to be brought to their exact places with respect to each other upon the platform in the work-yard, and so marked, that, after being numbered and taken to pieces, they could again be restored to the same relative position. This was done upon the complete cir- cular courses by drawing lines from the centre to the circumference, passing through the middle of each set of stones; and likewise concentric cir- cles through the middle of each tier or circle of stones, so as to indicate to the eye their relative position to each other: but to render the marks not easily delible, where those lines crossed the joints, a nick was cut and sunk into the surface of the two adjacent stones; for doing which, a piece of thin plate-iron was employed, with sand, upon the principle that stones are sawn ; so that not only the sight, but feeling, could be employed in bringing them together again exactly ; for the same or a similar plate being applied to the nick, the least irregularity of its position would be discoverable. In a similarmanner the stones of the base courses were marked by lines drawn parallel to the length of the steps, and others per- pendicular to the same, the crossings being sawn in as before described. There was, however, a nicety in this part of the work, that required par. ticular attention, and that was in forming a pro- vision for setting the four radical stones, that oc- cupy the four radical dovetails into which each LIG step was formed, as may be observed in the seve- ral figures of Plate III. Those stones were form- ed, from the work of the rock’s being actually moulded off,‘and from the manner, already de- scribed, of bringing those moulds to agree after they were brought home from the rock, those stones were laid upon the platform thereby, and then marked with lines upon their own substance; in the manner just mentioned: and as the dis- tances of each of those stones were then ascer‘ tained by guage-rods of white fir-wood, while upon the platform; it must be expected, as each step was reduced to a level plain, as the platform was, that when laid upon the rock in their due positions and distances, by the guage- rods, they would nearly fit the dovetails that had been cut in the rock to receive them ; and where there was the least want of fitness, as might pos- sibly happen with bodies of so rigid a nature, either the stone or the rock was cut, till each stone would come into its exact relative position, and then all the rest would follow one another by their marks, in the same manner as they had done upon the platform. “It is necessary to be noticed, that the waist ofeach piece of stone had two grooves cut, from the top to the bottom of the course, of an inch in depth, and three inches in width: applicable to those grooves were prepared a number of oak wedges, somewhat less than three inches in breadth, than one inch thick at the head, nearly three-eighths thick at the point, and six inches long. The disposition of these grooves is shewn in the courses of Plate III. where the little black parallelogram figures, placed along the lines de- scribing the joints of the courses, represent the tops of the grooves, and their place on the right hand or left of thejoint line shew in which stone the groove is cut. It is also to be noted, that where the flank side of a stone was not more in length than a foot, or fourteen inches, one groove was generally deemed sufficient; but those of eighteen inches or upwards had, generally, in themselves or the adjoining stone, a couple of grooves. “ The mortar was prepared for use by being beat in a very strong wooden bucket, made for the purpose , each mortar—beater had his own bucket, which he placed upon any level part of the work, and with a kind of rammer, or wooden pestle, first beat the lime alone, about a quarter of a 2 H 2 b LIG *- 236 LIG m w peck at a time, to which, when formed, into a complete, but rather thin paste, with sea-water, he then gradually added the other ingredient, keeping it constantly in a degree of toughness by continuance of beating. When a stone had been fitted and ready for setting, he whose mortar had been longest in beating came first, and the rest in order: the mason took the mortar out of the bucket; and, if any was spared, he still kept on beating; if the whole was exhausted, he began upon a fresh batch. The stones were first tried, and heaved into and out of their recesses, by a light moveable triangle, which being furnished with alight double tackle, the greatest number of all the pieces could be purchased by the sim- ple application of the hand; and this made our stones to be readily manageable by such ma- chinery as could commodiously be moved and carried backward and forward in the yawls every tide. To the first stone, and some few others, we took the great tackle, that we might hoist and lower them with certainty and ease; but there were not in the whole above a dozen stones that required it. “The stone to be set being hung in the tackle, and its bed of mortar spread, was then lowered into its place, and beat down with a heavy wooden maul, and levelled with a spirit level: and the stone being brought accurately to its marks, it was then considered as set in its place. The business now was to retain it exactly in that position, notwithstanding the utmost violence of the sea might come upon it before the mortar was hard enough to resist it. The carpenter now dropped into each groove two of the wedges already described, one upon its head, and the other with its point downward, so that the two wedges in each groove would then lie heads and points. With a bar ofiron of about two inches and a half broad, three-quarters of an inch thick, and two feet and a half long, the ends being square, he could easily (as with a rammer) drive down one wedge upon the other, very gently at first, so that the opposite pairs of wedges being equally tightened, they would equally resist each other, and the stone would therefore keep its place; and in this manner those wedges might be driven even more tight than there was occasion for; as the wood being dry, it would by swelling become tighter; and it was possible that by too much driving, and the swelling of the wedges, the stones might be broken; and farther, that a moderate fastening might be effectual, a couple of wedges were also, in like manner, pitched at the top of each groove, the dormant wedge,'or that with the point upward, being held in the hand, while-the drift wedge, or that with its point downward, was driven with a hammer; the whole of what remained above the upper surface of the stone was then cut off with a saw or chisel ; and generally a couple of thin wedges were driven very moderately at the but-end of the stone; whose tendency being to force it out of its dove— tail, they would, by moderate driving, only tend to preserve the whole mass steady together; in opposition to the violent agitation that might arise from the sea. “ After a stone was thus fixed, we never, in fact, had an instance of its having been stirred by any action of the sea whatever; but, considering the unmeasured violence thereof, the farther security by trenails will not seem altogether unnecessary, when we reflect, that after a stone was thus fixed in its place by wedges, a great sea coming upon it, (often in less than half an hour) was capable of washing out all the mortar from the bed under- neath it, notwithstanding every defence we could give it by plaster or otherwise; and that when the bed of mortar was destroyed, the sea acting edgewise upon the joint would exert the same power to lift it up, that the same sea would exert to overset it, in case its broad base was turned upright to oppose it; and as the wedges only fixed and secured the several pieces of which each course consisted to each other, and had no ten- dency to keep the whole course from lifting to- gether, in case the whole should lose its mortar bed; itseemed therefore highly necessary to have some means of preventing the lifting the whole of a course together, till the solidity and conti- nuity of the mortar should totally take away that tendency. Adverting now to what was said, thata couple of holes, to receive oak trenails of one inch and three quarters in diameter, were bored in the work-yard through the external or projecting end of every piece of stone: we must now suppose these stones set in their places, and fixed by wedges; then one of the tinners, with ajumper, began to continue the hole into the stone of the course below, and bored it to about eight or nine inches deep: but this hole was bored of a less size, by one-eighth of an inch in diameter, than L1G 237 M the hole through the stone above; in conse- quence, the trenails, having been previously dress- ed with a plane till they would drive somewhat freely through the upper hole, would drive stiny into the under one, and generally would become so fast as to drive no farther before their leading end got down to the bottom; and if so, they were sufliciently fast: but as they sometimes happened to drive more freely than at others, the following method was used to render them fast, for a cer- tainty, when they got to the bottom. The lead- ing end of every trenail was split with a saw, for about a couple of inches, and into this split was introduced a wedge, about one-eighth of an inch less in breadth than the diameter of the trenail; it was a full quarter of an inch in thickness at the head, and sharpened to an edge: when therefore the head of the wedge touched the bottom of the hole, the trenail being forcibly driven thereupon, would enter upon it, till the whole substance wasjambed so fast, that the trenail would drive no farther ;. and as the wood would afterwards swell in the hole, and fill the little irregularities of boring by thejumper, it became so fast that, as it seems, they could sooner be pulled, in two than the trenails be drawn out again. The tre- nail (originally made somewhat too long) being then cut ofi“ even with the top of the stone, its upper end was wedged cross and cross. There being generally two trenails to each piece of stone, no assignable power, less than what would by main stress pull these trenails in two, could lift one of these stones from their beds when so fixed, exclusive of their natural weight, as all agitation was prevented by the lateral wedges. The stone being thus fixed, a proper quantity of the beat mortar was liquefied, and the joints having been carefully pointed up to the upper surface, the grout so prepared was run in with iron ladles, and was brought to such a consist- ency as to occupy every void space; and though a considerable part of this was water, yet that being absorbed by the dry stones, and the more consistent parts settled to the bottom, the vacuity being at the top, this was repeatedly refilled till all remained solid: the top was then pointed, and, when necessary, defended by a coat of plaster. “ The several courses, represented in Plate III. are shewn as they would appear, when completed with the whole of their wedges and trenails; and besides these, there being also generally two lewis holes upon the upper surface of each stone, those served as temporary fixtures for the work of the succeeding course. “ It was the same evening’s tide, of the 11th of August, that the basement was completed and the centre stone of Course VII. was landed. Of the preceding courses, each was begun by the stones that engrafted in the dovetail recesses cut in the rock; these stones therefore being im- ‘ moveable by any assignable force acting horizon- tally, rendered those so likewise that depended upon them; but having now brought the whole upon a level, we could not have this advantage any longer; it therefore became necessary to at- tain a similar advantage by artificial means. For this purpose, the upper surface of Course VI. (Plate III. Figure 6) had a hole of one foot square cut through the stone that occupied the centre; and also eight depressions, of one foot square, sunk into that course six inches deep, which were disposed at regular distances round the centre: these cavities were for the reception of eight cubes of marble, in masonry calledjog- glee. As a preparation for setting the centre stone of Course VII. a parallelopiped (which, for shortness sake, I will call the plug) of strong hard marble from the rocks near Plymouth, of one foot square and twenty~two inches in length, was set with mortar in the central cavity, and therein firmly fixed with thin wedges. Course VI. being thirteen inches in height, this marble plug, which reached through, would rise nine in- ches above it; upon this, the centre stone (see Plate IV. Course VII.) having a hole through its centre of a foot square, was introduced upon the prominence of the plug, and being bedded in mortar, was in like manner wedged (with wedges on each side the plug) and every remaining cavity filled with grout. By this means, no force of the sea, acting horizontally upon the centre stone, less than what was capable of cutting the marble plug in two, was able to move it from its place: and to prevent the stone more effectually from being lifted, in case its bed of mortar happened to be destroyed, it was fixed down in the manner above described, by four trenails; which being placed near to the corners of the large square of that stone, they not only effectually prevented the stone from lifting, but aided the centre plug in preventing the stone from moving angularly, LIG 238 W , J or twisting, which it might otherwise have done, notwithstanding its weight, which was two tons nearly. “ After setting the first centre stone of Course VII. we immediately proceeded to set the four stones that surround it, and which were united thereto by four dovetails, projecting from the four sides of the centre stone. These stones be— ing fixed in their dovetails by a pair of wedges on each side, at bottom and top, as has already been mentioned, and held down by a couple of trenails to each surrounding stone, and still far- ther steadied'byjoint wedges at the head of the dovetails, and also in the mitre, ordiagonaljoints, between each surrounding piece; the whole form- ed a circular kind of stone of ten feet diameter, and above seven tons weight: and which being held down by acentrc plug and twelve trenails, became in effect one single stone; whose circum- ference was sufficient to admit of eight dovetail recesses to be formed therein, so as to be capable of retaining in their places a circle of eight pieces of stone, of about twelve hundred weight each, in the same manner, and upon the same principle, that the radical pieces of stone were engrafted into the dovetail recesses of the rock; and which being in like manner wedged and tre- nailed, we proceeded with circular tiers of stone, in the manner shewn in Plate 1V. Figure 1. It is however to be remarked, that the mode of ap- plying the wedges and trenails being sufficiently explained in the several figures of Plate III. and also in Plate IV. Figure 1, to avoid a repetition of small work, the several succeeding figures simply shew the general shapes and disposition of the different pieces composing a course, and other incidental larger matters, wholly omitting the particular application of the wedges and tre- nails ; yet it is to be observed, that they were every where equally applied, till we got to the top of the solid. “ My much esteemed master and friend, Mr. IVeston, who came from London to be witness of our proceedings, arrived at Plymouth during this interval. I went off with him early on “Ted- nesday morning, the 17th, attended by Mr. Jes- sop and his company, and landed upon the reek at ten: Richardson and company were then about to begin to set the fifth tier, or circle of stones, which was toscontain the eight cubes before de- scribed. These cubes were so disposed upon the LIG w surface of Course VI. that the cavities cut on the under side of Course VII. to take the upper half of each cube, should constantly fall in the broad part of the stones of the fifth circle; which will appear plain by considering the dotted lines rela- tive to Course VII. upon the surface of Course VI. (see Plate III. Figure 6.) There could con- sequently be no application of wedges in the upper course to the fastening of the circle of stones (No. 5.) upon their respective cubes: when therefore the stones respectively came upon them, we put as much mortar upon the top of the cube as would in part make good the joint between it and its cavity, but not enough quite to fill it; because, if too full, there was no ready way for the superfluous mortar to escape; but a hole, of the size of those for the trenails, being pre- viously bored through each of these pieces, an- swerable to the middle of each cube; when the stone was set, wedged and trenailed, then it was very practicable, by dressing a trenail so as to become a ram-rod, to drive as much mortar down the hole as would completely fill every vacancy between the stone and its cube; insomuch that we soon perceived, that if this was attempted be- fore the stone was completely trenailed down, it would very easily raise the stone from its bed, as might indeed be expected from the prin- ciples of hydrostatics: but, being done after such completion, it brought the "whole to the most solid bearing that could be wished; and, when the cement was hardened, answered the end quite as effectually as if they had been wedged. “ It may here be very properly said, that since those cubes could be of little use in keeping the work firmly together, before the mortar was har- dened; and after that had taken place, they could be of no use; because the number of one hun- dred and eight trenails, of which one of these courses consisted when complete, being supposed sufficient to keep it from lifting and moving out of its place; as the mortar hardened, and every additional course was an addition of its own weight upon the former, if those cubes could have been dispensed with in the first instance, they might have been so ever after. This reason- ing I can very well admit to be true; yet, when we have to do with, and to endeavour to control, those powers of nature that are subject to no cal— culation, I trust it will be deemed prudent not to omit, in such a case, any thing that can without L1G 259' LIG W difficulty be applied, and that would be likely to add to the security. It may farther be remarked, that as this building was intended to be a mass of stone, held tagether by the natural and artificial union of its parts, it would have been out of cha- racter, that, when completed, it should be be- holden to certain parts of wood for its consoli- dation. “ I have mentioned, that I originally conceived more than one way of preventing the courses from shifting place upon one another. My first con- ceptions were to form a rise (or a depression) of three inches, bounded by a circle somewhat about the diameter of that in which the joggles are placed; which step, or depression, would have formed a socket, whereby the courses would have been mutually engrafted, not much different from what nature has pointed out in the basaltine co- lumns of the Giant's causeway: but, considering how much unnecessary trouble and intricacy would be hereby introduced, by one part of the bed of the same stone being liable to be three in- ches higher than the other, I judged that the end would be very sufficiently answered by the much more plain, easy, and simple method ofjoggles; especially as, for this purpose, the firmest and toughest kind of stone might be chosen, and the numbermultiplied at pleasure. One plug in the middle, ofa foot square, and eight joggles of a foot cube each, of the hardest marble, disposed in the manner described, seemed to me, along with the additional strength and security arising from the trenails, as also from the infinite num- ber of little indentures upon the surface of the courses, as well as the lewis holes, each being filled with an extuberance of mortar, which, when hard, would in effect become a steady pin; from the cohesion of the mortar as a solid, promising to be no less than that of the stone, together with the incumbent weight of every part of the building above; every joint, thus separately con- sidered, seemed in point of firmness so satisfactory to my mind, that if the whole of this proved too little, it was out of my power to conceive what would be enough. “ In the morning and evening’s tide of the 17th, we set the whole of the fifth tier, and conse- quently the whole of the eight cubes were then inlaid. The morning of the 18th we again land— ed, and in this morning and evening’s tide, though rough, we had got set five pieces of Circle VI. and had landed the remaining three; as also one of the largest pieces of moorstone for the east side, (see Plate IV. Figure 1.) This evening’s tide we worked with links, and it began to blow so fresh that we had much ado to keep them in, being obliged to make a fire of them upon the surface of the work. We were under the necessity at last to quit the rock with some precipitation, and were very glad to get into our yawls; things being left in the following posture. Two of the pieces, Tier 6, were simply dropped into their places, on the north-west side, while the third piece, being about a ton, and the piece of moorstone near upon two tons, were chained together, and to the work of Course VII. that was already set; these two loose pieces being upon the top of that course, near the east side: the triangles were lashed down upon the floor of the work, as we had practised several times be- fore. The sea became so rough in the night, that the Weston, at the transport buoy, was obliged to slip, and make for an harbour. The bad wea- ther continued to increase till the 28th, when there was a violent storm at sou th-west. “ The 29th, I perceived with my telescope, from the Hoa, the buss to ride safe, but could not see the shears, or indeed any thing else upon the rock distinctly, except the breakers. The day follow- ing being more clear, and the sea somewhat sub- sided, I immediately went on board the Eddy- stone boat to reconnoitre. The wind b'ei'ng north-west, I passed the rock several times under sail, but there was no possibility of landing. I observed that not only all the wozk which had been completely set was entire, but that the two stones mentioned to have been simply lowered into their places, also remained therein, and that the five hundred weight still rested upon the stone whereon it was left. The west face of the building had got so complete a coat of sea-weed, that it was only distinguishable from the rock by its form: but the shears and triangles were en- tirely gone; the two pieces of stone, that had been chained together and to the work, were also gone; the Windlass frame broken and much da- maged, and the roll gone; the fender piles and the transport buoy however remained in their places. “ It was the 3d of September before the com- pany could make a landing to do any thing upon the rock; so that since the 18th ult. there had O L1G I * been an interval of fifteen days, in which we had been totally interrupted by bad weather, in the very prime part of the season. However, every thing having been expedited on shore, to\get refitted for work, this day I went out therewith, and her gan to set up our new shears, Windlass, 86c. and with the shears got up the piece of Portland, of Circle 6, which was set, as also the others that had been left loose in their dovetails; but the tide of flood coming on, had deepened the water too much before we could try to get up the other. “ September the 5th, the seventh circle was finish- ed and the eighth begun ; and this day the wind being variable from north-east to north-west, and very moderate, was remarkable, as being the’first time of the people having 'worked till they were obliged to quit the rock for refreshment: and now every thing being reinstated, it was some time before we met with any thing but the ordi- nary interruptions. “ The fineness of the season continued to favour the expediting of our works, insomuch that Course VIII. which was begun upon the 8th, was executed in five days, being entirely completed on the 13th, at the same hour. Every thing went regularly on till the 20th; so that in return for our continued interruption from the stormy wea- ther for fifteen days, our works had an uninter- rupted progression for eighteen days, when Course IX. was advanced to the fifth circle.” A series of land swells from the south-west pre— vented farther proceedings till the 30th of Sep- tember, when Course IX. was completed,“ and the masons proceeded to rectify the face of the work, where it was in any degree wanting there- of, that there might be no need hereafter to dis- turb any part of the coat of weed, which was likely to fix upon it during the winter.” This ended the operations for the year 1757. On the 12th of May, 1758, Mr. Smeaton ex— amined the work, and found it perfectly entire, except a small spawl, which had been washed from the rock itself; the whole did not seem to have suffered a diminution of so much as a grain of sand since the time he left it on the first of October of the preceding year: on the contrary, the cement, and even the grouted part, appeared to be as perfectly hard as the Portland stone itself; the whole having become one solid mass; and was entirely covered with the same coat of sea- . weed as the rock, the top of the work excepted, 4O LIG M which was washed so clean and white, that the lines upon it appeared more distinct than when they were in the-work-yard; the cube-holes and lewis—holes, however, from their being constantly filled with water, were grown over with green weed, like the outside. The fender-piles were indeed all gone, but this was a trifling disaster, as they could soon be renewed. The tenth course was set on the 5th of July, the eleventh on the 18th, the twelfth on the 24th, the thirteenth on the 5th of August, and on the 8th of that month the fourteenth, which com- pleted the fundamental solid. From the top of this course begins that part of the building, also called the solid, which includes the passage from the entry door to the well-hole of the stairs, as described Plate IV. Figures‘z, 3, 4, from which a more adequate idea can be obtained than any words could convey. Mr. Smeaton then proceeds to describe his me— thod of regulating the superstructure: As “ for the sake of the well—hole, we must necessarily lose our centre stone, the four stones, which in the former courses were united to it by dovetails, were, as now prepared, to be united to each other by hook-scarf—joints, so as to compose, in effect, one stone: and as, in consequence, we had also lost our centre cubes, it became expedient, that the work might have an uniform texture and strength, that. those four stones, making a com- plete circle for the staircase, should be provided with cubes, to prevent their being shifted by any shock applied horizontally, (see Figure 4) as well as with trenails to hinder them from lifting. By this means the principle of consolidation would be effectually preseved: but as the top of the fourteenth, or entry—door course, was twelve feet above the top of the rock, that is, twenty feet four inches above the base of the first course, the stroke of the sea must here become less violent, and therefore a less degree of resistance would be equally sufficient. And as the large cubes would too much out the work, which was here of con- siderably less area; and as several cubes would be requisite for the well-hole stones, I had deter— mined, above the entry-door course, to increase the number of cubes from eight to sixteen, and to diminish their size from twelve to six inches; but still to be of solid grey marble, and two of them to be introduced into each of the four well- hole stones.” rk L1G 241 LPG W W “ Upon the 9th of August, I marked out the en- try and staircase; and having unloaded the Eddy- stone boat, which was loaded with the first pieces of Course XV. we immediately proceeded with it; and frOm this time were blessed with such an uninterrupted continuance of fine weather, that upon the 20th of August, Course XVIII. was completed, which reunites the building into a complete circle, by covering the passage to the staircase: the external face of the stone of that course, which makes the cover or head of the entry-door, having the figures 1758, denoting the year in which this part of the work was accom- plished, cut in deep characters upon it. “ On the 24th of August, the fine weather, and in consequence the works, were interrupted, Course XX. being then in hand; and it was not till the 24th of September that, with every possible ex- ertion, Course XX IV. was finished; which com- pleted the solid, and composed the floor of the store-room. “ The 25th and 26th of September, Course XXV. being the first course of the superstructure, was successfully completed in its place; but, as the mode of construction now became entirely differ- ent from the former, it is necessary to give an account thereof, as also of the reasons for the change. The building was carried up solid, as high as there was any reason to suppose it ex- posed to the heavy stroke of the sea, that is, to thirty-five feet four inches above its base, and twenty-seven feet above the top of the rock, or common spring-tide high-water mark. At this height, as it was reduced to sixteen feet eight inches in diameter, it became necessary to make the best use of this space, and make all the room and convenience therein that was possible, consistent with the still necessary strength. The rooms being made of twelve feet four inches diameter, this would leave twenty-six inches for the thick- ness‘of the walls. These being made with single blocks in the thickness, so that sixteen pieces might compose the circle, would, from its figure, compose a stout wall; yet moorstone, as has been observed, being a tender kind of stone, in respect to the union of its component parts, any method of dovetail‘ing the blocks together, at this thick- ness, appeared to me impracticable to any good purpose. .What seemed to be the most effectual method of bonding the work together, was that of cramping with iron, which would confine each VOL. II. single piece to its neighbouring piece in the same circle: and if to this be added, that every piece should, at each end of it, lay hold of an inlaid piece, orjoggle, in the same nature as the cubes, then not only all the pieces in the same course would be united to each other by the cramps, but steadied from moving upon the under course by the joggles, and of consequence would be fasten- ed at thirty-two points ; for, in each course there being sixteen joggle-stones, as each end of each principal piece, at its base, took hold of half a joggle, there would be thirty-two points of confinement in the circle above; that is, the joggles being made to occupy the middle of the upper bed of each block, in that situation they would cross the joints of the course above. These joggles, as well as the rest, were of sawn marble, and made eight inches long, four inches broad, and three inches thick: each end of each block, therefore, would occupy four inches in length, four in breadth, and one inch and a half in the height ofeach joggle; and this I judged quite sufiicient to keep every course in its place, at the height that this kind of work was begun, and so as to constitute a piece of solid masonry. There was, however, another matter, that it seemed quite material also to attend to; and that was, to render the habitable rooms contained within those shells of walls, perfectly. dry and comfortable in all weathers; and this seemed to merit very parti- cular attention; for the seas that are said to rise up against, and in a manner to bury the house, in time of storms, would make effectual trial of every joint. “ The level joints being pressed together by the incumbent weight of the building, would keep firm and sound that cohesion of parts produced by the mortar; so that being once made water- tight, there was no doubt but they would so re- main : but with respect to the upright‘joints, the least degree of shrinking, either of" the stone or of the mortar between, tended to open thejoint, so that it might always remain leaky, in a greater or a less degree; for we know of no degree of separation of parts, however minute, short of ab- solute contact, which will stop or prevent the percolation of water. For this purpose I con- ceived, that if flat stones were introduced into each uprightjoiut, so as to be lodged partly in one stone, and partly in its neighbour (much upon the same idea that Dutch laths were for- 2'1 r4- - LIG 24 LIG merly introduced into the joints of chamber floors, to‘hinder the passage of wet) the water might be prevented from making its way through the uprightjoints of the walls. “The manner in which it was executed was as fol- lows: (see Plate IV. Figure 6). At each end of each stone, answerable to the middle between the inside of the wall and the outside,was sunk agroove, two inches and a half wide and three deep, running from the top to the bottom :' when therefore two contiguous pieces of stone were put together in their places, the two grooves being applied to each other, they would form a rhomb of six inches in length, and two inches and ahalf in breadth, which in this state would be an unoc- cupied cavity from the top to the bottom of each course; the rest of the joint, where the surfaces of the two stones applied to each other, was made good with mortar in the ordinary way, and brought together by the gentle blows of a beetle. For the groove mentioned, a solid rhomb was prepared, of about two inches thick by five inches broad, and in length a little less than the depth of the cavity, which generally was eighteen or twenty inches; and, for the sake of the firmness of those slender pieces of stones, 1 made choice of the flat paving-stones from Purbeck, which is a laminated marble of great strength and solidity. The joint-stones (which was the name we gave those rhombs) thus prepared, would readily go down the cavities; but, to fix them solid, a quan- tity of well-tempered mortar was prepared, made more soft than ordinary, by the addition of a little water; a competent quantity being put down to the bottom of the hole, thejoint-stone Was put down upon it; and, by the simple pres- sure of the hand, was forced down to the bot- tom, causing the semifluid mortar to rise up to the top, and completely fill the cavity: and, when forced down in the way described, having in this state a small quantity of superfluous mois- ture about it, a few very gentle blows, or raps, were given upon the top of it by the handle of a mason’s trowel, which producing a small degree of agitation, while the dry stones were absorbing the moisture, contributed (like the beating of mortar) to bring all the parts into their most friendly state of contact, and, in consequence, to their firmest state of union; and this happen- ed in the course of a few minutes, so that no far- ther agitation could be of any service. “ As the cramps, that were to bind the conti- guous pieces together,must cross the joints upon their upper surface, they were of course to be applied after the joint-stones were settled in their places. Precaution was therefore necessary not to apply too much exertion in forcing down the joint-stones: for, however gentle the operation may appear, according as it has been described, yet it was found advisable not to put in the joint- stones till an additional piece had been got down upon its joggles, and plain jointed at each side of the two pieces, whose joint-stone was to be put in ; for, by this means, there were the united efforts of all the joggles, and adhesion of the beds of two stones on each side of that where the effort was applied. Without an attention to this, the lateral force arising from merely pressing down a joint—stone, was capable of breaking the adhesion of the joint where it was applied. “ The cramping was applied the last thin". The top or flat bars of the cramps were about thirteen inches long, two inches broad, and five-eighths of an inch thick, and were turned down at each end about three inches in length; forming a cy- linder of one and one-eighth of an inch in dia- meter. Jumper holes were previously bored when upon the platform, and the cramps fitted to their places; the surface of the stone under each cramp being sunk three-fourths of an inch, so that the two stones together would completely receive, or rather bury, the cramps: the joint- stones, as said above, being made so much shorter than the height of the course, as not to interrupt the bedding of the cramp. The places for the cramps being prOperly fitted and cleared (as we now were not liable to be driven 01? the work in a moment, as had formerly been the case) we took the opportunity, whenever time allowed it, of fixing the cramps of a whole course together. There was no danger of the cramps not fitting; as, besides that all the cramps were forged to fit a gauge—bar having a couple of holes at the as- signed distance, they were also fitted and marked to their particular places at Mill Bay, while upon the platform. Every cramp being now ultimately tried to its place, it was then put into a kettle of lead, made red hot; and the cramp continued there till it was also reddish. About a spoonful of oil was poured into the two cramp-holes, and the cramp being put into its place, the ebullition of the oil, caused by the heat of the iron, quickly LIG 243 LIG w gave a complete oily surface, not only to the whole cramp, but to the whole unoccupied cavity in the stone; then the hot lead being poured upon it, the unctuous matter caused the metal to run into and occupy the most minute cavity un- filled, and completely to cover each cramp; and they became by this means defended from the salts of the sea, even had they remained uncover- ed, upon Mr. Rudyerd’s principle. Mr. Rudyerd had used coarse pewter. The lead we used was slag lead, which is harder and stiffer than fine lead: and, as we used no cramps, as an essential part of the building, till above the store-room floor, I judged pewter, merely for the sake of stiffness, there to be unnecessary. By cramping, in general, a whole course together, the contrac- tion of the iron in cooling would greatly add to the tightness wherewith every stone was bound to its fellow. Thus, according to this mode of fixing, (besides the union of the parts by the mortar itself) to resist all violence and derange- ment whilst it was doing, and before the indura— tion of the mortar, every course was retained in its place by sixteen joggles, and each single stone by two half-joggles at its lower bed; they were farther steadied to each other, by the joint-stones, and lastly by the cramps, which completely pre- vented a separation; and this method proved so effectual, that we were not only free from all de- rangement of the stones, when in their places, but I did not find aleaky joint, except one, in the whole building. Bya due consideration of Plate IV. with the particular references to it, the whole of this process will become perfectly intelligible. “ On Saturday, the 30th of September, Course XXVIlI. was completely set; and, being the first course upon which was rested the vaulted floor, which made the ceiling of the store-room and floor of the upper store-room; and, as here again occurred a difference in the mode of fixture, in this, as in all like cases, I attended the per- formance of the work: and that was the leading- in of the first circular chain, that was lodged in a groove cut round the middle of the upper surface of this course, which this day was satisfactorily performed; and the next day, Sunday, October the lst, Course XXIX. was set, and its circular chain leaded-in also; which operation, with the reason thereof, it will be proper here to describe. “ The ordinary way of fixing the several courses byjoggles and joint-stones, and also the bond- ing them together by cramps, has already been described; but those courses, upon which the floors rested and depended, seemed to demand every possible security. It will be seen, in the general section, Plate II. that each floor designs edly rested upon two courses: it will also appear, by inspection, that the circumference of the floors was not made to rest upon the sloping abutments of an arch, in lines tending towards the centre of the sphere, of which the under side of the floor was a portion, but it rested upon a triple ledge going circularly round the two sup- porting courses. In consequence of this, had each floor been composed of a single stone, this lying upon the horizontal bearings furnished by these ledges, would, while it remained entire, have no lateral pressure or tendency to thrust out the sides of the encompassing walls: and that, in efi'ect, the several pieces, of which the floors were really composed, might have the same pro- perty as whole stones, the centre-stone was made large enough to admit of an opening, from floor to floor, or man-hole, to be made through it; and being furnished with dovetails on its four sides, like those of the entire solid, it became the means by which all the stones in each floor were connected together; and consequently, the whole would lie upon the ledges like a single stone, without any tendency to spread the walls. But if, by the accident of a heavy body falling, or otherwise, any of those stones should be broken, though this might not destroy its use as a floor, or its properties as an arch; yet the parts would then exert their lateral pressure against the walls: and therefore, as a security against this, it be- came necessary that the circle of the enclosing walls should be bound together, and the building, as it were, hooped. “ This would be in a great measure brought about by the cramps tying the neighbouring stones together, as already described, for the or- dinary courses; but yet this was no absolute se- curity, because the outside stones might break and separate, between cramp and cramp: and, I suppose, it was for reasons of this kind, that Sir Christopher Wren, in the construction of the cupola of St. Paul’s, did not choose to depend upon cramping the stones together, of the course that served as a common base to the inside dome, and the cone for supporting the lantern; but 2 1 2 L1G o I.“ chose to surround the whole with continued chains of iron. Upon this principle, an endless chain was provided for each of the two floor courses; see Plate IV. Figure 7. The bars composing the links being one inch and a quar- ter square, that the most iron might be included in/a given space, the corners only were a little canted off; and the double parts being brought near together, the whole wascomprehended in a groove, of somewhat less than four inches wide, and as much in depth; into which the chains be- ing introduced and brought to a stretch, the rest of the cavity was filled with lead, of which each took about eleven hundred weight, in the follow- ing method. The chains were oiled all over before they came from the shore; and the circumference ofthe groove was divided into four parts by stops, or dams of clay, to prevent the lead from flowing farther than one quarter at a time. A couple of iron kettles were provided, capable of melting commodiously, when full, six hundred weight of lead each; and that quantity was brought in each to a full red; that is, somewhat hotter than we used for the cramps, as the iron of the chain, as well as the stone, were cold. The whole quantity of lead being brought to a heat that we judged proper, and the quarter groove being supplied with oil sufficient to besmear the whole surface, two persons, with each a ladle, as briskly as they could, poured the melted metal into the same quarter of the groove; and, as soon as it was full, and the lead began to set, one of the clay dams was removed, and the melted hot metal was poured upon the end of the former mass, till it was perceived to re-rnelt and unite with the fresh metal. This done, the dam at the other end of the first run mass was taken down, to prevent its cool- ing more than was necessary, and the third quar- ter was treated like the former; the end of the mass rendered solid by cooling, being re-melted by the fresh hot metal: lastly, both the remain- ing dams being taken down, and the metal at each end having a considerable heat, it was found practicable to dissolve both the ends of the former masses; first applying both ladies to that which had had the greater time to cool, and afterwards to the less: by this means the whole was brought to a solid consistence, and the chain entirely buried in the lead. It is however to be remarked, that to preserve proper impressions in the lead, for the joggles of the course above, those impressions 44 LIG were made by confining down bricks in proper places, which, when removed, the proper marble joggles were set with mortar in their places. “ Monday, October 2, we proceeded to set up the centre, composed of sixteen ribs, (see Plate VIII. Figure 3) for putting the floor together upon; but the weather continued broken till Saturday, the 7th, on which day the Eddystone boat came out, having on board the roof, or platform, for cover- ing the building, and protecting it from the en.- trance of the downfall spra '; together with the doors, iron-work, and timber for fitting up the same for habitation. This afternoon we landed, and went on with the setting of the outward circle of floor-stones, made the holes in the wall for fixing the hinges of the entry and. store—room doors. In particular, I caused the middle stone to be laid upon the centre, by way of weight, to keep it steady. Three of the four stones that were to connect with the centre-stone were laid upon the top of the wall, on the north-east side; and the fourth I caused to be hoisted and sus- pended upon the triangle, in the posture that is shewn Plate VI. at stage second. So that the triangle, which was all of it completely within the area of the top of the building, would be kept down by the weight of this stone, which was be- tween seven and eight hundred weight. The other three that lay upon the wall, I caused to be carefully drawn within the circumference thereof, so that there might not be the least projecting part for the water to strike against in flying up- wards; which I judged quite necessary, though the walls were then upwards of forty-three feet above the foundation-stone, and near thirty-five feet above the top of the rock.” The weather now set in so bad, that no farther operations of consequence took place that season. On the 10th of October, Mr. Smeaton was mor: tified with a copy of a resolution of the Trinity- Board, declining his proposal of exhibiting alight that winter upon the foundation of the building. “ During my stay in London, in the early part of the year 1759, I received regular accounts of the proceedings at Mill Bay, which were carried on with all the dispatch I could wish; but the wea— ther having continued unfavourable to visiting the works at the Eddystone during the winter, I got no report thereon till I received Mr. Jessop’s letter, dated the 27th of March, wherein he informed me that on the 21st of that month, being the first LIG 24 LIG W opportunity he could catch after the violent storm which had happened on the 9th preceding, they found not only the solid, but the hollow work perfectly sound and firm; all the mortar having become quite hard ; and, in short, every part of the work in the situation in which it was left by the workmen in October: the only derangement was, that the sea had carried away the south fen- der pile from the rock; and also, from the top of the wall, one of the three stones that I had taken care to draw within the verge of the circumfe- rence of the wall, as mentioned. They had found the fourteen pieces of stone set in the circumfe- rence of the floor, stuck quite firm to the wall, though two of the pieces requisite to complete the circle were left unset; and that, finding the centre itself quite tight and firm underneath them, they had lowered dOWn the stone suspended on the triangle upon it, and removed from the wall the other two remaining stones to lie upon the centre; and lastly, that they took down the triangle, and stowed it away in the well-hole for the stairs: but, on farther search, nothing of the buoy that was left upon the mooring chains was to be seen. “ Thursday, the 5th of July, I landed on the rock with the men; they proceeded to set up the shears and Windlass, while I inspected the work; and found every thing perfectly sound and firm, with- out the least perceivable alteration since we left it; except that the cement used the first year, now in appearance approached the hardness of the moorstone; and that used the last year of the full hardness of Portland. We now proceeded to set the floor. The. two remaining pieces of the outmost circle, which were left uncompleted last year, were soon set; and we proceeded to haul up the stones for the next circle (No. 4.) from the store-room.” The work now proceeded so rapidly, that the se- cond and third stories were completed in thirteen days. On the 8th of August, Course XLV. or the Cove Course, was completed with its two chains; and the next day, the elliptical centre for the balcony floor was set; and by the 16th, the in- terior area of the balcony floor was completed, the centre was‘ struck, and the outer circle of stones, which finished the cap of the main column, being parts of the corona, or cornice, was begun upon: see Plate'II. and Plate lV. Figure 9. “ Friday, August the 17th, the last pieces of the _ corona were set, and therewith the main column was completed. I now examined the perpendicu- larity of the whole building, by letting fall a plumb-line from the centre of the man-hole in the balcony floor to the centre of the bottom of the well-hole, being forty-nine feet and a'half; and found it to fall a small matter to the eastward of the centre of the well—hole; as near as I could - determine it, not more than one-eighth of an inch. I then measured the perpendicular heights of the several parts of the building, and found them as follow : Feet. In. “ The six foundation courses to the top oftherock— - - - - - - - - 8 4% ‘ “ The eight courses to the entry door - 12 021 “ The ten courses of the well-hole to the store-room floor - - - - - - - 15 2% “ The height of the four rooms to the balcony floor - — - — - - - - 34 4% “ Height of the main column, con- _0 O taining forty-six courses - - - t “ We proceeded this day to set up and lead- in the balcony rails, and completed them; and having brought out a temporary cover for the man-hole of the balcony floor, I this day applied it to use, as follows: a short tub, of about a foot high, was made without a bottom, and the smaller end of it being siz'ed as near as possible to the man-holes of the floors, it was driven into that of the balcony; and, by the time it was driven about four inches,,the compliancy of the wood to the stone rendered it quite tight; then the rest of its height, forming a border, and standing about eight inches above the floor, would prevent water from chipping into the rooms through the upper man-hole, or hatchway; and having also provid- ed another tub,-about nine inches deep, having a strong bottom in it, and so much more in dia- meter than the other, that it would, when invert- ed, cover it; this being applied as a cover, would in the greatest stress of weather defend the build- ing from the entry of water at the top.” On the 18th of the same month, the first course of the lantern was begun; on the 24th, the last stone, being that which makes the door-head of the lantern, was set; and on Sunday evening, the 26th, the whole of the masonry was completed. Stress of weather prevented the landing of the frame-work till Saturday, the 15th of September, LIG g -’ m 4—.— ————_———__________.._____ on which day, “ between three and four in the morning, the Weston was got into the gut, and delivered of her cargo, consisting of the pillars, sashes, and frame-work of the lantern. 1 gave my principal attention to the establishing the frame of the lantern upon a bed of lead, and the screwing of it carefully together; seeing that every joint was filled, and screw covered with white lead and oil, ground up thick for paint; and every crevice so full, that the bringing the screws home made the white-lead matter to ooze from every juncture; thereby to exclude all wet and moisture, and so as to prevent the iron-work from rusting. “ Sunday, September the 16th, was remarkably fine; so that by the evening the whole frame of the lantern was screwed together, and its ground- sill was rested upon a bed of lead; which was done in the following manner: The whole frame being screwed together, was raised from its bear- ing upon the stone about three-eighths ofan inch, by a competent number of iron wedges; and ad— justed by them to an exact perpendicular. Both the stone and the iron were taken care to be oiled before they were applied to each other; and one of the eight sides, having its wedges withdrawn, was run with hot lead; and making a place for it to overflow, as much could be used as would competently heat both the iron and stone, to bring them to a close bearing with the lead; then on the lead’s cooling, as the frame became sup- ported on one side by the lead, the wedges of a second side were withdrawn, and treated in the same manner, and so successively till the whole rested upon a solid basement of lead. It was not supposed that the succeeding mass could be suf- ficiently heated to re—melt the ends of the parts already leaded, as in the case of the chains; but being heated so as to bring them to a close con- tact, this Ijudged sufficient, as the lead so ap- plied had no other intent but to bear weight, and give the frame of the lantern one solid uniform bearinO'. “ Monday, the 17th. This morning was also ex- ceedingly fine; and the Weston being in sight, which was appointed to bring out the cupola, we began to set up our shears and tackle for hoist- ing it. This perhaps may be accounted one of the most difficult and hazardous operations of the whole undertaking; not so much on account of its weight, being only about eleven hundred, as 46 LIG m on account of the great height to which it was to be hoisted, clear of the building; and so as, if possible, to avoid such blows as might bruise it. It was also required to be hoisted a considerable height above the balcony floor; which, though the largest base we had for the shears to stand upon, was yet but fourteen feet within the rails; and therefore narrow, in proportion to their height. The manner in which this was managed, will, in a great measure, appear by the represen- tation thereof, in Plate VI. (see the uppermost stage); but is more minutely explained in the technical detail of that Plate. As the legs of the shears that had been used upon the rock would have been in the way of the cupola, they were now removed, as being done with there, and were used as a part of this machinery. About noon the whole of our tackle was in readiness; and in the afternoon the Weston was brought into the gut; and in less than half an hour her trouble- some cargo was placed upon the top of the lan- tern, without the least damage. “ Tuesday, September the 18th, in the morning, the wind was at south-east, with intervals of thick fog; however, between those, I had the satisfaction, with my telescope, to perceive the Eddystone boat, on board of which I expected the ball to be. The wind and tide were both un- favourable to the vessel’s getting soon near us; therefore, being desirous to get the ball screwed on, before the shears and tackle were taken down, one of the yawls was dispatched to bring it away. This being done, and the ball fixed, the shears and tackle were taken down. By this time the joiners had set up and completed the three cabin bedsteads, (for their plan and position be- tween the windows, see Plate IV. Figure 8.) “ On Friday, the 21st, all the copper sash-frames were got completely fixed in, and ready for re— ceiving the glass. “ On Sunday morning, the 93d, the yawl landed two glaziers and a coppersmith, with their utensils and materials; the former began to glaze the lantern, and the latter to fit and put up the fun- nels. This day, with my assistant, the mason, I began to fix twenty-four iron cramps; that is, three to each rib of the roof, and which were obliged to be fixed after the roof was together; and being fixed inside, and surrounding the ribs, served to key home the plates of the cupola t0 the ribs. For this purpose small wood wedges LIG 947 W were used, as being more supple, elastic, and compliant, than wedges of metal, and therefore more suitable to this particular purpose. This day also the Eddystone boat brought out and landed a plumber, with his utensils and materials. The most considerable work for the plumber was the covering the whole balcony floor with thick plates of lead; and which extended from the top of the plinth, or first course of the basement of the lantern, quite down to the drip of the corona. They were fitted on separately, in sixteen pieces, and soldered together, in place, with strong ribbed joints; and, to prevent the sea from laying hold of them at the drip, and beating them up, they were turned under about one inch and ahalf ; and being near half an inch thick, Ijudged them suf- ficiently stubborn to prevent being unripped. “ Thursday, the 27th, the lead-work upon the balcony and corona being now entirely finished, and the cupola completely keyed home to the ribs; the straps and bolts were applied at each angle of the lantern, for screwing it down to the floor of the balcony. “ Friday, September the 30th, the joiners finished their work, which consisted of the following ar- ticles. Three cabin beds, to hold one man each, with three drawers and two lockers in each, to hold his separate property, which were fixed in the upper room, or chamber. (See plan thereof, Plate IV. Figure 8.) In the kitchen, besides the fire-place and sink, were two settles with lockers, a dresser with drawers, two cupboards, and one platter case. (Figure 7, of the same Plate, shews how these were disposed.) In the lantern a seat was fixed, to encompass it all round, the door- way excepted, serving equally to sit upon, or stand to snuff the candles; and to enable a person to look through the lowest tier of glass panes at dis- tant objects, without having occasion to go on the outside of the lantern into the balcony. Be- sides the above, thejoiners had fixed the ten win- dow-frames, with their sashes; all which were bedded in putty, and falling into rebates cut for them in the original formation of the stone, they could be at any time removed, and replaced at pleasure, as they were fastened in only with wooden pins, driven into holes bored in the stone.” On Michaelmas-day, the glazing of the lantern was completed; on the lst of October, the copper funnel was finished, and tried by lighting a fire in the stove. . LIG “ The tackle was .also fixed for raising and low- ering the chandeliers; and those being hung, there was now nothing to hinder our making trial by lighting the candles, while it was daylight, to see that everything, regarding the light, ope- rated in a proper manner. Accordingly, this after- noon, we put up twenty-four candles into their proper places, and continued them burning for three hours; during which time we had a very effectual trial; for it had blown a hard gale of wind at south-east all day, which still continued; and, keeping a fire at the same time in the kitchen, they both operated together without the least in- terference; not any degree of smoke appearing in the lantern, or any of the rooms: and, by opening the vent-holes at the bottom of the lan- tern, it could be kept as cool as we pleased; whereas, in the late lighthouse, this used to be complained of, as being so hot, especially in sum- mer, as to give much trouble by the running of the candles. “ Wednesday, October the 3d, we began to fix the conductor for lightning. As the copper fun- nel reached through the ball, and from thence came down to the kitchen floor, above forty feet, (see Plate II.) I considered this as containing so much metal, that, if struck with lightning, it would thus far be a sufi‘icient conveyance; then joining the kitchen grate to the leaden sink, by a metal conveyance, the sink pipe of lead would convey it to the outside. From the sink pipe downwards, which being on thetnorth-east side, was consequently the least subject to the stroke of the sea, we continued the electrical communi- cation by means of a strap of lead, about one inch and a half broad and three-eighths thick, fixed on the outside by being nailed to oaken plugs, drove into two jumper-holes in the solid of each course; the prominent angles of the strap being chamfered off, it was bedded and brought to a smooth surface with putty. At the foot of the leaden strap, an eye-bolt of iron was driven into the rock; and to this was fixed an iron chain, long enough to reach at all times into the water; its lower end being left loose to play therein, and give way to the stroke of the waves: by this means an electrical communication was made from the top of the ball to the sea.” Every thing being now completed, notice was sent to the Trinity House, and, on Tuesday evening, the 16th of October, 1759, the lights L1G 248 fl were first exhibited, amidst the fury of a violent storm. This excellent building exhibited no other light than what was produced by twenty-four candles, which was not always sufficient, till 1809, when Mr. Robinson, surveyor of lighthouses to the corporation of Trinity House, superseded these candles by the same number of Argand lamps, each accurately fixed in the focus of a large paro- bolic reflector of richly plated copper, arranged on circular frames; and consequently giving light in every direction. The improved brightness of the light, by this exchange, exceeded the most sanguine expectation of all in the neighbourhood of Plymouth. The present light, in clear weather, may be seen at the distance of nearly thirty miles; and, im- mense as this distance is, it is exceeded by those at Flamborough Head in Yorkshire, and at Scilly, off the Land’soEnd of Cornwall, erected by the same gentleman. The lanterns are either of copper, or cast-iron, and are generally polygons of sixteen sides, about fourteen feet in diameter, surmounted by a lofty dome, and weighing from six to eight tons. The lights of Flamborough, Scilly, and several others, are made to revolve by machinery attached to the frame which supports the lamps and reflectors: this is done to distinguish them from other lights which do not revolve. In some places stained glass is used for the same purpose, which, by tinging the rays of light, effectually informs the mariner of his exact situation. The number of lamps and reflectors used in one lantern varies according to the importance of the situation, but is generally between seventeen and twenty-four: the most scrupulous care being taken that every part shall be so arranged as to give the greatest possible light. TECHNICAL REFERENCES TO THE PLATES. “ PLATE L—Aplan andperspective elevation ofthe Eddystone Rock, as seen from the west; skewing also the tlzeodolite. “ The representation is as I found the rock; Fi- gure 1 being the plan, and Figure 9. the upright view. The same letters refer to the same parts in both; the cross lines upon the plan answer to the cardinal points, east, west, north, and south, ac- cording to the true meridian. “ L is the landing-place, and C the summit of the rock; the general declivity being towards the LIG ‘ i _ I J ! —_—_ south-west; the grain of the laminated moorstone that com poses it being nearly parallel thereto. It has, however, considerable irregularities; for upon the line A B the rock makes a sudden drop of four and a half or five feet; and, by overhanging to the westward, when there is a ground swell at south-west, the sudden check causes the sea to fly in an astonishing manner, even in moderate weather. “ The surface of the rock is shewn, as supposed to have been for ages past; except where it is visibly altered by man’s hand, chiefly within the circular area of the late building. The flat treads of the steps cut by Rudyerd are marked D; the upright faces of the steps F; and E denotes the spawled parts, parallel to the grain of the rock. “ a b c d efg .h shew the remains ofthe cavities of eight of the twelve great irons fixed by VVinstan— ley; of which the stump of one only, viz. that at e, remained for my inspection; it was run in with lead, and had continued fast, till in planting a dovetail there it was cut out, and found club- ended. Which of the other holes, that are left unmarked, made up the remaining four, I could not make out; as doubtless several of them apper- tained to the additional work that he fixed in the fourth year. “ Figure 3. A pair of Rudyerd’s iron branches, to a scale three times larger than that of the plan; wherein A B is the main branch, or dovetail part; C D the key, driven hard in, but without touch~ ing the bottom; their depth in the rock is de- noted by supposing the line E F its surface. The holes in the branches served to fasten the timbers, by large bearded spike-bolts. Of those branches I traced thirty-six original pairs, of different sizes; and two more modern: their places are shewn in the upright, Figure 2, by inspection; and likewise in the plan, Figure l, at 1, ‘2, 3, 4, 5, and 6, 7, 8, 9, 10, 8:0. forming a double circle; also two pair of them at K, to fix the mast, on two sides, to the centre. The irons that remained in the rock, are distinguished in the plan by be- ing hatched with slant lines, the empty holes or cavities by being black. Those that remained whole, whether fast or loose, are distinguished in Figure ‘2, by their shapes. “ X. The place of the cave on the east side. R. A strong ring-bolt, put into the rock on the reconnnencement of the building in 1757, for fastening the western guy-chain of the shears. HARE EE'H‘ 1814?? 3535.0 [’11 7'1! 1. \ \ .0 w‘ w V \\\\\}\\\\\x W fig V. r. E,“ A“ _ \ “mm .l'nl/w I [114/1 -“ If [077. . ’ , .. V .4 . . , V n .{ IN 1:: 3w [-0 [6012-44. ~‘I‘II/4’ J ['17le INK/5, / /// |;.:v"‘ ’3 , [1L . J -,,’){1H"f 131” . A. (‘ Q U' 2 ‘ /)nm’/I /{// JI._[.AT1}'/1n/.rull. Lulu/(w,/'///I//:v//w/ /l'l/ [CY/r/m/ww/l X- ./, /irH'/}'r/4/I ”fin/uni" .W/V’z-Ijr‘fjg. 1,3147! F!” - m $13151); , 1S 3 Y 132;}; A]fi§1.fi2iiz'l‘,'iéén Inndnn,flcbli.rim7 1:1, R Art-«'lzolmon, X‘ J. Bart—3.81% lflll‘llvlll‘ (VtrretJfllv'. i r J 0.3. at .... 5‘5. .x. y. . I’L-ITIE' ll NU]. LEG HT EHQBUSEo l r .vHA. null, J'm/r (1'14?! 1 //II'/I. 0 n-1uL .L , ,1 22 [IL \§\\ \ x \ [fin/rural [51/ ”.7117ny ' Draw/1 [51/ Jll'lHWz-lm/awn. Adm/1w, I 71/1/13'1117/ lfI/ [fink/Indra” X‘ J. lu’urrIP/d, Wan/var dirrn’f, 1315. LIGHTHOUSE. L , 131,411.}; M///M/////////////////////////////%/ 523M 3 ”MM/”WMMfl/Mw iUMMMM/WW’Wflz/M' gkg/MM ‘ A». [13,. 2. M ////2 12. r/ / / / ‘ I fl/ Z47 /// / //// K/ . // , /// . I s .‘:::"Z/IM/////,{/; WWW/W ”WM/”MM N S 7:: / l{:l,l/////l///{///M/%/;///fll , ‘/ [WW/7M?” //// i ~~ ;//,/ MM / M/ 71/ ”0/ // // , ////" MW 5 ” // 'I/ / - / //////1 /' // Ml"?! ~ . //// V f” M/ ,1. . I I . a V’ 3‘! > 2.5 20 (.5 zu 0 ~ ‘ ma“ ' wifififliLV‘d—l - L-L— . 1’ ,lf'l“.L—L L—x—I ‘4'” M ’ . fl'e. ' llnmw 41/ JR LAWN/000” . lug/[mat by 7”” [ordain/hi:IIZv/ml 41/ fil’idzo/son Xr J. [flunk/d, WunfuurJ?)'r.’e‘(.1818. L1G 249 M “ Figure 2. r s t o w. The three-legged stool, steadied with cross braces. Upon the middle of the upper round plank r s was screwed down the theodolite T, to whose index was screwed thelong horizontal rule T S, divided into feet, inches, and parts, upon one edge, tending to the centre. Upon any marked point of the rock to be ascer- tained, suppose 1', the rod mg was set upright by a spirit level, and was preserved in an upright position by two small slips of deal, applied as shores or struts, in two different directions. The divided edge of the rule being brought against the upright rod, was shoved up by a short stafl", held in the hand tight against the rod, till a spirit level laid upon the top of the rule shewed it to be level. In this position the index would shew the degree and minute of the circle; the upright rod would mark the distance from the centre upon the rule; and the rule would mark upon the rod, how much the intersection was above its bottom at 1‘. “ PLATE II. No. l.—-South elevation of the stone lighthouse completed upon the Eddystone in 1759. “ A. The landing-place. “ B. The cave in the east side of the rock. “ C. The steps cut to mount the rock to the entry- door. “ D. An iron rod, serving as a rail to hold by, in passing to the foot of the ladder, occasionally put out from the entry-door at E. “ No.2.——Section of the Eddystone lighthouse upon the east and west line, as relative to No. 1, suppos- ing it the low water of a spring tide. “ In the section of the rock, A B shews the up- right face or drop, marked with the same letters as No. l, and the line B C shews the general direction of the grain, and slope of the rock to the south-westward. “ The dotted line a b shews the level of the base of the first stone. The black line c dis the base of the stone in the first course that is inter- sected by the east and west line; and efl is the level of the top of the first course, and bed of the second; 9, 3, 4, 5, and 6, mark relatively the tops of the six courses that bring the artificial part of the foundation upon a level with the reduced top of the natural rook ; e 6f, being the first entire course, marked VII. as being the seventh above the ground joint. “f. The foot of the temporary ladder;‘and there is shewn the manner in which the ground joint of VOL. 11. LIG — —r ~——.——-—— the stone-work was sunk into the rock, all round, at least three inches. “ h. The first marble plug, or centraljoggle, that went through the sixth course, and reached half way through the seventh ; and so in succession to the top of Course XIV. “ i h. The place of the marble cubic joggles inlaid between each two courses, which were in an octagon disposition round the centre. “ Z. Smaller cubes between the fifth and sixth course. “ Course XIV. terminates the entire solid; as upon it is pitched the entry and well-hole for the stairs. The temporary ladder, f g, to the entry- door D, is only put out when wanted; and then is lashed by eye-bolts to the stone; at other times, having ajoint in the middle, it folds, and is laid along in the entry. . “ Above the top of the entire solid, the centre stone being omitted to give space for the well, the cubic joggles were of double the number, and half the size. Course XXIV. terminated that part of the building called the solid: and here the habitable of the building began, whereof E is the lower store-room. “ F. The store-room door. “ G. The upper store-room. “ H. The kitchen. “ I. The fire-place, from which the smoke ascends through the floors and lantern, through a copper funnel, and through the ball. “ K. The bed-room. “ L. The stone basement of the lantern. “ M. The lantern door into the balcony. “ N. The cupola. “ The ascent from room to room is by perfora- tions through the middle or key-stone of every floor; and the detached figures shew the means, by inclined step ladders, removable at pleasure. “ PLATE III.—Plans of the rock after being cut, and prepared to receive the stone building. Sheav- ing the six foundation courses. “ Figure 1. Plan of the rock, as prepared for the stone-work, somewhat extended, to shew how it applies to Plate I. The line A B shews also here the place where the surface drops, as specified, Plate II. No. 2. “ In this figure, Course I. appears in its place, as fixed with its trenails and wedges. The part darker shaded, and marked D D, was not reduced to a dovetail on account of fissures, but was sunk 2 K C) d L1G M ' two inches lower than the rest of Course II. The stones laid therein would therefore be encompass- ed by a border, and held fast in every direction. The letters E. W. N. S. in all the figures, denote the cardinal points; the same letters, in every figure, denoting the same parts. “ The part of the rock marked C, rises above the rest by an ascent, or step, of fifteen to eighteen inches, according to the line D FGE; which, lying somewhat without the general contour of the building, and affording a firm abutment, the advantage was taken; and the work of the first and second course carried against it, as shewn at G. “ 1,2, 3, 4, 5, and 6. The level platforms, or steps, for the difi'erent courses, whose uppersides are even with these numbers in Plate II. No.~ 2. being upon the level of Rudyerd’s lowest step. “ X. A piece of stone engrafted into the rock, serving as a bridge to cross a chasm, Opened by cutting down the top of the rock to that level, into the cave. Of this stone is fo1med a part of the border that encircles the work. “ Figure 2 shews how the buttress, G, was termi- nated in the second course. It also shews the places of ”the trenails and wedges; which in all these figures are shewn in the same manner. The dotted lines every where refer to the course that is to come on; and shews how it will break joint upon the course supposed laid. “ Figure 3 shews how the space H I K, in Figure 2, is filled up in Figure 3, being confined in by the rise of the step L at H I, and the cramps a b; the ground proving here irregularly shattered by cutting the steps for the former lighthouse. “ Figure 4 shews the structure of Course IV. where, in this, as all the others, the stones lighter- coloured denote the Portland, the darker the moorstone. “ Figure 5. The position of threejoggle-holes, Y, between this course and the next above. “ Figure 6 shews Course VI. complete, which brings the whole work to a level with the reduced rock: it shews the joggle-holes for the eight cubes; and the central plug-joggle, fixed in place at 0, ready for the reception of the centre stone of Course VII. “ PLATE IV.-—-Plcms of all the difkarent courses from the top (9“ the rock to the top If the balcony floor inclusive. “ Figure 1. The proper plan of Course VII. rela- tive to the section, Plate II. No. 2. As being LIG M the first entire course, the trenails and wedges are shewn; but afte1 wards omitted 1n the draughts, to prevent crowding the figures. The black lines and dotted lines shew the joints of the alternate courses. The centre-stones, and the four stones surrounding, were alternately of the same size to the top of Course XIV. “ a. The centre plug, first set. “ h b. The square part of the centre-stone; from each of whose four sides a dovetail projects, and thereon are fixed the four stones cc, by joint wedges and trenails, as per figure; which five stones united make one stone, sufficiently large to receive eight smaller dovetail stones dd; and whose projecting parts form dovetails to receive another circle, or order of stones, fixed like the former. The cubic joggles are shewn at ee. “ Figure 2. The plan of Course XIV. ending the fundamental solid, and on which the entry and well-hole are begun. It also shews the diminu- tion from Course VII. Upon this figure is shewn the distribution of the smaller cubic joggles, which take place upon the entire solid. The entry here appears to have a small inclination with the E. and W. line, which was not noticed in the sec- tion, Plate II. No.0 ., to avoid ambiguities. “ Figure 3. The plan of Course XV. being the first of the ent1y door and well cou1ses. “ Figure 4. The plan of Course XVIII. shewing the work of the entry closed in, and the solid re- united. Also the manner of hook-jointing the four stones round the centre to each other; which, in the courses below the entry door, were united by dovetails to the centre-stone. Joint wedges were applied in the hook, as per figure. Thus the arrangement, in circles from the centre, was again complete. In the entry courses, as every piece had at least one cubic joggle and two tre- nails, the work was secure against all ordinary attacks of the sea: the weakness being on the east side; but when capped and bonded together by this 18th Course, the whole was again con- sidered as one entire stone, out of which the ca- vity had been cut. “ Figure 5 shews Course XXIII. ready for put— ting on the cap course of the solid. “ Figure 6. The cap course, making the store- room floor, in its finished state; the first course of the habitable part of the building, viz. Course XXV. being upon it; and shewing the store-room door, with its joggles, joint-stones, and cramps. PIA T1} IV. [NY I (7/1137 1 I Lil MM’H‘H U {U STE. FM 4. J’VIH (bi/12w / Z 70%, 5.0. .t/ \fi,‘ , w. J 3.. . 1h \ W \ é , 52/. / é / 7/; 7/” /%%7///4 ///////,///v/ flfl/ // ////,.//,, r/// I % . 1/ S [0 l ) Z72 A / Z/fiwfl/M .. S /2 //V/,/////// / ,/ /,// / C? 77W 4, \ J / . 4. 7 //, é? // / , y 7 / , //, 16wa 4 I“l\ , //M//%/////4‘flau ‘ , E 11 (7 ‘ [112’ 1311!] (bury (271/1372 (bl/7:5? E / 2mm") J’l/[l a)». nr . .L . fl/ . v/ TI. .1 I . I. .21. If .V .f l S N I!" , VII finnzw’ (I‘M/13'1” \ (IV/12W E ,i,,1 A ,1 L I "/g/I-urmi I; 1/ A‘Jz’nr'r'r |lJ|l [um/7071,‘fil/Jlia‘llfld ll]! [flir/m/va/ ,\"./. ffm'n'fl/d, ”71/7/1’III' .X'fz-rfi; 1/17,». I). -"i/VIfl/a'flll , (ll/’1. LIG . 252 size, 'of the first fair section for a stone building, as exhibited to the proprietors. The principal difference afterwards arose from finding less area upon the rock; and the necessity of size and con- venience in the habitable rooms. “ PLATE VI.-——A view qfthe rock on the east side; and (f the work advanced to Course XV. the first of the entry courses; skewing the manner of landing and hoisting the stones, 8m. in every qfter—stage of the building. . “ Figure ]. The boat Weston in the gut, deliver- ing her cargo. “ P Q. The two fender piles, to prevent her rubbing against the rock. “ X. The cave, here seen in front. “ D. The gulley, through which a momentary cascade makes its way; and which was proposed to be stopped. “ E F G. The shears; from the head of which are suspended the main tackle-blocks A B, whose tackle fall, after going to the snatch-block E, passes to the Windlass, or jack-roll, whose frame being of iron, is fastened to the rock, as per figure. “ The enlarged detached figurea shews the frame and roll frontwise, as seen from the snatch-block. “ b. The side view thereof, the roll being seen endwise. “ c. The manner of coupling the back-stay to the upright stancheons; and d shews, by a figure still more enlarged, the upper end of the stancheous for receiving the gudgeons of the roll. “ ‘Vhile the stone is hoisting, the man represent- ed at I is heaving—in the tackle-fall of the runner and tackle H K: for, till the stones are cleared of the boat, the shears lay out considerably, and the out-hawler guy-rope, L M, is slack. This crosses the gut, and is fixed by a ring-bolt to one of the rocks of the south reef. By such time, there- fore, as the stone is hoisted by the main tackle to the height of the entry door, the shears are got into the perpendicular; and then, by easing the out-hawler guy-tackle, L N, the stone comes into the entry door. “ The runner and tackle H K is hooked to the guy-chain, O, which crosses the work, and passes down to the ring on the west side of the rock; marked R in Plate 1. “ In the detached Figure 2, the anchor-like piece of iron, by which the main tackle-blocks are hung, is shewn to an enlarged scale at e fg h. i This an- LIG chor being suspended upon a round bolt at e, that passes through the tops of the two shear. legs, swings freely between them, and always putting itself in a perpendicular position, and producing fair bearings upon them, without any unnatural strain or twist, enables them to support the great— est weight possible. “ In like manner the two arms of the anchor, g h, having the two guy—tackles hooked to them, the action of those tackles is upon the suspending bolt, and the feet of the shears turning freely upon eye-bolts fixed in the rock, they are at liberty to conform themselves to the position wanted; so that the stress upon the legs is always endwise. “ After the building was raised to the height shewn Figure 1, the work was hoisted through the well-hole, till it arrived at the top of the solid, by means of the triangle and twelve fold blocks wherewith the work was set; and are shewn as standing upon the wall at the first vaulted floor, by the letters Ht [772, being the fourth stage: but after that was completed (the man-hole being too small, and the height too great, without losing time) a jack-roll was established, as shewn at the third stage in the lower store—room at Q: and a pair of moveable shears, the figure whereof is shewn at the fifth stage, as upon the wall, at the kitchen floor; which, instead of guy-ropes, had a back leg, longer than the rest, whose bot- tom or foot cut with a notch, stepped upon the internal angle of the opposite wall; and was long enough to suffer them to lean over sufliciently for the stone at P to clear the wall. The shears them‘ selves were prevented from falling over by a luff tackle, shewn upon the back leg, whose lower block hooked upon a lewis, in that stone the back leg stepped upon; by which it was brought tight and steady. W hen the stone was to be landed, this tackle being a little slacked, till the notch could be disengaged, and then set upon, the back leg would, by going over the wall, suffer the shears to come to the perpendicular, or beyond it. “ The stones now become in general less weighty, a common tackle was employed at the shear-head, which would go down to the entry door, and there met the stones hoisted by the great shears : the tackle-fall of the moveable shears, being taken to the jack-roll Q, the stones were got to the top of the building, in the same time they were raised from the boat to the entry door. “ The detached figure R’ is the plan of the more» LIGHT HOUSE . PLATE VI. 4 View of (it: [foo/c on the [11.51 .riJr, andof 17w work (ME/mm! Iv mume XV, him] Mr lit at (2er Zn Irv raw 3221‘, mm dw mum onam/Im/ (mt! 1%th (ha Jtom £0,131 way .rtaqe offlw Buildizg. dz l ] llrfi Double Jodie / / mun/wax dediredw, lszLV'wlzobn/z l‘lflmfidd; Wardour Jib-3&5). firaymmi by 10W?- LIGHT HOUSE . . PLATE m. ‘I’Ia/I/ and {Zarwéotiwwf f/w Wbrk K1215 WWI/Bag, m”), i 1.; fiu'nifilrp and ”#115115- . "Sb i 3 '12 g } fart oft/261704 E; I" A“ k ‘ ‘,\e"‘f”fimvfi$ ,.:"“‘_“ -' IL +4... M11 Bay v 12:9 . 1. ‘1'”;“5 l]. V “t 3‘ Q s 1’ _,___<_-.. “CL--- __‘___________+:; 1753‘. E. 12),. H. ‘ {I I 3“ ‘\ 121a. . G __________ WWI THEM“ -_; f‘ 7-,] ‘5‘,- [fix—y mi 4 LBJ; 1W ‘. ugwj Lu 1" L MUELLER, J 4 Jade fbr Mitt-Milka? lit/urar. 2 ,f o‘ 7 . ll 1:116 - E .D/wwz /I// lLViv/zdynn _ I’uMdr/wdart/Izdctfiremréllf‘thwlmon rialfiarn'eld, ”3111mm .W‘fic‘n’m, Englw'ai'lry ”Tlnmy/ L1G 2.53 L1G m Table shears; where the check, or safety rope, n, is shewn at the foot of the back leg. “ In this manner all the heavy materials were got up; the moveable shears rising with the work, till the cupola was to be set upon the lantern. “The sixth stage shews the apparatus used for this purpose. The great shears being now done with, were taken down and put through the win- dows of the uppermost room, and there, being well steadied, served as booms. The detached figure S being the plan of this stage, shews their particular disposition; wherein o p shew the places or feet of the legs of the shears used for this particular purpose; also marked with the same letters in the relative upright. In this the rope q r shews a side-stay to the leg 0 r; and s t is the stay of the leg 1) t, each fastened to q s, the extremes of the booms. “ From each end of the cross-tree at the head of the shear poles proceed the ropes w x, y x, which joining in one guy-rope at x, proceeds over a pulley in the end of the temporary timber at z: from thence, with the intermediation of a tackle 1, 2, it proceeds to, and fixes at the extreme end of the boom 3 ; and as the weight to be hoisted will principally lay upon this guy, the stay or shroud rope 3, 4, is passed from thence through the window of the room below, and is there fixed. “ It is now plain, that by the tackle 1, 2, the shears can be let go over as far as necessary, and brought back into the perpendicular; but to counteract this main guy, and keep all steady, the rope 5, 6, 7, with a small tackle upon it, per- forms the office of an out-hawler guy, fixing to the same ring in the rocks, as that of the main shears had before done. This apparatus enabled the cupola to be hoisted and set on whole without a bruise. “ PLATE VII.—-Plan and description of the work- yard at JlIiIZ-Bay, with its furniture and utensils. “ Figure 1. The general plan of Mill-Bay, wherein the dotted line a b c shews the line of low-water spring tides. “ de. The channel dug from low water to convey vessels to the head of the jettyfg. “ ll 2' k Z. The area of the work-yard. “ Since the removal of this work, has been built L the long-room. “ B. The baths. “ A C. The marine barracks. I) D. New streets of Stonehouse. “ Figure 2. Plan of the work-yard and jetty. ABC D. The line terminating the head of the channel. Now any vessel lying against the two large piles BC, on which a pair of shears being erected, can be unloaded of her cargo of stone, and delivered upon a wheel carriage; that pass- ing along thejetty to the turn—rail E, thecarriage is there turned round till it becomes fair with the rail-road BF; and passing along it, enters the work-yard, whose boundary is marked by G G G G. “ At T is another turn-rail, which enables the car- riage to go on with its burthen; either in the straight line, or to turn there and go along the rail-road in the middle of the yard, and arriving at any destined point, suppose H, it is there met by a roll-carriage; for which, planks being tem- porarily laid, as at I, the burthen (being trans- ferred on small rollers) will be easily moved thereon, to the extremity of the yard sideways; and thus stones can be deposited, as at KK (shewn edgewise upward) upon any point of the area of the yard, and returned by the same means. “The area bounded by the line G G, and the dotted line LL, is the Portland workshed. “ M denotes one of the bankers; to which, from the wheel carriage (supposed on the rail-road op- posite) strong joists being laid, as shewn by the dotted lines, the pieces of stone are brought on small rolls; the bankers having notches sunk therein, to receive the ends of thejoists. “ In like manner, the area N O was the shed for the moorstone workers. “ The square area, P Q, denotes the extent of a roof supported by four posts covering the plat- form; whereof a 6 represents the platings of rough stone walls; c (1 one of its principal floor timbers, 6 by 12; these being covered with three-inch planks, and brought to a true level, made a stout 'floor, upon which the courses were brought to- gether. “ R. The cabin for the foreman of the yard. “ S. A small store-room for tools and iron-work. “ G W. The store-shed for VVatchet lime and puz- zolana. “ V X. The shed for bucking or beating thelarger- parts ofthe puzzolana upon W Y, the bank with three cast-iron beds upon it. “ Figure 3. Supposedadetached figure, being the- ground-plan of the turn-rail at T, (Figure 2.) to an enlarged scale, wherein A B is a dormant circle LIG ”254 LIG of wood, well supported; of which C marks the ' centre-pin fixed in the transverse beam D D: EE being connecting studs. “ FF. Portions of the rails, whereon the wheels move, which are kept in place by the filletsff, nailed on each side. “ G G. The sleepers for supporting the rails at about a yard’s distance middle and middle; as Is also shewn near E, in Figure 2. “ Figure 4-. The plan of the moveable turn~rail, and Figure 5 the relative upright; shewing- also the section of the dormant circle. The three last figures having a mutual reference, the same parts are marked with the same letters: and further- more, in Figure 4 and 5. “ H, I. The rail part of the turn-rail, correspondent to those parts marked FF, Figure 3, in width and height. The rail parts, H,I, are strongly framed upon the cross beam K K, and connected by the pieces L, L. The whole being poized, with its burthen, upon the pin C, but without abso- lutely touching the dormant circle A B while turn- ing; for hearing only upon the flat shoulder of the pin, it turns easily; but, when it is bringing on, or wheeling off, the equilibrium upon the pin being destroyed, the ends, H, I, are then support- ed upon the dormant circle, and the wheels will move steady. “ Figure 7 shews the plan, and Figure 8 the up- right view of the wheel carriage, to the same scale as that of Figures 3, 4-, and 5. Also Figure 9, and Figure 10, give the upright views of the roll car- riage in two directions, to the same scale; which shew distinctly the manner of supporting the axis of the rolls on iron frames; and how the iron frames are kept upright by four pair of cross bars. “ Figure 1]. The upright of the capstan-roll, axis, and middle part of the bar to the same scale. At 1, Q, is shewn the capstan in full, to the scale of the yard; and 3, 4, and 5, mark the direction of the rope; which, from a snatch-block at 5, ascends to the upper block of the main tackle, suspended from the top of the shears, as per Figure 6, wherein the in-hauler guy-tackle is marked 7, being a runner and tackle; and the out-hawler, marked 8, are simple blocks. The guy-rope, 7, 6, was attached to a ring-bolt, pass- ing through a large rough stone, rammed into the ground; its place being shewn at 6, (Figure 2,) the out-hauler guy, 8, 9, being secured in the same manner. “ The marble rocks marked 10, go round the point of the bay. “ Figure 12. The elevation of the upper part of thejetty-head in front, with the shears upon it, to an enlarged scale; more particularly to shew the smaller parts. “ A, B. The front pair of piles, to which the cross beam C D is bolted; and in like manner to each pair of piles. “ E, E. The ends of the longitudinal half balks. V“ FF. The cross joists. “ G, G. The ends of the flat rails that the wheels of the carriage run upon. “ H H. A single cross timber, serving as a stop to the carriage at the end. “ I. The snatch-block. “ N.B. The scantlings are marked, because this jetty or scaffold, erected as slight as possible for a temporary purpose, sustained the whole ton- nage of the Eddystone matter, in and out, with- out derangement. “ The detached Figure 13, gives a part of the top of one of the shear legs, shewing how they were plated on each side, to support the bolt of the anchor from bending, and thereby from splitting the poles. “ Figure 14. The enlarged figure of the runner and tackle (marked 7, in Figure 6.) “ K. The runner-block of one large single pulley. “ L M. The tackle-blocks, of three pulleys each, making a purchase of twelve, equivalent to the great blocks. “ Figure 15.‘ An upright diagonal view of the main tackle blocks; having six pulleys each upon two pins; the larger tier being ten, and the lesser eight inches diameter. This figure dis- tinctly shews the method of salvagee strapping; being double, that the pins being readily knocked out, they could be frequently greased without trouble. “ N.B. The shears, blocks, and tackles, used at Mill-Bay, were nearly the same as at the rock; and one pair of main tackle blocks at each place, with the same pulleys, went through the whole service,- but the pins were renewed each season, and sometimes oftener, being of wood, on account of the salt-water; but were frequently greased. The main tackle-fall at each place was no larger a rope than of three inches circumference; being a white rope, remarkably soft laid, hawser-fashion; and which is of material consequence. 3.7. ‘LEGEETH 0 17 S 311, FLA 775' T7”. ( , l % | l , l’ I" 5 _ W“ l' 1 r A <\ \ S ., r. L \ \ I | l o t l J ! | I \ [(zwu' I 7nu'rh Dimenan: WMF. ....._ 1112‘“ 0" MW E.— I] ‘37 “WP“ .0 .52 F GW .._ H'.’ .50 : x-‘w f” .921, "21"” i I-‘WE _ low ZN X F F. .1. 2‘} 38 [JImm lfil/ I? A'IMn/mm. ' lz'mlnmw/ [I‘ll KEN/)9. [mm/0'11 'lh/I/IIr/u’d 41/ IfJ'I'c-lutla-(m X21 b’all'lir/(l, fl balm/1‘ .177er 11313. LIG 255 W - and B B the cross timbers for supporting the four “ PLATE VIII.——Descriptz'ons of supplemental mat- ters, having reference to the Eddystone building. “ Figure 1. An upright front view of the great tackle, or purchase-blocks of twenty sheaves, or pulleys. “ Figure 2. A side view of the same blocks, refer- ring to Figure 1. The advantage of this con- struction is, that the tackle-fall, or running-rope, may be reeved through the twenty sheaves, with- out a cross or interference; so that the standing part, or beginning, may be in the middle of the upper block: and the ending, hauling pa1t, or fall, upon the middle pulley of the same block The weight therefore being suspended by twenty ropes instead of six, as in common triple-blocks, the tackle-fall, as relative to a given weight, may be lesser, or of fewer yarns in the same propor- tion; which renders the whole much more flexible and pliant, and which, together with the advan- tage derived from the mode of reeving, occasions their rising and falling nearly upon a parallel. Beginning in the middle, the greater sheaves are reeved as far as can be on them; from thence go- ing to the first of the smaller sheaves, and reev- ing the whole of them throughout, you then go to the first of the greater sheaves, before left u11~ reeved, ending upon the middle sheave of the upper block; and thus arises a diminution of the friction from the more equal distribution thereof. “ Figure 3. An upright section of the store-room, to an enlarged scale; in it is shewn the centre whereon the upper store-room floor was turned; and in like manner the rest. “ Figure 4. The plan relative thereto, the letters being common to both. “ ab,cd. Two of the sixteen ribs, formed to the ci1cle of the vaults of the floors. These ribs are connected at their ends by two wooden rings, ef, g It i k; the former supported by four posts, three of which are shewn 1n their places, and the latte1 byeight; of which only one is shewn on the light hand, and one on the left, to avoid confusion. The rings are each made to take asunder, that after st1 ik- ing the centre they might be got out of the room. “ At 1 l, m m, two of the ribs are supposed taken out, to shew their bearings upon the rings; they were open centres, that it might be. seen under- neath when the joints were fair. “ Figure 7, of Plate IV. shews how the sixteen radii of stones would apply to the sixteen ribs. In this plan, Figure 4, A shews the well-hole, LlG middle posts, whose places are marked out by dotted little squares. “ Figure 5. An elevation, and Figure 6, the rela- tive plan of a dial stone, taken professedly from the general figure of the Eddystone lighthouse; being the design of the late James, Duke of Queensberry, and by him erected at Amesbury, Wilts, with adial upon it, by Mr. Ramsden. The drawing, of which this is a copy, was given'me by the Duke; and is placed here as an instance, that the Eddystone column may be applied to some uses of architecture. “ Figure 7. One of the silver medals given to the seamen as a token of the selvice. “ Figure 8. The tool wherewith the stones were got up from the bottom of the gut. “ A. One of the stones, with two trenail holes. “ Suppose this stone lying flat in the bottom of the gut, the side A uppermost. The tool has a pole or staff, I) b, about twelve feet long, suffi- cient to reach the bottom. This single prong, c, is forged to a very gentle taper, such as to be thrust eight or nine inches into a trenail hole, (all of them being bored to a gauge) it can be driven by the pole, till fast; observing that the arm e corresponds to the centre of gravity of the stone. The water is generally so clear as to see to the bottom; and, in case ofany ruffle by the wind, can be in a great measure freed from agitation, by looking through a speaking trumpet, whose mouth is put down eight or ten inches into the water. The rope d ef being then set upon by the main tackle, instead of its drawing out, the length of the arm g causes the prong to jamb the faster in the hole; and the staff being quitted by the hand, with a cord to hinder its flying off too far, the whole assumes the position of the figure; and, when brought above water, is lowered into a yawl. “ Figure 9. A section of one of themortar buckets, and in it the beater. “ Figure 10. One of the internal faces of the lan- tern’s glass frames, and therein the cross bars of iron, as they were actually fixed. Besides the flat at each end of each bar, distinguished by adarker shade, and through which the screws passed; each end was also cranked about an inch, so as to set the transverse part of the bars clear of the copper sash-frame; and they were cleared of each other at their intersection, by one of them being LIK 2 made straight, the other curved in that part. All the panes being taller than the candles, the chandelier rings are so hung, that when the can- dles are at rest, dispensing their light, that of one chandelier passes through the range of panes A, and that of the other‘ through the range B; and when the candles are snuffed, one of the rings of lights being seen through the range C, the other mounts to D, and vice versa. “ Figure 1]. The chain of triangles, from the Edd ystone to the flag-staff of the garrison of Pl y— mouth, for ascertaining their distance trigono- metrically. “ Figure 12. An enlargement of the work within the headlands of the Sound. “ The whole country about Plymouth Sound be- ing very uneven, I could not readily obtain a base better, than by very carefully measuring the two lines B G, B \V, taking the intercepted angle 'W B G; whence the right line W G was obtain- ed, making a base of 1871 feet, and which I can— not suppose to err more than half a foot. Again, the nearest place from whence the two beacons, W, G, could be commodiously seen for the pur- pose, was the point S; and all the three angles of the triangle W S G, being likewise carefully taken, I conclude the angle VVSG: 10° 23', taken true to a minute; that is, to figd part of the whole angle. The line S W could therefore be determined within 73d part; which being considered as a new base oflarger extent, may be esteemed true within fiath part of the whole. From this, and the angles taken as marked upon the scheme, the lines W P, \V M, and W E, were successively determined; and finally FE, the dis- tance of the flag-staff from the Eddystone, came out very near, but somewhat less, than fourteen miles. But the interior harbour of Plymouth, called Sutton Pool, being about three furlongs farther from the Eddystone than the flag-staff, the whole distance may be esteemed fourteen miles and a quarter from Plymouth harbour.” LIKE ARCS, in the projection of the sphere, the parts of lesser circles containing an equal num— ber of degrees with the corresponding arcs of greater circles. LIKE FIGURES, in geometry, such as have their angles equal, and the sides about the equal angles proportional. LIKE SOLIDS, such as are contained under like planes. 56 LIN W LIME-STONE, a calcareous stone, which being sufficiently burned or calcined, falls into powder on the application of water; and being then mix- ed with water and sand in ce1tain proportions, forms a Strong cement. LIME- STONE is either pure or mixed. The best for the use of building is that which contains a certain portion of clay and iron. See CEMENT. LlME-KILN, a kiln for the purpose of burning lime. Kilns for this purpose are constructed in a variety of ways, to save expense, or to answer to the particular nature of the fewel. See KI LN. LIME, Quick, a. term applied to lime in its most powerful or caustic state, before it has been ren- dered mild by the absorption of carbonic acid gas, or fixed air. LINCOLN CATHEDRAL, a cathedral 1n the city of Lincoln, of which it is not only the most pro- minent object, but is most interesting as a sub- ject of history, antiquity, and art. This magni‘ ficent structure, from its situation on the summit of a hill, and from the flat state of the country to the south-east and south-west, may be seen at the distance of twenty miles. Raised at a vast expense, by the munificence of several prelates, it discovers, in many parts, singular skill and beauty, particularly in its western front, which must attract the attention of every traveller. The sec being translated from Dorchester to Lincoln in 1088, St. Remigius de Fescamp, the first bishop, founded a cathedral church, which was so far ad- vanced in the course of four years, as to be ready for consecration. All the bishops of England were summoned to attend on that occasion. Re- migius died two days before the intended so- lemnity. His successor, Robert Bloet, finished the cathedral, dedicated it to the Virgin Mary, and greatly enriched it. In his time, the bishop- ric of Ely was taken out, and made independent of that of Lincoln. The cathedral having been destroyed by fire in 1124, was rebuilt by Alex- ander de Blois, then bishop, who arched the new fabric with stone, to prevent a recurrence of a similar accident; and greatly increased the size and augmented the ornaments of it, so as to ren- der it the most magnificent sacred edifice in his time. Bishop Hugh Burgundus enlarged it by the erection of what is now called the New Work. He also built the chapter-house. This prelatc died in 1200, and two kings (John of England and William of Scotland) assisted to carry his LIN 257’ LIN M body to the cathedral, Whe1e 1t was enshrined 1n silver, according to Stukeley , but Sanderson says ‘ the sh1ine was of beaten gold. Bishop Gynewell added the chapel of St. Mary Magdalen. Bishop Fleming built a chapel on the north side, in which he was buried: on his monument is his figure in free-stone, pontifically habited. Bishop Alnwick was a considerable benefactor to the ca- thedral, and built the stately porch at the great south door. Bishops Russell and Longland built two-chapels: to both these prelates are altar- tombs, though the latter was interred at Eton. The cathedral church consists of a nave, with its aisles , a transept at the west end, and two other . transepts, one near the cent1e, and the other to- wards the easteln end; also, a choir and chance], with their aisles, of corresponding height and width with the nave and aisles. The great tran- sept has a nave towards the east: attached to the western side of this transept is a gallilee, or grand ‘ porch; and on the southern side of the eastern aisle are two oratories, or private chapels; while the northern side has one of nearly similar shape and character. Branching from the northern side are the Cloisters, which communicate with the chapter-house. The church is ornamented with three towers; one at the centre, and two at the western end: these are lofty, and decorated with varied tracery, pillars, pilasters, windows, 4 Ste. The dimensions of the Whole structure, ac- cording to the accurate measurements of Mr. T. Espin, of Louth, are as follow : the height of the two western towers 180 feet. Previous to the year 1808, each of these was surmounted by a central spire 10! feet high. The great tower in the centre of the church, from the top of the cor- ner pinnacle to the ground, is 300 feet; its width 53 feet. Exterior length of the church, with its ' buttresses, 524 feet; interior length, 482 feet; width of western front, 174 feet; exterior length - of great transept, 250 feet; interior, 9.22; width, 66; the lesser or eastern transept 170 feet in length, 44 in width, including the side chapels; width of the cathedral, 80 feet; height of the vaulting of the nave, 80 feet. The chapter-house is a decagon, and measures, interior diameter, 60 ‘ feet 6 inches. The Cloisters measure 118 feet on the north and south sides, and gran the eastern and western sides. The grand western front, wherein the greatest variety of styles prevails, is certainly the workmanship of three, if not more, VOL. II. distinct and distant eras. This portion of the fabric consists of a large square-shaped facade; the whole of which is decorated with door-ways, windows, arcades, niches, Ste. It has a pediment in the'centre, and two octangular staircase turrets at the extreme angles, surmounted by plain spire- shaped pinnacles. The upper transept and the choir appear the next in point of date. These are in the sharp-pointed style; and their architec- ture is very irregular, having pillars with detached shafts of Purbeck marble, in different forms, but 'all very light: those 011 the sides of the choir have been strengthened. The vaulting is gene- rally simple; the ribs of a few groins only have a filleted moulding. A double row of arches or arcades, one placed before the other, is continued round the inside of the aisles, beneath the lower tier of windows. The windows, which are lofty and narrow, are placed two or three together; the greater buttresses in front are ornamented in a singular manner with detached shafts, terminat- ing in rich foliage. This part of the fabric was probably built by bishop St. Hugh. The great transept, the gallilee porch, and the vestry, are nearly of the same, but in a later style. The vestry is vaulted,'the groining having strong ribs; and beneath it is'a crypt with groins, converging into pointed arches. The nave and central tower were next rebuilt, probably begun by bishop Hugh de Welles, as the style of their architecture is that of the latter part of the reign of John, or the beginning of Henry III. Part of the great tower was erected by bishop Grosthead, who finished the additions which had been made to the old west front. The part extending from the smaller transept to the east end appears to have been built by bishops Gravesend, Sutton, and D’Alderby, about the conclusion of the thirteenth, or commencementof the fourteenth century. The latter prelate built the upper story of the mod tower, and added a lofty spire, which was con- structed of'tiniber, and covered with lead. This was blown down in a violent storm in the year 1547, and the damages then sustained were not wholly repaired till 1775. That nothing might be wanting to render this church as splendid in its furniture as itwas elegant in its workmanship, it received the most lavish donations; So sump- tuously was it supplied with lid) shrines, jewels, Ste. that, Dugdale informs us, HenryVIII. took away 2621 ounces of gold, and 4285 ounces of 9.! I. LIN" silver, besides precious stones of great value. This cathedral had formerly a great number of costly sepulchres and monumental records; of many, not a vestige remains; nOr are the places knOwn where they stood. At the Reformation, what the ravages of time had left, the zealots pulled'down or defaced; so that, at the close of the year 1548 there was scarcely a perfect tomb re- maining. On the north side of, and connected with the cathedral, are the Cloisters, of which only three sides remain in the original state. Attached to the eastern side is the chapter-house, a lofty ele- gant structure. It forms a decagon, the groined roof of which is supported by an umbilical pillar, consisting of a circular shaft, with ten small fluted ' columns attached to it; having a‘band in the centre, with foliated capitals. One of the ten sides forms the entrance: in the other sides are nine windows, having pointed arches with two * lights each. Over the north side of the Cloisters is the library, which contains a large collection of books, and some curious specimens of Roman antiquities. It was built by Dean Honeywood. LINE (from the Latin lined) a quantity extended in length only. A line may be conceived to be formed by the motion of a point. Lines have no real existence except at the termination or termi- nations of the surface of a body: thus, a line'is the junction of two surfaces, and therefore can have no thickness. Lines are of two kinds, viz. straight or curved. Straight lines are all Of the same species; the species Of curves, which are infinite, are divided into geometrical and mechanical. LINE, also denotes a French measure, containing the 12th part of an inch, or the 144th part of a foot. LINE, Equinoctial, the common intersection of the equinoctial and the dial planes. LINE, Geometrical, in perspective, any straight line in the geometrical or primary line. LINE, Horary, or HOUR LINES, in dialing, the in- tersection of the hour planes with the dial plane. LIN E, Horizontal, a line parallel to the horizon. In perspective, it is the vanishing line of horizontal planes. LINE, Vertical, the intersection of a vertical plane with the picture, passing along the station line. LINE, Visual, a ray of light reflected from the Object to the eye. l. 920‘ LIN LINE OF DIRECTION, in mechanics, the line in which motion is communicated. LINE OF LIGHT, in light and shade, a line on the curved surface Of a body, such that any point taken in it will be lighter than an adjacent point taken out of it indefinitely near. LINE OF MEASURES, a term used by Oughtred to denote, the line on the primitive circle, in which the diameter of any circle to be projected falls. In the stereographic projection of the sphere, the line Of measures is that in which the plane of a great circle perpendicular to the plane of projec- tions, and the oblique circle which is tO be pro— jected, intersect the plane of projection; or, it is the common section of a plane passing through the eye and the centre of the primitive at right angles to any oblique circle to be projected, in which the centre and pole of such circle are to be found. LINE OF SHADE, in light and shade, a line on the curved surface of a body, formed by a tangent surface Of rays from the luminary to that of the body. LINE OF STATION, the intersection ofa plane pass- ing through the eye perpendicular to the picture and to the geometrical or primary plane, with the primary plane itself. LINES, Division, or Gradation of, the various pro- portions into which lines may be divided; as arithmetical proportion, geometrical proportion, the squares of the distances from the beginning, and harmonical proportion. LINES OF THE PROPORTIONAL COMPASSES, are those oflines, Of circles, of polygons, of planes, and Of solids. LINES ON THE PLAIN SCALE, are the following, viz. of chords, of sines, of tangents, of secants, of semitangents, and of equal parts. LIN es OF THE SECTOR, are the following, viz. of equal parts, of lines, of chords, of sines, of tangents, of secants, of polygons, Of numbers, of hours, of latitudes, of meridians, Of planes, and of solids. LINEAR PERSPECTIVE, the title given by Brook Taylor to his two celebrated essays on perspective. LIN ING, the covering of the interior surface of a hollow body. When the exterior surface is co- vered with any thin-substance, the body is said to be cased. LINING, in canal making, the thickness or coat of LIS 259 puddle sometimes applied -to the bottoms and sides of canals, to_,prevent them from leaking. LINING OF A WALL, a timbe1 boarding, the edges of which are eithe1 rt bated O1 grooved and tongued. Shops a1e generally lined, as are like- wise water-closets, to the height of five or six feet. LINING- -0UT STUFF, the drawing Of lines on a piece of timber, boald, or plank, so as to cut it into boards, planks, scantlings, or laths. LININGS 0F BOXINGS, for window-shutters, the wooden boards or wainscotted framin gs which form the backs of the recesses into which the shutters are depressed. In good work, the linings are not ‘ onlygrooved and tongued into the inside lining of the sash-frame, but also into the framed ground around the margin of the window, and inner sur- face Of the wall. LININGS OF A" DOOR, the internal facings of joinery surrounding the aperture of a door, placed in the thickness, and at right angles to the face of the wall, through which the aperture is made. The linings which cover the sides of the door are called jambs, or jambg-Zz'm'ngs, and that which covers the head is called the sofiit. LININGs OF A SASH-FRAME, the vertical pieces of wood, parallel to the surface of the wall. In good work, the linings are always grooved to receive the tongues in the pulley—piece. LINTEL (from the French linteau) a beam of tim- ber over an aperture, for sustaining the superin- cumbent part above, and the- soffit, whether of wood or plaster, underneath. The number of timbers required to lintel an aper- ture depends 011 the thickness of the wall: their depth, or altitudinal dimension, consists, in gene- ral, of as many inches as there are feet in the horizontal dimension of the aperture under them} If the wall be solid, without apertures above, the depth should be still greater. Lintels should be laid close to each other. LINTELs, are also a species of wall timbers, and which, with bond-timbers and wall-plates, are all called by the general name of FIR-IN-BOND. LINTELS, in some old books on carpentry, are also called wall-plates,- but the word is not now used in this sense, unless the joisting or tie-beams rest upon it; and then it is both a lintel and a wall-plate. LIST (fiom the Saxon lystan) or LISTELO (Ita- lian). See FILLET. 'LON . _._.... . ,. . LISTING, in carpentry and joinery, the act of cutting away the sap-wood from one or both edges ofaboard. LOBBY (from the German laube) a small hall or waitingaoom, or the entrance into a principal apartment, where there is a considerable space between it and a portico or vestibhle, but the length or dimensions will not allow it to be ‘ considered as a vestibule or anti-room. LOCK (from the Saxon loc) a well-known instru— ment for securing doors, and preventing their being opened, except by means of the key adapted to it. Methods of constructing locks are almost infinite; Bramah and Rowntree’s locks have been considered as the most secure; but the former are not proof against picklock keys. There is also one invented by Mr. Stansbury, which has considerable merit. LOCK, or VVEIR, in inland navigation, all those works of wood or stone, 01 of both combined, for the pu1pose of confining and raising the water of a river. The term lock, or pound-lock, more particularly ' denotes a contrivance, consisting of two gates, or two pair of gates, called the lock-gates, .and a chamber between them, in which the surface ‘ . of the water may be made to coincide with that of. the upper or lower canal, according as the upper or lower gatesare opened, by which means boats are raised or lowered from one level to another. ~ Loo); PADDLES, the small sluices used in filling and emptying locks. . LOCK SILLS, the angular pieces of timbe1 at the bottom Of the lock, against which the gates shut. LOCK VVEIRS, or PADDLE WEIRS, the over-falls behind the upper gates, by which the waste water of the upper pond is let down through the paddle holes into the chamber of the lock. LOCUS (Latin) in geometry, the line described by the intersection of two lines in motion. LOG HOUSES, the huts constructed by the Americans of the trunks of trees. LOGISTIC SPIRAL, or PROPORTIONAL SPIRAL, one whose radii are in continued proportion where the radii are at equal angles , 01 it may be defined, a spi1al whose 1adii every whe1e make equal angles with the tangents. LONGIMETRY (from the Latin Zongus, length, _ and Greek aswfe’w, to measure) the aitof measuring lengths, accessible and inaccessible. 0 L 0 4d 4d LUC 260 LYI .LOOP HOLES, the small narrow windows in cas- tellated buildings. LORME,PH1LIBERT DE, an eminent French architect, born at Lyons, in the early part of the sixteenth century. He went to Italy, when he was but fourteen years of age, to study the art for which he seemed to have a natural taste, and .there his assiduity attracted the notice» of Cardinal Cervino, afterwards Pope Marcellus II. who took him into his palace, and assisted ' him in his pursuits. He returned to France in 1536, and was the means of banishing the Gothic taste in buildings, and substituting in its place the Grecian. ‘He was employed by Henry II. for whom he planned the horseshoe at Fontainbleau, and the chfiteaus of Anet and Meudon. After the demise of that king, he was made inspector of the royal buildings by Catharine de Medicis; and under her direction be repaired and augment- _ ed several of the royal residences, and began the building of the Thuilleriesa In 1555, he was created counsellor and almoner in ordinary to the king; and, as a recompence for his services, he was presented with two abbacies. These honours, it‘is said, made him arrogant, which occasioned the poet Ronsard to satirize him in a piece, in- titled La Truelle Crossée, or ‘r‘ The Croziered Trowelf’ De Lorme took his revenge, and shut the garden of the Thuilleries against him; but- the queen took part with the poet, and severely repri- manded the reverend architect. De Lorme died in 1577. He published Dix Livres d’Arckitec- ture, and Nouvelles. Inventions pour bielz Bdtir et (3 petits, Frais. LOZENGE (from the French) aquadrilateral figure of four equal sides with oblique angles. LUCULLEUM MARMOR, a hard stony kind of‘ marble, of a good fine black, and capable of an elegant polish, but little regarded from its want of variegations. When fresh broken, it is seen to be full of small but very bright shining particles, appearing like so many small spangles of talc. It had its name from the Roman consul Lucullus, who first brought it into use in that city. It is common in Italy, Germany, and France. We have much of it imported, and our artificers call it the Namur marble; the Spaniards call it marble of Buga. LUFFER BOARDING, a series of boards placed in an aperture so as to admit air into the interior, but to exclude rain. It is frequently used in lan- terns. A very celebrated one is that upon .the church of St. Martin Outwich, in Bishopsgate— street, opposite the City of London Tavem. The plan is circular, and the apertures four in number, with pilasters between them. LU N E or LUNULA (from the Latin lama, the moon) the space between two unequal arcs of a circle. LUNETTE (French) apertures in a cylindric, cylindroidic, or spherical ceiling, the head of the aperture. being also cylindric or cylindroi- dic, as the upper lightsin the nave of St. Paul’s cathedral. LUTHERN. (from the Latin Zucerna, light or Ian- tern) a kind of Window over the cornice in the roof of a building, standing perpendicularly over the naked of the wall, and serving to, illuminate the upper story. The French architects distinguish them into va-v rious forms, as square, semicircular, bull’s eyes, flat arches, and Flemish. LYING PANELS, those in which the fibres of the wood are placed horizontally. 251 W M. MAG MADERNO, CHARLES, an eminent Italian architect, born at Bissona, in Lombardy, in 1556. He went at a very early age to Rome, where his uncle, Dominico Fontana, was at that time in full employ as an architect. His genius for sculp- ture became manifest, and he was placed with an artist in that branch of the fine arts. His pro- gress in modelling was such as led his uncle to confide to him the management of some build- ings then in hand, which he executed with so much skill, that he was advised to devote himself entirely to architecture. 0n the death of Sixtus V. Maderno was appointed to design and execute the magnificent tomb for his interment. The public works which were carried on under Cle- ment VIII. were chiefly committed to the care of this artist, and so high was his reputation in the succeeding pontificate, that, on the succession of Paul V. in 1605, he was appointed to finish the building of St. Peter’s; his plans being preferred to those of eight competitors, and the work was placed under his direction. He was afterwards employed upon the pontifical palace on the Qui- rinal mount. Another work, for which he is cele- brated, was the raising a fine fluted column found in the ruins of the Temple of Peace, and placing it on a marble pedestal in the square of St. Maria Maggiore. His genius was by no means confined to architecture, he was sent by the pope on a commission to examine the ports of the ecclesi- astical states, and afterwards surveyed the lake of Perugia, and surrounding country, in order to divert the inundations of the river Chiana. He was consulted upon most of the great edifices. undertaken in his time in France and Spain, as well as in the principal towns of Italy. His last work of consequence was the Barberini palace of Urban VIII. which he did not live to complete. He died of the stone in l629,whenhe had attained to the age of seventy-three. He had seen ten popes, by most of whom he had been regarded with favour. MAGAZINE, Powder, a building constructed for keeping large quantities of powder. These ma» gazines were formerly towers erected. in the town MAG walls; but many inconveniences attending this situation of them, they are now placed in differ- ent parts of the town. They were at first con- structed with Gothic arches; but M. Vauban, finding these too weak, constructed them in a semicircular form, of the following dimensions: sixty feet long within, and twenty-five broad; the foundation eight or nine feet thick; and eight feet high from the foundation to the spring of the arch; the floor about two feet from the ground, to prevent damp; and consequently six feet for the height of the story. The thinnest part, or hanch of the arch, is three feet thick, and the arch made of four lesser ones one over the other, and the outside of the whole terminated in a slope to form the roof; from the highest part of the arch to the ridge is eight feet, which makes the angle somewhat greater than ninety degrees; the two wings, or gable ends, are four feet thick, raised somewhat higher than the roof, as is customary in other buildings; as to their foundations they are five feet thick, and as deep as the nature of the ground required. The piers, or long sides, are supported by four counterforts, each six feet broad, and four feet long, and their interval twelve feet; between» the intervals of the counterforts are air-holes, in order to keep the magazine dry and free from damp- ness; the dices of these air-holes are commonly a foot and a half every way, and the vacant round them three inches, the insides and out- sides being in the same direction. The dices serve to prevent an enemy from throwing fire in to burn the magazine; and, for a farther precau- tion, it is necessary to stop these holes with seve- ral iron plates, that have small holes in them like a skimmer, otherwise fire might be- tied to the tail of some small animal, and so drive it in that way; this would be no hard matter to do, since, where this precaution had been neglected, egg-- shells have been found within, that have been carried there by weasles. To keep the floor from dampness, beams are laid lengthwise, and to prevent these beams from being seen rotten, large stones are laid under them; MAG 262 MAN ‘- these beams are eight or nine inches square, or rather ten high and eight broad, which is better, and eighteen inches distant from each other; their interval is filled with dry sea-coal, or chips of dry stones; over these beams are others laid cross- wise, four inches broad and five high, which are covered with two-inch planks. M. Belidor would have brick walls made under the floor, instead of beams, and a double floor laid on the cross-beams; which does not appear to be so well as the manner proposed here; the reader is, however, at liberty to choose the me- thod he likes best. To give light to the magazine, a window is made in'each wing, which is shut up by two shutters of two or three inches thick, one within and the other without it; that which is on the outside is covered with an iron plate, and is fastened with bolts, as well as that on the inside. These win- dows are made very high, for fear of accidents, and are opened by means ofa ladder, to give air to the magazine in fine dry weather. There is likewise a double door, made of strong planks, the one opens on the outside, and the other within; the outside one is also covered with an iron plate, and both are locked by a strong double lock; the store-keeper has the key of the outside, and the governor that of the inside: the door ought to face the south nearly, if possible, in order to render the magazine as light as can be, and that the wind blowing in may be dry and warm. Sometimes a wall of ten feet high is built round the magazine about twelve feet distant from it, to prevent any thing from approaching it with- out being seen. Mr. Muller has proposed some alterations, by way of improvement, in M. Vau- ban’s construction. If large magazines are required, the piers or side walls which support the arch should be ten feet thick, seventy-two feet long, and twenty-five feet high; the middle wall, which supports the two small arches of the ground floor, eight feet high, and eighteen inches thick, and likewise the arches: the thickness of the great arch should be three feet six inches, and the counterforts, as well as the air-holes, the same as before. Magazines of this kind should not be erected in fortified towns, but in some inland part of the country near the capital, where no enemy is expected. It has been observed, that after the centres of semi- circular arches are struck, they settleat the crown r and rise up at the hanches; now as this shrink- ing of the arches must be attended with ill conse- quences, by breaking the texture of the cement after it has been partly dried, and also by opening thejoints of the voussoirs at one end, Dr. Hut- ton has proposed to remedy this inconvenience, with regard to bridges, by the arch of equilibra- tion; and as the ill effect is much greater in powder magazines, he has also proposed to find an arch of equilibration for them also; and to construct it when the span is twenty feet, the pitch or height ten, which are the same dimen- sions as those of the semicircle, the inclined ex- terior walls, at top, forming an angle of 113°, and the height of their angular point above the top of the arch equal to seven feet; this curious question was answered, in 1775, by the Rev. Mr. Wild- bore, and the solution of it may be found in Hut— ton’s Miscellanea ZlIathematica. MAIN COUPLES, see COUPLES. MALLET (from the Latin malleus) a large kind of hammer, made of wood, much used by artificers who work with a chisel, as stone-cutters, masons, carpenters, joiners, Sic. MANSARDE ROOF, see CURB Roor. The word is derived from Mansart, the inventor. lVIANSART, FRANCIS, an eminent French archi- tect, born at Paris in 1598, was son of the king’s carpenter, and received those instructions which led him to eminence, as an architect, from the celebrated Gautier; but for the high rank to which be attained in his profession, he was in- debted to the force of his own genius. His taste andjudgment, united with a fertile imagination and sublime ideas, enabled him to equal, the greatest masters in his plans; he was, however, too apt to alter his designs, and even, in aiming at perfection, to demolish what was already. not only well done, but scarcely to be surpassed. This character was the means of preventing him the honour of finishing the fine abbey of Val-de— Grace, founded by Anne of Austria, which he had commenced in 1645, and which, when raised to the first story, the queen put into other hands, to prevent its destruction by him who had reared it. He was employed by the president Longueil to build his great Chateau des Maisons, near St. Germain’s; and, when a considerable part of it was erected, he pulled it down again, without acquainting the master with his intentions. After this, it is to his credit, that he finished it in a MAR. 263 MAR W t very noble style, and it is reckoned one of the finest architectural monuments of that age. A better idea cannot be given of his character than this: Colbert applied to him for a design of the principal front of the Louvre, and Mansart pro- duced many sketches of great beauty, but when told he must fix upon one to be invariably fol- lowed, if approved, he declined the business. His last work was the portal of the Minims in the Place Royale; he died in 1666, at the age of sixty-nine. He is known as the inventor of a ’ particular kind of roof, called the mansarde. He had a nephew, Jules-Hardnuin, who was also eminent in his profession as an architect, and was educated by his uncle. He became a favourite 'of Louis XIV. and was enabled, under his patron- age, to realize a large fortune. Some of his principal works were the Chateau de Clagny, the palace of Versailles, the house of St. Cyr, the gallery of the Palais Royal, the palaces of Louis- le-Grand and des Victoires, and the dome and finishing of the Invalides. He died suddenly at Marly, in the year 1708. MANSION (from the Latin mansio, an inn) adwell- ing—house, or habitation, especially in the country. Among the ancient Romans, mansio was a place appointed for the lodging of the princes, or sol- diers, in their journey; and in this sense we read primttm mansionem, file. It is with us most com- monly used for the lord’s chief dwelling-house within his fee, otherwise called the capital mes- suage,or manor—place : and mansion-house is taken in law for any house or dwelling of another, in case of committing burglary, 8w. MANTLE—TREE (from the Welsh) the lower part of the breast of a chimney; formerly consisting ofa piece of timber, laid across the jambs, for supporting the breastwork; but, by a late act of parliament, chimney-breasts are not to be sup- ported by a wooden mantle-tree, or turning piece, but by an iron bar, or brick or stone arch. MARBLE, avariety of lime-stone, of so compact a texture as to admit of a beautiful polish. The different kinds of marble are infinite, therefore any attempt to class them would necessarily oc- cupy much more space than we can allow to this article :' they all agree in being opaque, excepting the white, which becomes transparent when out into thin pieces. In the Borghese palace,‘at Rome, are some specimens of marble exquisitely white, so flexible, that if poised horizontally on M any resisting 'body placed on a plane, a saliant curve will be formed by the two ends touching the plane. A similar property is acquired in a ‘ small degree by statuary marbles exposed to the action of the sun, which no doubt weakens the adhesion of the particles. It is this which fre- quently occasions the exfoliation‘of projecting parts, and the artist would do well to ascertain, by experiments, the kind of marble that has the least tendency to this desiccation. The greater part of the quarries, which supplied the ancients with marble, are entirely unknown; in the Napoleon Museum are preserved the most exquisite specimens of many of them, the grand repositories of which are consigned to oblivion, unless chance should guide some penetrating eye to their dark recesses. Marble is found in almost every mountainous part of the world, the most valuable is brought from Italy: there are, however, many fine varieties in Great Britain, those of Derbyshire, Devon- shire, Anglesea, and Kilkenny, are too well known to need any particulardescription. MARBLE, Polishing of. The art ofcutting and polishing marble was, of course, known to the ancients, Whose mode of proceeding appears to have been nearly the same with that employed at present; except, perhaps, that they were unac- quainted with those superior mechanical means which now greatly facilitate the labour, and diminish the expense of the articles thus pro- duced. The following description, together with some preliminary observatibns, communicated by a person practically acquainted with this subject, relate to the manufactory of Messrs. Brown and Mawe, at Derby. , An essential part of the art of polishing marble is the choice of substances by which the prominent parts are to be removed. The first substance should be the sharpest sand, so as to cut as fast as possible, and this is to be used till the surface becomes perfectly flat. After this the surface is rubbed with a finer sand, and frequently with a third. The next substance after the finest sand is emery, of different degrees of fineness. This is followed by the red powder called tripoli, which owes its cutting quality to the oxyd of iron it contains. Common iron-stone, powdered and levi- gated,'answers the purpose very well. This last substance gives a tolerably fine polish. This, however, is not deemed sufficient. The last polish MAR 264 MAS is given with putty. After the first process, which merely takes away the inequalities of the surface, the sand employed for preparing it for the emery should be chosen of an uniform quality. Ifit abounds with some particles harder than the rest, the surface will be liable to be scratched so deep as not to be removed by the emery. In order to get the sand of uniform quality, it should be levi- gated and washed. The hard particles, being generally of a different specific gravity to the rest, may by this means be separated. This me- thod will be found much superior to that of sift- ing. The substance by which the sand is rubbed upon the marble is generally an iron plate, espe- cially for the first process. A plate of an alloy of lead and tin is better for the succeeding processes, with the fine sand and emery. The rubbers used for the polishing, or last process, consists of coarse linen cloths, such as hop bagging, wedged tight into an iron plane. In all these processes, a constant supply of small quantities of water is absolutely necessary. The sawing of marble is performed on the same principle as the first process of polishing. The saw is of soft iron, and is continually supplied with water and the sharpest sand. The sawing, as well as the polishing of small pieces, is per- formed by hand. The large articles, such as chimney-pieces and large slabs, are manufactured by means of machinery, working by water or steam. MARGIN (from the Latin margo) of a door or shutter, the surface surrounding the frame be- tween the moulding and the extreme arris which terminates the face. MARQUETRY (from the French) inlaid work; a curious kind of work, composed of pieces of hard fine wood, of different colours, fastened, in thin slices, on a ground, and sometimes enriched with other matters, as tortoise-shell, ivory, tin, and brass. There is another kind of marquetry made, instead of wood, of glasses of various colours; and a third, where nothing but precious stones, and the richest marbles, are used: but these are more properly called mosaic work. The art of inlaying is very ancient, and is supposed to have passed from the east to the west, among the spoils brought by the Romans from Asia. Indeed, it was then but a simple thing ;‘ nor did it arrive at any tolerable perfection till the fifteenth century, among the Italians. It seems finally to have arrived at its height in the seventeenth century, among the French. MASONRY, the art of preparing stones, so as to tooth or indent them into each other, and form regular surfaces, either for shelter, convenience, or defence; as the habitations of men, animals, the protection and shelter of goods, SEC. The chief stone used in London is Portland, which comes from the island of Portland, in Dorsetshire. It is used for public edifices, not only, in ornaments, mouldings, and strings, but in all the exterior parts. In private buildings, where brickwork predominates, it is used in strings, window-sills, balusters, steps, copings, 8tc. It must be observed, however, that under a. great pressure it is apt to splinter or flush at the joints, and for this reason the joints cannot be made so close as many other kinds of stones will admit of. When it is recently quarried it is soft, and works easily, but acquires great hardness in length of time. The cathedral of St. Paul, VVest- minster-bridge, and almost every public edifice in London, are constructed wholly, or in part, of Portland stone. Purbeck stone.comes from the island of Purbeck, in: Dorsetshire also. It is mostly employed in rough work, as steps and paving. Yorkshire stone is also used where strength and durability are requisite, as in paving and copinv. Ryegate stone is used for hearths, slabs,_and copings. In Edinburgh, a very fine stone, called Craig- leith, brought from a village of the same name, in the neighbourhood of that city, is most commonly used in the construction of edifices. They have also very good stone from the Hails quarry, but rather inferior in point of colour. . This Craigleith quarry produces two kinds of rock, one of a fine cream or bufl'colour, called the liver rock, which is almost unchangeable, even though exposed in a building to the weather. The city of Glasgowis built of various kinds of stone, the best of which are, the Posse] and the Lord President’s quarry; most other kinds are not only perishable, but liable to change their colour. - ~ In the north of England, stone fit for hewn work is chiefly of a reddish colour. There is a very good white stone, however, in the vicinity of MAS 96 v Q MAS Liverpool, of which several of the public build- ings are constructed. All the stone fit to be squared, or squared and rubbed smooth, for the use of building, 18 mostly' composed of sand. The stone used for the same purpose in the south of England is, in some parts, entii‘ely'chalk, and in other parts limestone. The Bath and Oxfordshire stone has so little grit in its texture, as to be wrought into mouldings with planes, as in joinery, and the surfaces are finished with an instrument called a drag. Marbles, with regard to their contexturc and variegation of colour, are almost of infinite va- riety: some are black, some white, some of a dove colour, and others beautifully variegated with ev ety kind of rich colour. The best kind of white marble is that called statua1y, and when cut into thin slices becomes almost transparent, which property the others do not possess. The texture of marble, with regard to working, is not generally understood, even by the best workmen, though upon sight they frequently know whether it will receive a polish or not. Some marbles are easily wrought, some are very hard, and other kinds resist the tools altogether. Mortar is another principal material used in cementing the stones of a building. The reader who wishes to obtain a full knowledge in this de- partment of masonry, may consult the article CEMENT, where he will receive satisfactory in- formation. Wherever it is intended to build upon, the ground must be tried with an iron crow, or with a rammer: if found to shake, it must be pierced with a borer, such as is used by well-diggers; and if the ground proves to be generally firm, the loose or soft parts, if not very deep, must be ex- cavated until a solid bed appears. “the ground proves soft in several places to a great depth under apertures, and firm upon the scite of the piers, turn inverted arches under the apertures, so that if the foundation sink, the arches will resist the re-action of the ground, then the whole wall will sink uniformly or de- scend in one body. Should the ground he even of a uniform texture, it is always eligible to turn inverted arches under apertures, wherever there is a part of a wall carried up from the foun- dation to the sill of thataperture: it is from neglecting this circumstance, that the sills of “l“dOWS in the ground stories of buildings are "~. UL. 11. fiequently broken; indeed it is seldom or never othemise. ' A1ches adequate to this purpose should rather be ofa parabolic form than circula1, the figuie of the parabola being better adapted to preserve an equi— librium than the arc of a circle, which is of uni~ form curvature. If unfortunately the soft parts of the ground prove to be the scite of the piers, and, consequently, the hard places under the apertures, build piers under the apertures, and suspend arches between the piers with their con- cave side towards the trench as usual. Formore information upon this subject, the reader will refer to the article FOUNDATION. In walling, the bedding joints have most com- monly an horizontal position in the face of the work, and this disposition ought always to take place when the top of the wall terminates in an horizontal plane or line. In bridge building, and in the masonry of fence walls upon inclined sur- faces, the beddingjoints on the face sometimes follow the upper surface of the wall or terminating line. The footings of stone walls ought to be construct- ed of large stones, which, if not naturally nearly square, should be reduced by the hammer to that form, and to an equal thickness in the same course; for if the beds of the stones in the founda- tion taper, the superstructure will be apt to give way, by resting upon mere angles or points with inclined beds instead of horizontal. All the ver- tical joints of any upper course should break joint, that is, they should fall upon the solid part of the stones in the lower course, and not upon the joints. When the walls of the superstructure are thin, the stones which compose the foundation may be so disposed that their length may reach across each course, from one side of the wall to the other. In thicker walls, where the difliculty is greater in procuring stones of sufficient length to reach across the foundation, every second stone in the course may be a whole stone in the breadth, and each interval may consist of two stones of equal breadth, that is, placing header and stretcher al- ternately. But when those stones cannot be had conveniently, from one side of the wall lay a header and stretcher alternately, and from the other side lay another series of stone in the same manner, so that the length of each header may be two-thirds, and the breadth of each stretcher 2 M MAS 266 MAS W one-third of the breadth of the wall, and so that the back of each header may come. in contact with the back of an opposite stretcher, and the 1 side of that header to come in contact with the E side of the header adjoining the said stretcher. In broad foundations, where stones cannot be procured for a length equal to two-thirds of the breadth of the foundation, build the work so that the upright joints of any course may fall on the . middle of the length of the stones in the course below, and so that the backs of each stone in any course may fall upon the solid of a stone or stones _ in the course below. The foundation should consist of several courses, of which each superior course should be of less breadth than: the inferior one, say four inches on each side in ordinary cases, and the upper course project four inches on each side of the wall. The number of courses mustbe regulated by the weight of the wall, and by the size of the stones of which the foundation consists. A wall which is built of unhewn stone is called a rubble wall, whether with or without mortar. Rubble work is of two kinds, coursed and un- coursed. Coursed rubble is that of which the stones are gauged and dressed .by the hammer, and thrown into different heaps, each heap con- taining stones of the same thickness; then the masonry is laid in courses or horizontal rows, which maybe of different thicknesses. The un- coursed rubble is that where the stones are laid 7 promiscuously in the wall, without any attention to placing them in rows. The only preparation which the stones undergo, is that ofknocking off the sharp angles with the thick end of the scab- bling hammer. Walls are most commonly built with an ashler facing, and backed with brick or rubble work. Brick backings are common in London, where brick is cheaper; and stone backing in .the north of England and in Scotland, where stone is cheaper. Walls faced with ashler, and backed with brick or uncoursed rubble, are liable to be— come convex on the outside from the greater number ofjoints, and from the greater quantity of mortar placed in each joint, as the shrinking of the mortar will be in proportion to the quan- ‘tity, and therefore a wall of this description is much inferior to one of which the facing and backing are of the same kind, and built with equal care, even though both sides were uncoursed rubble, which is the worst of all walling. Where the outside of a wall 15 an ashler facing and the inside coursed rubble, the courses of the backing should be as high as possible, and set with thin beds of mortar. In Scotland, whe1e stone abounds, and where perhaps as good ashler facings are constructed as any in Great Britain, the backing of their walls most commonly consists of un- coursed rubble, built with ve1y little care. In the north of England, where the ashler facings of walls are done with less neatness, they are much more particular in coursing of their backings. Coursed rubble and brick backings are favourable for the insertion of bond timbers: but in good masonry wooden bonds should never be in con- tinued lengths, as in case of fire or 1ot, the wood will perish, and the masonry, being reduced by the breadth of the timber, will be liable to bend at the place where it was inse1ted. When it is necessary to have .vall timber for the fastening of battens for lath and plaster, the pieces of tim- ber ought to be built with the fibres of the wood perpendicular to the surface of the wall, or other- wise in unconnected short pieces, not exceeding nine inches in length. In an ashler facing the stones generally run from twenty-eight to thirty inches in length, twelve inches in height, and eight or nine inches in thickness. Although both the upper and lower beds of an ashler, as well as the vertical joints, should be at right angles to the face of the stone, and the face bed and verticaljoints at right angles .to the beds in an ashler facing, where the stones run nearly of the same thickness, it is .of some ad- vantage, in respect of bond, that the back of the stone be inclined to the face, and that all the backs thus inclined should run in the same direction, as this gives a small degree of lap in the setting of the next course; whereas if the backs were parallel to the front, there could be no lap where the stones run of an equal depth in the thickness of the wall. It is of some advantage likewise to select the stones, so that a thicker one and a thinner one may follow each other alternately. The disposi- tion of the stones in the next superior course, should follow the same order as in the inferior course, and every vertical joint should fall as nearly as possible in the middle of the stone below. In every course of ashler facing, with brick or rubble backing, thorough-stones (as they are techni- cally termed) should be introduced, and their MAS 67 MAS ‘— number should be proportioned to the length of the ecurse, and every such stone of a superior course should fall in the middle of every two like stones in the course below; this disposition of bonds should be strictly attended to in all long courses. Some wallets, in order to shew or demon- strate that they have introduced sufficient bonds in their work, choose their bond stones of greater length than the thickness of the wall, and knock or cut off their ends afterwards. This method is far from being eligible, as the wall is not only liable to be shaken by the force applied to break the end of the stone, but the stone itself is apt to be split. In every pier where the jambs are coursed with the ashler in front, every alternate jamb stone ought to go through the wall with its beds per- fectly level. If thejamb stones are of one entire height, as is frequently the case when architraves are wrought upon them, and upon the lentil crown- ing them, in the stones at the ends of the courses of the pier which are to adjoin the architrave jamb, every alternate stone ought to be a thorough stone; and if the piers between the apertures be very narrow, no other bond stones will be neces- sary in such short courses. But where the piers are wide, the number of bond stones must be pro- portioned to the space: thorough stones must be particularly attended to in the long courses below and above windows. Bond stones should have their sides parallel, and of course perpendicular to each other, and their horizontal dimension in the face of the work should never be less than the vertical one. All the vertical joints, after receding about three quar- ters of an inch from the face with a close joint, should widen gradually to the back, and thereby form hollow wedge-like figures for the reception of mortar and packing. The adjoining stones should have their beds and vertical joints filled with oil putty from the face to about three quarters of an inch inwards, and the remaining part of the beds with well prepared mortar. Putty cement will stand longer than most stones, and will even remain prominent, when the stone itself is in a state of dilapidation, by the influence of the corroding . power of the atmosphere. It is true that in all newly built walls cemented with oil putty, the first appearance of the ashler work is rather unsightly, owingr to the oil of the putty disseminating itself into the adjoining stones, which makes the joints H appear dirty and irregular: but this disagreeable effect is removed in ayear, or less; and if care has been taken to make the colour of the putty suitable to that of the stone, thejoints will hardly appear, and the whole work will seem as if one piece. This is the practice of Glasgow. In London and Edin- burgh fine water putty is used instead of it. All the stones of an ashler facing should be laid on their natural beds. From a neglect of this‘cir- cumstance the stones frequently flush at thejoints, and this diSposition of the lamina sooner admits the corroding power of the atmosphere to take place. In building walls or insulated pillars of very small horizontal dimensions, every stone should have its beds level and without any concavity in the mid. die; because if the beds are concave, when the pillars begin to sustain the weight of the fabric the joints will in all probability flush. It ought likewise to be observed that every course of ma- sonry of such piers ought to consist of one stone. An arch, in masonry, is a part of a building sus- pended over a given plan, supported only at the extremities, and concave towards the plan. The supports of an arch are called the spring walls. The whole of the under surface of the arch oppo- site to the plan is called the intrados of the arch, and the upper surface is called the extrados. The boundary line, or lines of the intrados, or those common to the supports and the intrados, are called the springing lines of the arch. A line extending from any point in the springing line on one side of the arch, to the springing line on the opposite side of the arch,is called the clwrd or span of the arch. If a vertical plane be supposed to be contained by the span and the intrados of the arch, it is called the section of the hollow of the arch. The vertical line drawn on the. section fromthe middle of the spanning line to the intrados, is called the height of the arch, as also the middle line of the arch, and thepart of the arch at the upper extremity of this line is called the crown of the arch. Each of the curved parts on the top of the section, between the crown and each extremity of the span- ning line, is called the hamzches or flanks of the arch. The section of almost every given arch used in building has the following properties : the upper part is one continued "curve, concave towards the 0 M D d d M MAS 268 M AS span, or two curves forming an interior angle at the crown,both concave towards the spanning line. Every two vertical lines on the section equidistant from each extremity, and parallel to the middle line, are equal. , The above definitions and propositions not only apply to arches with level bases, but also to arches which stand upon inclined bases. When the base of the section or spanning line is parallel to the horizon, the section will consist of two equal and similar parts, so that if one were conceived to be folded upon the other, the boun- daries of both would coincide. Arches, the intrados of which is the surface of a geometrical solid that would fill the void, are vac riously named, according to the figure of the sec- tion of that solid perpendicular to the axis, as cir- cular, elliptical, cycloidal, catenarian, parabolical, 8Le. . Arches of the circular kind have two distinctions, viz. the semicircle, and those of segments less than a semicircle, are called scheme or skene arches. There are also pointed, composite, lancet, or Gothic arches, which are formed in the face of the wall, or in sections parallel thereto, with the in- trados of the arch. When the extremities of an arch rise from sup- ports at unequal heights, such an arch is called a rampant arch. When a vertical line is drawn upwards, through each extremity of the spanning'line, so as to cut off equal and similar parts of the intrados, the arch is called a horse-shoe arch, or moresque arch. H ence, in this kind of arch, the spanning line is less than any other line or chord drawn parallel to the span, but under the top of each said vertical line. When the upper line or side of an arch is parallel to the under line or side, the arch is called an ex- tradossed arch. A simple vault is an interior concavity extended over two parallel opposite walls, or over all the diametrically opposite parts of one circular wall. An arch or vault are frequently understood as synonimous; but the distinction which we shall here observe is, that an arch, though it may be extended over any space, has a very narrow in- trados, not exceeding four or five feet; whereas a vault may be extended to any limit more than four or five feet. Thus, we frequently say an arch in a wall, but we never say a vault in a wall; though nothing is more common than to say a J; J vaulted apartment, a vaulted room, a vaulted eel- lar, Ste. So that a vault, as Sir Henry V’Votton has observed, . is an extended arch; we shall therefore apply arch to the head of the aperture in a wall which shews eurvilineal intersections with the faces of the wall, and the word vault to arched apartments. We frequently, however, call the stone-work suspended over an apartment an arch as well as a vault, so that every vault is an arch, but every arch is not a vault. The intrados ofa simple vault is generally formed of the portion of a cylinder, eylindroid, sphere, or spheroid, never greater than the halfofthe solid ; and the springing lines which terminate the walls, or'where the vault begins to rise, are generally straight lines parallel to the axis of the cylinder, or cylindroid, or the circumference of a circle or ellipse. A circular wall is generally terminated with a spherical vault, which is either hemispherical, or a portion of the sphere less than a hemisphere. A vaulted apartment, surrounded by an elliptic wall, is generally covered with a spheroidal vault, which is either a hemispheroid, or a portion less than a hemispheroid. A conic surface is seldom employed in vaulting, but when the vault is to have this kind of in" trades, the intrados should be the half of a cone with its axis in a horizontal position, or a whole cone with its axis in a vertical position. All vaults which have a horizontal straight axis, are called straight vaults. Besides what we have already denominated an arch, the concavities which two solids form at an angle, are called an arch. If one cylinder pierce another of a greater dia- meter, the arch is called a cylindro-cyiindric arch - y a the cylindro being applied to the cylindric part which has the greater diameter, and the cylindrie to that which has the less. If a cylinder pierce a sphere of greater diameter than the cylinder, the arch is called a sphero- c'z/Zindric arch; and, on the contrary, if a sphere pierce a cylinder of greater diameter than the sphere, the arch is denominated a cylindro—sp/teric arch. lfa cylinder pierce a cone, so as to make a com- plete perforation through the cone, two complete arches will be formed, called cono-ryh'ndric arches; and, on the contrary, if a cone pierce a cylinder, so as to make the interior concavity through the “£55,; ’ ‘.&1 m“ l‘ pity.“ ”6/, t .1 PLAT/2' 1) 'MA § QN'R‘Y. , _ 3.9 ,... uwfiugmfi; {QYASH 4W //./ . :2 __ __ :1: : 1/; ///// 7/ , .%W%M .N\.. ". I‘MHW. :v..\1.\x. \ . . -4. . . .. Ly. . Illkrlpflii . . .ll. / I}... mflHLMW. (1.. .. :9: 7% :. . ‘ /. fl , N . / f”? / // %% ,/a%v $:.é: f.mmwflh.-.AW%%%W% m»_ ,Exgéég - ---- = fl/ .-,E§§:§_ /// .---,E§§§§% W ...§§; g? .u. 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Every species of arches is thus denoted\by two preceding words; the former ending in} 0, signi- fying the principal vault or surface cut through, and the latter in ic, signifying the kind of aper- ture which pierces the wall or vault. ' When two cylindric vaults, or two cylindroidic vaults, oracylindric or cylindroidic vault, pierce each other, and also their axis, so that the dia- meter of each hollow may be the same when mea- sured perpendicular to a plane passing through the axis of both surfaces, the figure so formed is called agroin: but for more particular informa- tion on this point, see the article GROIN. The formation of stone arches, in various cases, has always been looked upon as a most curious and useful acquisition to the operative mason, or to the architect, or other person who is appointed to superintend the work. In order to remove the difficulties experienced in the construction of cylindric or cylindroidic arches, both in straight and circular walls, we shall here shew an example of each. First, let it be required to construct a semi-cylin- droidic arch, cutting a straight wall with its axis oblique to the surface of the wall, but parallel to the horizon. Let A B C D (Plate II. Figure 1) be the plan of the aperture, A D and B C being the plan of the jambs; and A B and D C the plan of the sides of the wall; produce D A and C B to G and F: draw the straight line I G M FE at right angles with A G and C F: bisect G F at M : draw M H K perpendicular to G F; make M H equal to the height of the intrados of the arch, and describe the semi-ellipsis G H F, which is the section of the intrados of the arch: make G I, H K, and F E, equal to the breadth of the beds of the arch-stone, and describe the semi- ellipsis l K E, which is the section of the extrados of the arch. Now suppose the distances between the joints around the intrados. of the arch to be all equal, and all the joints to tend to the centre M; divide the semi-ellipsis into such an odd number of equal parts, that each part may be in breadth equal to what is intended for the thick- ness _of the stones at that part; produce E I to S, and extend the whole number of these parts from G to S; and through the points of division draw lines perpendicular to G S, or parallel to A G. Through all the points of division of the ellipsis G H F, draw lines parallel to G A to meet A B; then take the lengths of all the parts of the lines so drawn that are terminated by G F and A B, as follows: viz. make the first line on the left of G A equal to. the first on- the right. of GA, and the pointh will be obtained; and the second on the left of G A equal to the second on the right ofG A, and the point 0 will be ob- tained; proceed in this manner until all the other points are obtained; then a curve being drawn through all the points A, b, c, d, 8tc. to T, will i' give the one edge of the envelope of the intrados of the arch; and by producing the perpendiculars erected upon G S to the points e,f, g, 8m. and making the several distances be, cf, dg, 8L0. equal to A D or B C, the points D, e,f, g, &c. to U, will give the other edge of the envelope by tracing a curve through them; then A l) c (I, h cfe, c dgf, 8Lc. are the sofiits of the stones. Tofind any bevel which thejoints on theface of the arch makes with that on the intrados (f the same. Let p q be one of thejoints tending to the centre M of the section of the arch: with the radius M G describe an arc G N 0, cutting 12 g at N; draw N P parallel to G A, cutting A B at P: draw P Q parallel to F G, cutting G A at Q: draw M L parallel to G A, cutting A B at L, and _j.oin L 0; then Q L M is the bevel required: in the same manner may all the remaining bevels. be found. Again, let p q r s be the section of an arch stone, then making two bevels, one to q p s, and the other to rsp, will be all the bevels that are neces- sary for that stone. Having obtained the several bevels, we shall now proceed to work the arch- stone, whose section isp 9 rs: first work the lower bed of the stone, corresponding to the joint p q, then. draw a line for the soffit, which work also by means of the bevel q p s; then gauge the Soffit to its breadth, and work the upper bed of the stone by. means of the bevel 7‘ 8p; then take the sofi‘it mould from the envelope, and draw the ends of the stone which coincides with the faces of the wall; then with the face bevels Q L M, and V L‘M, work the face of the stone. Note. That finding the bevels for half the arch will be sufficient by reversing them. MAS 270 MAT The other arch standing upon D C shews the ends of the stones in the face of the wall; its boundaries are two ellipses of equal height to those of the section. To construct a cylindro-cyltndric arch, or a cylin- dric arch in a cylindric wall, the axis of the aper- ture being at right angles with the axis of the cylindric wall. Let A B C D be the half plan of the wall, B C being half of the convex curve, A D half of the concave curve, C D the middle line of the aper- ture tending to the centre of the concentric circles which form the plan, and A B parallel to CD, being the jamb. Through C draw EF perpendicular to C D: make C E and CF half the breadth of the aperture: from the centre C, with the radius C E or CF, describe the semi- circle E G F, which will be the section of the intrados: produce C E and CF to H and I, making E H and F 1 each equal to the breadth of the beds, and describe the semicircle H K I: divide the intradossal curve B G F into the num- ber of parts answering to the number of arch stones, and proceed to find the envelope, as de- scribed, for the straight wall, which will give the moulds for the sofiits of the stones as before. T 0 find the curves of the ends of the beds upon the face of the arch. Let L M represent a joint: draw L N and M O perpendicular to H 1, cutting the plan of the wall at N and O: draw N P parallel to C l, cutting NI 0 at P: in L M take any number of points t and 3/, and draw ts and yw parallel to L N, cutting the plan at s and w, and N P at r and v: draw M Q, tn, 3/ as, perpendicular to L M: make M Q, tu,y x, respectively equal to P O, r 3, etc, and Lx it Q will be the curve of the joint re- ‘ quired, which gives the face line of the upper bed of the lower stone, and the face line of the lower bed of the upper stone. 1n the same man- ner all the other face lines of the beds are to be found. The templet must be cut in the shape of L M Q. T 0 form an arch stone. First make one of the beds, then make the sofi‘i t, then form the other bed, then form the face lines of each bed, then run a draught round the three face lines, then between these work the face of the stone in lines perpendicular to the horizon. This will be easily found by drawing a vertical line upon the section of each stone. :5 It is only necessary to draw the moulds fo1 one half of the arch, as the reversing of them in their application gives the stones of the other half. _ The joints of any arch whatever may be found in the same manner, provided that the planes of the beds intersect a vertical plane perpendicular to the curve in the middle of the aperture. It 1s obvious, on finding the face lines of the beds, that the low est face line IS the quickest, and part of the plan of the wall itself; the next face line is flatter, or has less curvature, and thus each successive face line has less curvature as it comes nearer to the top; and, if there were ajoint in the top, the face line of the beds would be quite a straight line. Indeed, the face lines of two or three courses might be wrought with straight edges, as the difference could hardly be per- ceived. MATERIAL (from the French materiel) in archi- tecture, the different kinds of bodies, or sub- stances, used in the construction of edifices, as wood, stone, brick, mortar, 8m. It is chiefly from the valuable work of Vitruvius, that we are furnished with information respecting the nature of the materials used by the Greeks and Romans, and of the particular modes in which they were disposed in their buildings. From the accounts published by modern travellers and sci- entiflc artists, we are also furnished with further information respecting the practice of these people. The materials chiefly made use of by them were timber, marble, stone, bricks, lime, and metals. With regard to timber, the proper time for felling was reckoned from the beginning of autumn to the latter end of February, when the moon was in the wane. They considered wood when quite green, or too much dried, as equally unfit for working. For joists, doors, windows, they re- quired that it should have been out three years, and kept for a considerable time covered with cow-dung. The Greeks most usually made use of white mar- bles, as Pentilie, Pariah, and that of Chios. The latter was very transparent. The Romans employed many sorts, of various colours, and procured from many different coun- tries, which were subjected to them in Asia, Africa, and Europe. The ancients frequently included under the term marble, all hard stones which would receive a MAS QNRY. PLATE I. I- 107100)”; [11]) [Ly/5rd [31/ £372.11” [own A" .l. liar/ir/n’ ,Wnrr/our J'h-rrf, 131.1). 12/1,!”qu IfI/ [ti/(our. 5‘1] l’.\'ir/10/.;‘0ll. MAT 2 smooth fine polish; the modems confine the name marble to such calcareous stones as are capable of receiving a fine polish. Alabaster: this substance resembled marble in taking a smooth fine polish, but it is much softer and more easily worked. Gypseous alabaster, when polished, is slippery to the touch; it fre— quently contained as much carbonate of lime as to cause it to effervesce with acids; it was pro- cured from Upper Egypt between the Nile and Red Sea, also from Syria and Carmania. The calcareous alabaster is white, yellow, red, and bluish grey ; the fracture is striated or fibrous, in hardness inferior to marble; it is known under the denomination of common and oriental ; Italy and Spain produce the best. The stone which was employed appears to have differed very materially in its qualities; some be- coming considerably harder in being exposed to the air, was worked immediately on being taken . out of the quarry; but there was some ofa softer kind, which, previous to being used, required to have its quality proved by two years exposure to the effects of the atmosphere. Of tiles, they had, 1. The unburnt kind, which were dried five years in the sun; and, ‘2. Those baked by fire, after having been made two years, they preferred a white chalky earth dug in the au- tumn, exposed during the winter, and made bricks in the spring. The Greeks proportioned the size of the bricks to the nature of the edifice: the largest for public buildings, were five spans each way; those of the middle class were four spans; and the smallest, called by Vitruvius, Diodori, or by Pliny, Lydii, were two spans long and a foot broad ; these last were for private houses. It appears that. those dried in the sun were mixed with chopped straw. Dr. Pocock describes one of the pyramids constructed of brick: he mea- sured some thirteen inches and a half long, six inches and a half broad, and four inches thick; also others, which were fifteen inches long, seven inches broad, and four inches and three quarters thick. At Rome they were found by De Quin- cey of three different sizes; the least were seven inches and a half square, and one inch and a half thick; the middle-sized were sixteen inches and a half square, and eighteen to twenty lines in thick- ness; and the largest were twenty-two inches square, and twenty—one to twenty-two lines in thickness. 71 MAT Three kinds of sand are mentioned, that is, pit, river, and sea sand; of these, pit sand was rec- koned the best; the white was preferred to the black or red coloured, and the carbuncle to all; of the river sand, that was considered best which was found near torrents; the least value was put upon sea sand, and it was required to be well washed, to dissolve the saline matter before used in plas- tering or rough casting walls. Lime for plastering walls .was made from shells, river pebbles, or a sort of pumice stone; the best sort of lime was accounted that made from white stone, which was dense and hard, and lost one- third of its weight in burning in a kiln, where it was kept about sixty hours. Their mortar was composed of one part lime and three of pit or two of river sand. ' Metals were used, 1. Iron for chains, hinges, handles, and nails. 2. Lead for roofs, pipes. 3. Copper and brass were still more used for many of these purposes, or, 4. Copper, brass, and lead, mixed into a bronze for statues, bases, and capi- tals of columns, and in doors. Amongst the modems, change of climate, natural productions, and the habits of mankind, have from time to time led to considerable changes in the kinds of materials used for the various purposes of architecture, also in the modes of preparation, and application of them. “Nth regard to timber. Oak, for the greatest strength and durability, should be chosen from those soils where it has taken the longest time in arriving at maturity, and of two pieces equally dry, that should be chosen which has the greatest specific gravity, and that which will have its specific gravity least changed by being soaked in water: this observation will indeed apply to tim- ber in general. A decay of the top is almost a certain indication of a decay of the tree; and a decayed branch or rotten stump bespeaks a de- fect in that part of the tree where it is situated. In a similar soil, trees which grow near the out- side of a forest will be more durable than those near the middle of it; and in the same tree, the side which grew towards the north will be stronger than the south side. When perfection of strength and texture is alone consulted, all sorts of timber are cut down in the winter, being at that time freest of sap, and most readily seasoned, and rendered fit for the purposes of building; but on account of the bark of the M AT 279, W oak being of great use in tanning leather, that woodis always, in England, cut in the spring, or rather from April toJune, according to the state of the season, and soon after the sap begins to ascend and the leaf to appear; if it is cut before the sap rises, the bark adheres to the wood, and cannot be stripped off, and if left until the leaf is quite expanded, the bark is less valuable; when the tree is felled and suffered to lie in the trunk, it will shrink in size; but this is probably from its discharging water, because, ifa dry tree be laid . in a damp place, it will increase both in weight and size. The part called the sap varies in quan- tity in different trees; it is least in bad soils, where the growth is slow; it is of very little use. Oak used in damp situations, appears to decay gradually from the external surface to the centre of the tree; the outside ring or addition it re- ceived in the last year of its growth decaying first, and afterwards that next within it, and then the following one. This appears to proceed from two causes; first, from the outward ring being, where whole trees are used, first exposed to the action of the atmosphere, which cannot reach the second until the first is destroyed; secondly, from the centre part of the tree having arrived at a greater degree of maturity than the outward rings, which are many years younger. But this must be understood only of trees which are not past their prime before they are cut down; for when a tree begins to decay from age, that part of the tree which is oldest, namely, the central part, decays first; to this succeeds the parts which are next oldest, being the ring next the centre, and the other annual rings in succession gradually ap- proaching the bark. A judicious builder will therefore, in the choice of his timber, always carefully examine the central part of the tree, especially of that which is next the root, and more particularly if the tree is large, and has the appearance of great age. The best mode of seasoning oak is to put it in water. This, if in the log, should be done for a whole year or more, but, if cut in planks, less time is necessary ; in either case alternate soaking and drying is to be preferred. This, in planks, is very practicable; but, in regard to logs, one soaking and drying gradually in the shade, is, on account of the great labour attending the operation, most generally practised. After the planks have been soaked in water, they are dried by placing a strong MAT I‘— I - : pole in a horizontal position, at such a height as will admit of one end of each plank being placed on the ground, and the other resting against the pole edgewise, placing a plank first on one side of the pole, and then another on the other side alternately, thus leaving a space for the air to pass freely and dry them, and being exposed edge- wise to the sun, they are not liable to split. In ash, there is little difference in the quality through the whole thickness of the tree, the out side is rather the toughest : it soon rots when ex- posed .to the weather, but will last long when pro- tected. Of elm, some sort will decay sooner than the brown or red. It is improper for roofs or floors, being generally cross-grained, and very liable to warp; it also shrinks very considerably, not only in breadth, but lengthwise. It answers well when used under water; it is not liable to split, and bears the driving of bolts and nails better than any other timber. Beech is hard and close. There is a black or brown, and a white kind: the brown is tough, and sometimes used as a substitute for ash; it is improper for beams, because a small degree of dampness in the walls very soon rots the ends; it is fittest for furniture, or where constantly under water. Poplar is of a very close quality, is liable to the same objections as the beech in beams, but is well adapted for floors and stairs, being not readily inflamed: it rots soon when exposed to the weather. Asp resembles the poplar in appearance; it is soft and tough; itlasts when exposed to the weather; and is equally good thrgouh the body of the tree. The sycamore and lime are subject to the same objections, in roofing and flooring timbers, as the poplar and beech. The lime is something like the ash, and, like it, is greasy when worked smooth : it is suitable for furniture. Birch is equal in quality quite across the body of the tree; it is very tough, but does not last when exposed to the weather; it is also subject to be destroyed by the worms. . Chesnut, viz. the sweet, or Spanish, (not the horse-chesnut,) is frequently found in old build- ings in England: and although difficult to be distinguished from oak, differs from it in this, that wherever a nail or bolt has been driven into oak before it was dry, a black substance appears MAT 27:3 MAT W 1 ' round the iron, which is not the case in ches- nut. The walnut-tree is, in Britain, now too valuable to be used in the framings of roofs or floors; and in furniture it has long been superseded by ma- hogany; it is now used chiefly in stocks of fire- locks, fowling-pieces, pistols, 8C0. Mahogany is used chiefly in furniture, and also sometimes in doors and window sashes; it is sawn out and seasoned by perching out in the winter, and drying in the open air; the use of fire is not advisable. This beautiful timber was introduced into England about the beginning of the last cen- tury : its first application was in a box for holding candles, made by a Mr. Wollaston for a Dr. Gib- bons, who had afterwards a bureau of it; the Duchess of Buckingham had the second bureau. It very soon came into general use. It is divided chiefly into Jamaica and Honduras; the former is by much the hardest and most beautiful: they may be readily distinguished before they are oiled; the pores of the Honduras appear quite dark, those of the Jamaica as iffilled with chalk. Fir, being cheaper, and more easily wrought than oak, and next to it in usefulness, is more used in Britain than any other kind of timber. That most generally employed in carpentry is distin- guished by the name of Meme], (which includes Dantzic and Riga); Norway, (which also includes Swedish,) is much used for the smaller timbers, and answers well either when exposed to the air, or under ground. Dranton, or Dram, is suitable for flooring. All these are very durable. Ameri- can fir is much softer, but suitsinside joinery work, such as panels and mouldings. What is termed in England white deal, and in Scotland pine-wood, that is, fir deprived of its resinous part, being very durable when kept dry, is much used by cabinet-makers ; but, as it will not stand the weather, it is little used in carpentry or jomery. . Evelyn makes the following observation on the use of fir :——“ That which comes from Bergen, Swinsund, Mott, Longland, Dranton, (called Dram,) being long, straight, and clear, ofa yel- low and more cedary colour, is esteemed much before the white for flooring and wainscot; for masts, those ofPrussia, which we call spruce, and Norway, especially from Gottenburgh, and about Riga, are the best.” The torulus, as Vitruvius terms it, and heart of deal, VOL. 1;. kept dry, rejecting the alburnum or white,is ever- lasting; nor is there any wood which so well agrees with the glue, or which is so easy to be wrought. It .is also excellent for beams, and other timber work in houses, being both high and exceedingly strong, and therefore of very great use for bars and bolts of doors, as well as for doors themselves; and, for the beams of coaches, a board of an inch and a half thick will carry the body ofa heavy coach with great ease, by reason of a natural spring, which is not easily injured. It was for- merly used for carts and other carriages, and also for the piles to build upon in boggy grounds. Most of Venice and Amsterdam is built upon them. For scaffolding also, there is none com- parable to it. Under the head offir may be classed cedar, a wood of great durability, but too expen- sive to be used in Britain. Evelyn makes the following observations upon timber; some of which are well worthy of atten- tion :— “ Lay up your timber very dry, in an airy place, yet out of the wind or sun, and not standing up- right, but lying along, one piece upon another, interposing some short blocks between them, to preserve them from a certain mouldiness which they usually contract while they sweat, and which frequently produces a kind of fungus, especially if there be any sappy parts remaining. “ Some there are yet, who keep their timber as moist as they can by submerging it in water, where they let it imbibe to hinder the cleaving; and this is good in fir, both for the better stripping and seasoning, yea, and not only in fir but other timber. Lay, therefore, your boards a fortnight in the water, (if running the better, as at some mill— pond head,) and then setting them upright in the sun and wind, so as it may freely pass through them, (especially during the, heats of summer, which is the time of finishing buildings,) turn them daily, and thus treated, even newly-sawn boards will floor far better than many years’ dry seasoning, as they call it. But, to preventall possible accidents, when you lay your floors, let the joints be shot, fitted, and tacked down only for the first year, nailing them for good and all the next; and by'this means they will lie staunch, close, and without shrinking in the least, as if they were all one piece. And upon this occasion, I am to add an observation, which may prove’ of no small use to builders ; that if one take up deal 2 N IVIAT 974i M boards that may have lain in the floor a hundred years, and shoot them again, they will certainly shrink (toties queries), without the former method. Amongst wheelwrights, the water-seasoning is of especial regard; and in such esteem amongst some, that I am assured, the Venetians, for their pro- vision in the arsenal, lay their oak some years in water before they employ it. Indeed, the Turks not only fell at all times of the year, without any regard to the season, but employ their timber green and unseasoned ; so that, though they have excellent oak, it decays in a short time by this only neglect. “ Elm felled ever so green, for sudden use, if plunged four or five days in water, (especially salt water,) obtains an admirable seasoning, and may immediately be used. I the oftener insist on this water-seasoning, not only as a remedy against = the worm, but for its efficacy against warping and distortions of timber, whether used within or exposed to the air. Some, again, commend bury- ing in the earth, others in wheat; and there be seasonings of the fire, as for the scorching and hardening of piles, which are to stand either in the water or in the earth. “ When wood is charred, it becomes incorrup- tible; for which reason, when we wish to preserve piles from decay, they should be charred on their outside. Oak posts, used in enclosures, always decay about two inches above and below the sur- face. Charring that part would .probably add several years to the duration of the wood, for that to most timber it contributes much to its dura- tion. Thus, do all the elements contribute to the art of seasoning. “ And yet even the greenest timber is sometimes desirable for such as carve and turn, but it chokes the teeth of our saws; and for doors, windows, floors, and other close works, it is altogether to be rejected, especially where walnut-tree is the material, which will be sure to shrink. There- fore, it is best to choose such as is of two or three years seasoning, and that is neither moist nor over dry; the mean is best. Sir Hugh Plat in- forms us, that the Venetians used to burn and scorch their timber in a flaming fire, continually turning it round with an engine, till they have gotten upon it a hard black coaly crust; and the secret carries with it great probability, for the wood is brought by it to such a hardness and dryness, that neither earth not water can pene- MAT —_‘_—. —-—- trate it; I myself remembering to have seen char- coal dug out of the ground amongst the ruins of ancient buildings, which had in all probability lain covered with earth above fifteen hundred years. “ Timber which is cleft is nothing so obnoxious to reft and cleave as what is hewn; nor that which is squared as what is round; and therefore, where use is to be made of huge and massy columns, let them be bored through from end to end. It is an excellent preservative from splitting, and not 1m:- philosophical; though, to cure the accident, painter’s putty is recommended; also, the rubbing them over with a wax-cloth is good; or before it be converted, the smearing the timber over with cow-dung, which prevents the effects both of sun and air upon it, if, of necessity, it must lie ex- posed. But, besides the former remedies, I find this for the closing of the chops and clefts of green timber, to anoint and supple it with the fat of powdered beef broth, with which it must be well soaked, and the chasms filled with sponges dipt into it. This to be twice done over. “ Some carpenters make use of grease and saw- dust mingled ; but the first is so good a way,” says my author, “that I have seen wind-shock timber so exquisitely closed, as not to be discerned where the defects were. This must be used when the timber is green. “ We spake before of squaring; and I would now recommend the quartering of such trees as will allow useful and competent scantlings, to be of much more durableness and effect for strength, than where (as custom is, and for want of observa- tion) whole beams and timbers are applied in ships or houses,with slab and all about them, upon false suppositions of strength beyond these quarters. For there is in all trees an evident interstice or separation between the heart and the rest of the body, which renders it much more obnoxious to decay and miscarry, than when they are treated and converted as l have described it ; and it would likewise save a world of materials in the building of great ships, where so much excellent timber is hewed away to spoil, were it more in- practice. Finally, “ I must not omit to take notice of the coating of timber in work used by the Hollanders, for the pre- servation of their gates,“portcullises, draw—bridges, sluices, and other huge beams and contignations of timber, exposed to the sun and perpetual injuries MAT 275 MAT W of the weather, by a certain mixture of pitch and tan-upon which they strew small pieces of cockle and Other shells, beaten almost to powder, and mingled with sea-sand, or the scales of iron, beaten small and sifted, which encrusts, and arms it, after an incredible manner, against all these assaults and foreign invaders; but if this should be deemed more obnoxious to firing, I have heard that a wash made of alum has wonderfully protected it against the assault even of that devouring element; and that so a wooden tower or fort at the Piraeum, the port of Athens, was defended by Archelaus, a commander of Mithridates, against the great Sylla. “ Timber that you have occasion to lay in mortar, or which is in any part contiguous to lime, as doors, window-cases, groundsels, and the extre— mities of beams, Ste. have sometimes been capped with molten pitch, as a marvellous preserver of it from the burning and destructive effects of the lime; but it has since been found rather to heat and decay them, by hindering the transudation which those parts require; better supplied with loam, or strewings of brick-dust, or pieces of boards ; some leave a small hole for the air. But though lime be so destructive whilst timber lies thus dry, it seems they mingle it with hair, to keep the worm out of ships, which they sheathe for southern voyages, though it is held much to retard their course. Wherefore, the Portuguese scorch them with fire, which often proves very dangerous; and, indeed, their timber being harder, is not so easily penetrable. “ For all uses, that timber is esteemed the best, which is the most ponderous, and which, lying long, makes deepest impression in the earth, or in the water, being floated; also, what is without knots, yet firm, and free from sap, which is that fatty, whiter, and softer part, called by the ancients albumum, which you are diligently to hew away. “ My Lord Bacon, Exper. 658, recommends for trial of a sound or knotty piece of timber, to cause one to speak at one of the extremes to his compa- nion, listening at the other; for if it be knotty, the sound,says he, will come abrupt. “ For the place of growth, that timber is esteemed best which grows most in the sun, and on a dry and hale ground ; for those trees which suck and drink little are most hard, robust, and longer lived—instances of sobriety. The climate contri- butes much to its quality; and the northern situa- tion is preferred to the rest of the quarters; so as that which grew in Tuscany was of old thought better than that of the Venetian side; and yet the Biscay timber is esteemed better than what they have from colder countries; and trees of the wilder kind and barren, than the over-much culti~ vated and great bearers.” Dr. Parry has published an excellent paper on the causes of the decay of wood, and the means of pre- venting it. From it we take the liberty of abridg- ing what follows; but would recommend a careful perusal of the whole of it to those who wish for farther information on the subject. Wood, Dr. Parry supposes to be subject to des- truction from two causes, rotting and the depreda— tions of insects. Of rot there are two supposed kinds : the first takes place in the open air; the second under cover. When perfectly dry, and in a certain degree of temperature, both animal and vegetable matters seem scarcely capable of spontaneous decay. On this principle, fish and other animal matter is often preserved. “ Similar causes produce the same effect on wood. Even under less rigid circumstances of this kind, as in the roofs and other timber of large buildings, it continues for an astonishing length of time un- changed. Witness the timber of that noble edi- fice, Westminster—hall, built by Richard II. in 1397 ; and the more extraordinary instance quoted by Dr. Darwin, in his ingenious work the Phy- tologia, of the gates of the old St. Peter’s Church in Rome, which were said to have continued with- out rotting, from the time of the Emperor Constan- tine to that of Pope Eugene IV. a period of eleven hundred years. On the other hand, wood will re- main for ages, with little change, when continually immersed in water, or even when deeply buried in the earth, as in the piles and buttresses of bridges, and in various morasses. These latter facts seem to shew, that if the access of‘ atmospherical air is not necessary to the decay of wood, it is at least highly conducive to it.” Putrefaction is the cause of rotting, and putrefac- tion is occasioned by stagnant air and moisture. The moisture of the air, coming in contact with wood of a lower temperature, is condensed in the same manner, as is more visible in our glass win- dows. In order to prevent the bad effects of this condensation, currents of dry air ought to be made to pass in contact with the timber. Of the advan- ' 2 N 2 \\ MAT 2 76 MAT tages of this, the Gothic architects seemed aware; for _it was common with them to leave openings for this purpose—a practice which we would strongly recommend in cellars, 8w. “ l t appears that the contact of water and air are the chief causes of the decay of wood. If, there- fore, any means can be devised, by which the access of moisture and air can be prevented, the wood is so far secure against decay. This principle may be illustrated, by supposingacylinder of dry wood to be placed in a glass tube or case which it exactly » fills, and the two ends of which are, as it is called, hermetically sealed, that is, entirely closed, by uniting the melted sides of each end of the tub. Who will doubt that such a piece of wood might remain in the open air a thousand years unchanged? Or let us take a little more apposite illustration of this fact, that of amber, a native bitumen or resin, in which a variety of smallflies, filaments of vegetables, and others of the most fragile sub- stances, are seen imbedded, having been preserved _ from decay much longer probably than athousand years, and with no apparent tendency to change for ten times that period.” These observations lead to the theory of painting timber, for the purpose of preserving it. Mr. Batson of Limehouse is of opinion, that the dry-rot proceeds from a plant, called boletus [acry- . mans, one of the fungus tribe, and is one of the few that have leaves, as the mistletoe. But Dr. Parry justly observes, that these plants “ begin merely because decayed wood is their proper soil.” “ The smell which we perceive in going into vaults or cellars, where this process is going on, arises partly from the extrication of certain gases, min- gled perhaps with some volatile oil, and partly from the efi’luvia of those vegetable substances, which have already been said to grow on it, and which, though they begin merely because the de- cayed wood is their proper soil, yet afterwards tend probably to the more speedy decomposition of the wood itself. “The following, then, appears to be the whole . theory of the dry-rot, that it is a more orless rapid decomposition of the substance of the wood, from moisture deposited on it by condensation, to the action of which it is more disposed in certain situa- tions than in others ; and that this moisture ope-- rates most quickly on wood, which most abounds with the saccharine or fermentable principles of _ the sap.” Thus far Dr. Parry. * . 3 Charring of wood is known to be a most effectual mode of preservation against rotting. » The incorruptibility of charcoal is attested by nu- merous unquestionable facts. At the destruction of the famous temple at Ephesus, it was found to be erected on piles that had been charred ; and the charcoal in Herculaneum, after almost 2000 years, was entire and undiminished. To this property of charred wood Sir C. Wren does not seem to have attended, when about to build St. Paul’s. It is said, he thought piles were not to be depended on for a foundation, excepting when always wet; and therefore dug to a great depth through a dry soil, in order to come at a solid foundation for part of that cathedral. Charcoal has also been found useful as a defence to the surface of wood, when used as a paint. We lately had a good instance of the effect of sand used for this purpose. At Studly Royal, we saw a temple to appearance of stone, but which on ex- amination we found to be wood covered with paint, and dusted over with sand. We were informed it had stood about 50 years ; and the deception was still so complete, that the spectators supposed the pillars to be stone, till minutely examined. For marble, being plentiful in Italy and France, these countries have been able to make aconsider- able use of it, even in the main walls of their edi- fices; but being seldom found in sufficient quan- tities, and of proper quality, in the more northern parts of Europe, it has been here chiefly confined to interior columns, pavements, chimney-pieces, and sometimes stairs. The kinds of stone are as various, as the countries in which the buildings are constructed. Sand-stone being very generally found stratified, even in thin laminae, being readily cut into different forms, and being, if properly selected and used, sufficiently durable, it has, in northern countries, been in most frequent use. It is a general accompaniment of coal strata, and is also often found where the latter does not occur. It varies in its component parts, being at different places argillaceous, siliceous, and calcareous. Its position in the earth assumes all directions, from the horizontal to a vertical plane. The proportio‘nal thickness of its strata, laminaz, or beds, varies from that of thin slate to many feet each. The upper beds are usually very thin or soft, or both; if sufficiently hard, they are em- ployed in floor pavements, and for covering roofs. Under these the beds generally, in useful quarries, MAT 277 MAT W increase in thickness, hardness, and tenacity. The position of the laminae, always require strict atten- tion, that the worked stone may, if possible, be laid in the building upon its natural bed; for although some instances occur, as in the Isle of Portland and at Grinshill, in Shropshire, where the difference is not apparently great, yet in all stone (even granite) it is sufficiently well known to work- men. Some stone, as that of Bath, is so soft when taken out of the quarry, as to be very conveniently worked with tools resembling those used by car- penters; yet when exposed for some time to the atmosphere, it becomes hard and durable. This last, indeed, cannot be deemed sand-stone, being nearly altogether calcareous. Besides the before mentioned, there is a very beautiful stone, dug in the hills near Dunstable, in the parish of Tottenhoe, from whence the stone receives its name. It has the appearance of in- durated chalk. It is easily worked, and hardens by exposure to the weather. It should, however, be placed upon a plinth of some other stone, or kept by other means from contact with the ground, otherwise it is, in this situation, liable to be injured by the frosts. The houseof the Duke of Bedford, at VVoburn Abbey, is built chiefly with this stone, as are various other large houses in the neighbour- hood of the quarries. Proofs of its durability may be seen in many old churches. From the close— ness of its texture, the beauty ofits colour, and the facility with which it is worked into mouldings, Ste. it is peculiarly fit for house-building, both externally and internally. It may be now readily conveyed to London, by means of the Grand Junc- tion Canal. The very perfect preservation of many beautiful churches in the counties of Lincoln, Rutland, and Northampton, are evidences of the excellence of the stone of which they are built. in the central parts of Scotland, different varieties of sand-stone, which accompany coal, are used ex- tensively in building houses, 8tc.; and this circum- stance has not a little contributed to the fine ap- pearance of the new streets, squares, and public buildings in the cities of Edinburgh and Glasgow. I’lints, where they abound, and where other stone is scarce, are sometimes used in walls of consider- able height; and notwithstanding their small size, and irregularity of shape, are broken so as to com- pose a face of considerable smoothness. The church and steeple of Rickmansworth, in Hert- fordshire, affords a fine specimen of this kind of building. But bricks or squared stones are gene- rally used as quoins for this sort, of work. In Scotland and Sweden, granite is made use of as a building material. It lies in large masses, gene- rally separated by gunpowder into moderate, though still large dimensions, which are againcut into suitable scantlings, by means of iron instru- ments called plugs and feathers. They are not only worked into plain square forms, but also mouldings of considerable delicacy, by means of pointed tools, of different sizes and weights. At Aberdeen, in Scotland, where excellent granite is produced, and the working of it brought perhaps to the greatest perfection, there are handsome por- ticos, consisting of columns, bases, caps, and entablatures, executed in granite with great nicety. In the middle of the city, a public building, whose front is composed ofa full Doric order, is wholly completed with this excellent material. There are two sorts of granite, the one grey and the other red; the last,being the hardest, is most difficult to work, consequently the former is most frequently employed; it consists of feldspar, mica, and quartz. It is much employed for paving the carriage-way of streets, and in the curbing of the flat side pave- ments; also for piers and footpaths of bridges; and for facings and copings to quays and wharfs. At Aberdeen, it is employed in constructing very extensive piers, for protecting the entrance of the harbour ; and in the Eddystone and Bell-Rock lighthouses, it composes the facings, where they are exposed to the action of the sea. VVhin, basalt, and schistus, are also used in rubble work. The former dressing freely with the ham— mer, in one direction, may readily be formed with good faces, but not being stratified, their beds are uncertain, and not easily improved by art; the latter, that is, schistus, is just the reverse, having naturally good beds, but being in few instances willing to dress square across the laminae: they are, indeed, where expense is not an object, worked to a face by the laborious operation of striking per- pendicularly with a wedge-mouthed hammer or stone axe: both kinds are laid, sometimes promis- cuously, and at others in regular courses. Limestone, where found regularly stratified, afl‘ords good building stone, and combines the advantages of both the former, having naturally good beds, and dressing readily for a face. A species of schistus affords a covering for roofs, r n—a *‘ ‘ totally unknown to the ancients, and which, when good ofits kind, and properly prepared and laid on, is both very effectual and beautiful; for a farther account of which, see SLATE. Bricks have, in England, become a material very generally employed in constructing all kinds of buildings. The country is provided by nature with abundant supplies ofcoal for burning bricks, which can, by means of the sea or numerous inland navi- gations, be, with great facility, conveyed to the large towns and populous districts, where the ‘de- mand has long been very great. Clay of proper quality is usually found, either upon the spot or immediate vicinity; a very limited number of workmen, properly arranged, can manufacture a great number of bricks in a stated time; these can readily be removed to the place where they are to be employed; being light to handle, and of a rectangular shape, the workmen lay them with facility and case. By means of bricks, walls can be made much thinner than with almost any kind of stone, they are therefore cheaper, and occupy less space; in forming doorways, windows, chim- neys, apertures, and angles ofall kinds, the facility they afford is greater than that of any other durable material. A building, whose walls are made with bricks, dries soon, is free from damp; and, if properly made, and thoroughly well burnt, bricks endure equal to most, and longer than many kinds of stone. For the best modes of manufacturing them, see BRICK. Tiles have long been employed in England for covering the roofs of buildings situated in towns, and of farm-houses and cottages in the country"; but of late years the use of them has been much circumscribed by the extension of that of slates. For the mode of manufacturing and using them, see T1 LE. Respecting sand, the ancient and modern prac- tices agree nearly in all that need be said; that which is of an angular shape, hard texture, and perfectly free from earthy particles, is admitted to be best. For the circumstances necessary to be attended to in employing it, as well as lime, see CEMENT. In regard to metals, in modern times, the use of copper and bronze has, for building purposes, been mostly abandoned. Brass has been continued in locks, pulleys, sash-windows, handles, sliding plates, connected with bells, and sundry other pur- poses in fitting up the interior of apartments. MAT 278 MAT Iron has been applied to many purposes unthought of in former times. The improvement and general introduction ofcast iron bids fair to create a totally new school of architecture. It has already been oc- casionally employed in bridges, pillars, roofs, floors, chimneys, doors, and windows; and the facility with which it is moulded into different shapes,will continue to extend its application. The before- mentioned purposes, to which it has already been applied, are more particularly noticed in the dis- cussions of practice in the different dranches of architecture, under their respective heads. Glass, as a building material, was little if at all known to the ancients, and its introduction alone has been productive of comforts and elegancies to which the most refined of the Greeks and Romans were utter strangers. Their oiled paper, transpa- rent horn, talc, shells, and linen, would now, even to an English peasant, appear a miserable expe- dient. For an account of its manufacture, and application to architectural purposes, see GLASS. Besides the materials which have already been enumerated as composing the principal members, as walls, roofs, floors, doors, windows, chimneys, stairs, and pavements; hair is also necessary in the composition of mortar for plastering the surface of walls and ceilings; likewise various paints and papers, for covering them and other parts of the work; all which are described, with the modes of applying them, in their proper places. This article, as well as that in INDIAN ARCHI- TECTURE, has been, by permission, extracted from the Edinburgh Encyclopedia, now publish- ing by Dr. Brewster. The acknowledgment of the latter article was inadvertently omitted in its proper place, and the Author therefore embraces this opportunity of stating it as his opinion, that much pains have been taken by the writer, Mr. Telford, the Engineer, in selecting and arranging this curious and interesting subject, which has never before appeared in so full and connected 3 form. MATHEMATICS (from the Greek yuanammt) the science which treats of the ratio and comparison of quantities, whence it is defined the science of ratios; some writers call it the science qf quan- tities, but this is inaccurate,since quantities them- selves are not the subject of mathematical in- vestigation, but the ratio which such quantities bear to each other. MA'I‘ 279 MAT W The term mathematics is derived from ”new, mathesis, discipline, science, representing with justness and precision the high idea that we ought to form of this branch of human know- ledge. In fact, mathematics are a methodical concatenation of principles,reasonings, and con- clusions, always accompanied by certainty, as the truth is always evident, an advantage that parti- cularly characterizes accurate knowledge and the true sciences, with which we must be careful not to associate mataphysical notions, conjectures, nor even the strongest probabilities. The subjects of mathematics are the comparisons of magnitude, as numbers, velocity, distance, 8Lc. Thus, geometry considers the relative magnitude and extension of bodies; astronomy, the relative velocities and distances of the planets; mechanics, the relative powers and force of different machines, Sic. 8Lc. some determinate quantity being fixed upon in all cases, as a standard of measure. The study of mathematics is highly useful to the architect, particularly arithmetic, geometry, men- suration, and mechanics. Geometry enables him to take his dimensions under the most difficult circumstances, and to lay out the various parts of his design, while it furnishes him with rules for ex- ecuting the same. Mensuration is the applica- tion of arithmetic to geometry, and shews him how to find the exact proportion of his labour, according to the difficulty of executing a certain uniform portion of a work, and to estimate the quantity of materials employed therein: that branch of mathematics called mechanics, enables him to compute the strength and strain of the materials he employs. In short, without the aid of mathematics, he is unfit for his profession, and the more he understands, the fewer difficulties he will have to encounter in the prosecution of his art. Mathematics are naturally divided into two classes; the one comprehending what we call pure and abstract; and the other the compound or mixed. Pure mathematics relate to magnitudes generally, simply, and abstractedly, and are there- fore founded on the elementary ideas of quantity. Under this class are included arithmetic, or the art of computation; geometry, or the science of mensuration and comparison of extensions of every kind; analysis, or the comparison of mag- nitudes in general; to which we may add geome- trical analysis, which is a combination of the two latter. Mixed mathematics are certain parts of physics, which are, by their nature, susceptible of being submitted to mathematical investiga- tion. We here borrow from incontestible expe- riments, or otherwise suppose bodies to possess some principal and necessary quality, and then, by a methodical and demonstrative chain of rea- soning, deduce from the principles established conclusions as evident and certain as those which pure mathematics draw immediately from axioms and definitions, observing, that these results are always given with reference to the experiments on which they are founded, or the hypothesis which furnished the first datum. To illustrate this by an example: numberless experiments have shewn us, that all bodies near the earth’s surface fall with an accelerated velocity, and that the spaces passed through are as the squares of the time they haveoccupied in falling. This, then, the mathematician considers as a necessary and essential quality of matter, and with this datum he proceeds to examine what will be the velocity of a body after any given time, in what time it will have acquireda given velocity, what time is necessary for it to have generated a given space, 8Lc. and in all these investigations his conclusions are as certain and indisputable as any of those which geometry deduces from self-evident truths and definitions. Again, in optics, having estab- lished it as a principle of light, that it is trans- mitted in right lines while no obstacle is opposed to the passage of the rays; that when they become reflected, the angle of incidence is equal to the angle of reflection; that in passing from one medium to another, of different density, they fly off from their first direction, but still follow a certain geometrical law; these principles, or qualities of light, being once admitted, whatever may be its nature, be it material or imma- terial, or whatever may be the medium through which it passes, or the surface by which it is reflected, are matters totally indifferent to the . mathematician; he considers the rays only as right lines, the surfaces on which they impinge as geometrical planes, of which the form only enters into his investigation: and from this point all his inquiries are purely geometrical, his inves- tigation clear and perspicuous, and his deduction evident and satisfactory. To this class of mathe- matics belong mechanics, or the science of equi- librium and motion of solid bodies; hydrodyna- MAT 280 mics, in which the equilibrium and motion of fluids are considered ; astronomy, which relates to the motion, masses, distance, and densities, of the heavenly bodies; optics, or the theory and effects of light; and, lastly, acoustics, or theory of sounds. Such are the subjects that fall under the con- templation of the mathematician, and, as far as a knowledge of these may be considered bene- ficial to mankind, so far, at least, the utility of the science on which they depend must be ad- mitted. It is not, however, the application of mathematics to the various purposes of society, that constitutes their particular excellency; it is their operation upon the mind, the vigour they impart to our intellectual faculties, and the dis- cipline which they impose upon our wandering reason. “The mathematics,” says Dr. Barrow, “ effectually exercise, not vainly del-ude, nor vexa— tiously torment studious minds with obscure subtilties, but plainly demonstrate every thing within their reach, draw certain conclusions, in- struct by profitables rules, and unfold pleasant questions. These disciplines also inure and cor- roborate the mind to a constant diligence in study; they wholly deliver us from a credulous simplicity, and most strongly fortify us against the vanity of scepticism ; they efi'ectually restrain us from a rash presumption, most easilyincline us to a due assent, and perfectly subject us to the government of right reason. While the mind is abstracted and elevated from sensible matter, it distinctly views pure forms, conceives the beauty of ideas, and investigates the harmony of propor- tions; the manners themselves are sensibly cor— rected and improved, the affections composed and rectified, the fancy calmed and settled, and the understanding raised and excited to more divine contemplations.” LIST of the most celebrated MATHEMATiCiANs, with the Names of their WORKS, or the SCI ENCES in which they were eminent, and the Co UNTRI ES where they flourished; chrono- logically arranged. B C NM”: SCIENCE. counter. 960 Chiron the Centaur - Astronomy .- - - . - .. . - - ~ - - Thessaly 747 Era rfNabonassar. . . ....... .. ... .. . . . . ... . . Babylon 722 Confucms it'll-u. . Ethics. .. ....ooo- .. nun. China 600 Thales- . - . - . - - - - .. Prediction of an Eclipse - . Greece Anaximander . - - . . - Celestial Globes- - . - - - - - - - Ditto 500 Cleostratus- - Astronomy . . . . . . . .. . . . . ~Ditto Anaxagoras - - - - - -Philosophy - - - . - - - - - ' ~ - . Ditto Anaximenes.......‘Su11-dja1...... - nos... no. Ditto Pythagoras . - - . . - - . 47 Eu. System of Astronomy Ditto MAT _7_ L g B C. NAME. acumen. ooux'rnr. 400 Euctemon - - - - - - - - Astronomy ------- . ------ Greece Meton- ----------- Metonic ('ycle -------- -- Ditto Plato . - - - - - - - - . . - Geometry and Philosophy“ Ditto Hippocrates . . - - - - - Quadrant of Lanes ------- Ditto mnopides . a o o a o o . . Geometry o s ....... . ..... Ditto Zomdorus . - o o . . u - Ditto ......... o o a o o ..... Ditto 300 Aristotle - - - - . - - - - . Philosophy ------ - - - . - . - - Ditto -Calippus neg-cocoon Astronomy cocoon-oOu-aoo Ditto Dinocrates - . . - - - - - Architecture - - - . - - - - . - - - Ditto Theophrastus - - . . . - History and Mathematics - - Ditto Xenocrates - - - . - - - . Architecture -------- - - - - Ditto Eudoxus - - - - - - - - - - Geometry and Astronomy - - Ditto PytheaSo . - - «- - . . - - - Navigation and Astronomy . Gaul Archytas - - - - . - - - . - Mathematics andPhilosophy Greece Arlstaaus - - - - . . - - - . Conic Sections ------- - . - . - Ditto Dinostratus - - . ~ - - ~Quadratix .. - - - . - - . - ~ - - ~ Ditto Menechmug ....... 0 Geometry . o o . . . .v . . . . . . Ditto 200 Apollonius ----- - - - Geometry & Conic Sections Ditto Archimedes- - - - - - - - Geometry and Mechanics - - Sicily Aristarchus- - - . - - - Astronomy ------------ Greece Eratosthenes- - - - - - . Measure of a Degree ------ Ditto - Elements of eometr Euchd «nu-Hug andOptics .......... ¥.§Ditto Aratus - - - - ----- - . Poetry and Astronomy - - - - Ditto Aristillus --------- - Philosophy and Astronomy . Ditto Nicomed-es . - - - - - - - Conchoid -. ------ N~ ------ Ditto . Length of Year, umber . 100 Hipparchus - ~ - . - . g ofthe Stars . . . . . _ . . . _ Ditto Ctesibius .......... Water Pumps ...... . . o ... . Ditto Hero ------------ . Hero’s Foun. Clepsydra - - - Egypt Manilins - . - - - - - . - - Poetry and Astronomy - - - - Rome Manlius ----- - ----- - Astronomy ----------- - . - Ditto 0 Julius Czesar- - - - - - . Calendar reformed- - - . . . - . Ditto Sogigenes . . . . . . . . 9 Astronomy .............. Egypt Posidunius - - . - . - - - Mechanics and Mathematics Rome ’i‘heodosius . . . . . . . . Spherics . . ........ . . . - . . Ditto 0 Cleomedes - - - - . . - - Astronomy - ----- - - - . - . - Ditto Geminus - - - - - - - - ~ - Geometry and Astronomy- - Rhodes Vitruvius -------- Architecture - - ~ - - ------- - Rome l\Ienelaus - . - - - - - - Spherical Trigonometry . - - - Ditto Jamblicus ------ . - - Philostuphy - - - . . - ~ ------ Syria. 100 Frontinus (Sixtus) . ~ Enginery - - - - . - . - - - - - . - - Rome Nicomachus ------ - Mathematics - - - - - - - - - - - - Greece Hypsicles o . ...... .Ditto ...... . . . . . . . . . . . . Ditto Ptolemy .......... Aimagest. . . ..-........ .. Egypt 200 Diophantus ------- Diophan. Analysis~ - . . ~ - - - Greece 300 Jamblicus ------ - - - Philosophy ------- - - - - - - . Syria Pappus ------ - - - . - Geometrical Loci - - - . - ~ - - Greece Theo“ ...... s . . . . . Philosophy 0 . . . c . . . n o . . . Dino 400 Hypati, daughter of Theou . . . ..... Proclus - - - ~ ~ - - - - - Commentary on Euclid- - - . Ditto Diocies . . . o u ...... Cissoid . . . . . .......... o Ditto Sere11us.........u Geometry. ........ ...... Ditto 500 Mai-inns colonic-cl Dino ...... .c... ecu... Naples Anthemius- - . - . - - - . Architecture; Domes- - - - . - Rome Entocius .......... Geometry ........ ...... Greece Isidorus - - . - . - - - ~ . Architecture .. - - - - ~ - - - - - Rome 600 The Venerable Beda ------ - - - - . . ~ . - - - - . - - - England 642 Alesandrian Library destroyed 4 ”00 Almansor, the Vic [Oi-ions .....-. Hero the Youngeru Geometry . - - - . ~ . -- - - - - - Greece 800 Almaimon, Calif- - - - Astronomy - - - - - ~ - - ~ ~ . - . . Arabia ‘Kirasched . ...... . 0 Ditto ...... o . .......... Persia, Alfragan.......... Ditto ........-...---... Arabia, Albgtegui.. ...... o Ditto ~.....--...--..... Ditto Thebit Ibn Chora--- Ditto ................ Ditto 900 (Gebert) Silvester II. Mathematics - - ~ - - - - - - - - - Spain 1000 Ibn Ionis ......... Astronomy -----'----~--o Arabia Geber Ben Alpha - Comment on Almagest - - ~ - Ditto Commentary on Diophanes Ditto A5tr0n0my"' soon. as. o u u o Saracen 1100 Alhazen ------- ~ - - Optics and Astronomy - . - - Ditto 1200 Leonard (de Pisa)” First European Algebraistn Italy Nassir Eddin ------- Astronomy . - - - . - - . . . . . - - Persia Alphonso, King of ' . . ‘ ' ' . . . Castile . . . _ . ‘ . . ; Alphonsine Tables Spam MAT 281 M AT ,___f — I AD. NAME. SCIENCE. COUNTRY. A.D. NAME. COUNTRY. A.D. NAME. COUNTRY. 1200 Halifax, or Sacro- 1500 Byrgius ---- Italy 1700 Gravesande - Holland b0560'---~-~- .gMathcmatics .~......oroao England JordanusNemorarius Mathematics - Bacon-- ...... .... Philosophy "nun“... Campanus - - ~ - - - - - Theory of Planets Vitella and Pecam. - Optics England 1300 Albano - - - - - . - - ~ . - Physic and Mathematics. . . Italy Ascoli - -- .. . - ~ - - - - 1\Iathematics - - - - - ~ . - - - n Ditto John of Saxony - - - - Astronomy 1400 Bianchini ......... Ditto . . . .. . . u . . . . . . o o - - Ditto Moscholpulus, Mod. Magic Square- - - . ~ - - - - . . ~ Greece Purbach ------ - - . . - Astronomy - - - . . . . . . - . . - - Vienna Regiomontanus .... Ditto .................. Ditto Cusa, Cardinal ----- Astronomy Henry,Duke ofVisco Sea Charts Uleugh Beigh,Prince Astronomy - - - ~ - - - - - - - - - . Tartary BernardofGi-anolachi Ditto Lucas dc Burgo . - - - Geometry and Algebra Novera, Dominic - - - Astronomy - - - - ----- - . - - - Italy 1300 Copernicus ~ - . ----- System of Astronomy - - - - - Germany Apian, Peter - - - - - . Mathematics and Cosmogony Ditto Apian, Philip ... .. Sun-dials .... ~--------- - - Ditto Buteo too~----o..o Geometry ...........u.-. France Cardan-... ....... Ditto ..... ...... ..... ..Ita]y Commandine - . . . . - Mathematics ----- -- - - - . - - Ditto Durer, Albert- - - - - - Geometry and Perspective - - Germany Vieta ---------- . - Angular Sections -------- France Brahe, Tycho ------ Astronomy - - . . - - . - - - ~ - - - Denmark Bacon, Lord Francis Philosophy - - - - - - ’ - - . - - - . England Galileo - - - - - , . - - - . Law of falling Bodies - . - - - Italy - Present 5 stem of L0 a- 1600 Briggs ..........3 rithms {yum}; g England Des Cartes - - - - - - - - Equation of Curve Lines - - France Kepler - - - . . . - . . - - Laws of Celestial Motions. . Germany Napier . . - . o n . . . . . . Logaritiims - . o ....... . \ . 0 Scotland Torricelli . - - - - - - - . Gravity of the Atmosphere Italy Cavalerius- - - - . - - - . Indivisibles- . - . - . - . . . - . - - Milan Brounker- . . ~ - - ' - - - Continued Fractions ------ Ireland Fermatu . . . . . . . _ . . gMait. et Min. Theory of Lumbers ..... o....-. Pascal - - - - . - . - - - - ~ Doctrine of Probabilities . . Ditto Wallis - . . - - - - - - - - - Arithmetic of Infinites . - - - England Bernouilli, James - - Mathematics - - - - - - - - - . - - Swiss Barrow ...........‘Di[to ...... ..... an... England Hooke - - - .. - - . . . . . Philosophy and Mechanics. Ditto Huygens - ' - - - Evolute of Curves - - - - . - n Holland Leibnitz o---'----- DiffCalcnlus..-.--on.-o. Germany L’Hopital - - - - - . - - - Mathematics . - . - - - - . - . - - France Roemer, Dan. - . - . - - Progressive Motion of Light Denmark 1700 Newton, Sir‘J. - - - - ~ Various - - - - - ~ - - . ------- England Bernouilli, John- - - - Mathematics - - - - - - - . - - - . Swiss Bradley .. - - - - . . - ' Aberration of the Stars . - - - England Cotes .o.-........ luathemarics ........o--. Ditto 'raylor c....o.... , Increments....oo.--....u Ditto Clairaut- - - - - - . - . - - Mathematics - - ~ - . - - .. . -- France Llaclanrin.. ....... Ditto .n........--oaco.. Scotland De Moivre ........ Ditto ...-........u.... England Simpson ...... u... Ditto -.-.............-. Ditto D‘Alembert - - . - - - . Partial Ditferences- - France Euler ~ . - - - - . Mathematics: - - - . . . - . r . - - Germany Landon . - - Residual Analysis - - - - - - - - England W'aring - - - - - Mathematics . - - . - - . - - - - . - Ditto ‘ France In...) lieu. Inevita- Besidcs the foregoing, who were mostly celebrated in the branches affixed to their names, the following were so multifarious in their studies and productions, that it would be injustice to their talents to give a preference by noticing any one to the exclusion of the rest. We therefore merely subjoin a list of their names, and the countries in which they were born. A.D. rune. COUNTRY. 1500 Maurolycus- . Sicily Nonius. . . . . . Portugal Sturrnius . . - . France Tartaglia - . - . Venice Werner ' - - . Germany Ferrari . . . . . Italy Mercator . . - Denmark V0 L. H. A.D. saute. COUNTRY. 1500 Ramus - - . - - France Records - . . - Ditto Reinhold - - - Germany Rothman- - - - Ditto Stifi‘elius .. - . Ditto Ubaldi Guido Italy Porta, Baptista Naples 1600 1700 Billi, De ' - . - Clavius . . - - . Ditto Castel - o 0 I Q C France Bayer ----- - Prussia. Beauregard- . France Beaume, De- Italy De Dominis- . Ditto Gassendi - - - - France Gellibrand - - England Gundling - .. Germany Halifax, or Longomon- Denmark tanus ----- Harriot ------ England Horrox- - - . - . Ditto Kircher - - ~ ~ Germany LucasValerius Italy Metius ------ Holland Oughtred - ~ . England Pitiscus,Bar- thelemi - - E Germany Romanus- - - - Flanders 'Ursinus ~ . - - - Germany Bartholin - - ~ Denmark Borelli - - - - - Naples Bullialdus Dechales - .. Savoy Frenicle - ~ . . France Girard, Albert Holland Gregory, J. and D. - - Henrion ~ - ~ - France Hevelius - - . - Poland Horrebow . - Denmark Mersennus ~ ~ France Riccioli - - - - Italy Roberval -- - France Slusius ------ Flanders Snellius, R. and W. .. Holland Tacquet - - - - France Tchirnhausen Vincent, St. Gre Viviani . - - - - Tuscany Vlacq Ward, Seth- - England Witt, John de Holland Amontons - . - France Auzout - . . - - Ditto Bachet - - - . . Ditto Fagnani . . - . Italy Flamsteed - - England Grimaldi- - - . Italy Guido Grandi Ditto Hudde - . . . - . Holland Keri - . - - - - - Hungary Kinghuysen Lagnay - - . - Lieutard ' - . - Meraldi . . - . lMolyneux . . Oldenburgh . Ozanam - . - - Pall-n...“ Picart----u Reyneau . - . Schooten - - - - \Vren s England France Ditto Italy Ireland Bremen France England France Ditto Holland England France Brackenridge England Cassini D T. and J.)( - - l\1ce Craig, J. ---- Scotland not... MENTS. '20 MATHEMATICAL INSTRUMENTS, Hire Philip; France -- Scotland France Laloubere Lomsberg Manfredi . - - Italy Marchetti - ~ Ditto Meibomius ~ - Germany D’Omerique,H France Pemberton - - England Prestet ----- France Saunderson- . England Saurin . - - - - - France Sterling - - - - Scotland Ulloa- - - - . - - Spain Varignon- . u France Verbiest VVolfius - . . . . Prussia Bellidor Bernouilli, Jas. John, E Swiss and Daniel Bougainville France Boguer De la Caille - Clarke, Dr. S. Collins. - . - ~- Courtivron - - Cramer - . . - . Dodson - ~ - ~ - Dollond . . . - Fatio Fountain- - - - England Goldbach Guisnée Herma Halley Jacquier - - - - Koenig . . . o . Long . . . . . . . M‘Laurin - . . Mairan . - - - . Mariette - - - - Maupertuis- - Mayer- - . - - - Germany Montmort - - - France Nicole - - - . - . Ditto Riccati - - - - - Italy Robins ' Simson - . - . - England Walmsley Agnesia,Donna Spain Atwood . - - - England Bailly o - o A o I France Bezout Ditto Borda - . . . . . Ditto Carnot . - - ' - Ditto Emerson .. .. England Horsley Ditto Harris - - - - . - Ditto Herschel . .. Ditto Kestner Lalande Maskelyne - - Montucla . - - Pingre- . . . . . Robison . - - - Steward - . - ~ Vandermond Vega Wargentin France England Ditto France Geneva England Ditto Swiss England France Swiss France Scotland France Ditto Ditto 04-. France Ditto Ditto Ditto Scotland Ditto see INSTRU- MBA 282 MEASURE (from the Latin mensura) in geometry, any certain quantity assumed as one, or unity, to which the ratio of other homogeneous or similar quantities is ex pressed. This definition is somewhat more agreeable to practice than that of Euclid, who defines measure as “ a quantity, which being repeated any number of times, becomes equal to another ;” which only answers to the idea of an arithmetical measure, or quota part. p MEASURE OF AN ANGLE, an arc described from the vertex in any place between its legs. ‘Hence angles are distinguished by the ratio of the arcs, described from the vertex between the legs, to the peripheries. Angles then are distinguished by those arcs ; and the arcs are distinguished by their ratio to the periphery. See ANGLE. It is, however, in many cases, a more simple and more convenient method to estimate angles, not by the arcs subtending them, but by their Sines, or the perpendicular falling from one leg to the other. Thus it is usual, among those who level ground, to say that the ground rises or falls one foot, or one yard, in ten, when the sine of the angle of its inclination to the horizon is one-tenthofthe radius. Angles of different magnitudes are indeed proportional to the arcs, and not to the Sines, so that in this sense the sine is not a true measure of the comparative magnitude of the angle; but in making calculations, we are more frequently obliged to employ the sine or cosine of an angle than the angle or are itself. Nevertheless, it is easy to pass from one of these elements to the other by means either of trigonometrical tables, or of the scales engraved on the sector. MEASURE OF A F1GURE, 0R PLANE SURFACE, a square, whose side is one inch, foot, yard, or other determinate length. Among geometricians, it is usually a rod, called a square rod, divided into ten square feet, and the square feet into square digits; Hence square measures. See MENSURATION. MEASURE or A LINE, any right line taken at pleasure, and considered as unity. MEASURES, Line qf, see LINE. MEASURE OF THE MASS, 0R QUANTITY OF MATTER, in mechanics, is its weight; it being apparent, that all the matter which coheres and moves with a body, gravitates with it; and it being found by experiment, that the gravities MEA M of homogeneal bodies are in proportion to their bulks: hence, while the mass continues the same, the absolute weight will be the same, whatever be its figure: but, as to its specific weight, it varies as the quantity of surface varies. See VVEXGHT. MEASURE OF A NUMBER, in arithmetic, a num- ber which divides another, without leaving any fraction; thus 9 is a measure of 27. MEASURE OF A SOLID, a cube, whose side is one inch, foot, yard, or other determined length. Among geometricians, it is sometimes a rod, or perch, called a cubic perck; divided into cubic feet, digits, Sac. Hence cubic measures, or mea- sures of capacity. See CUBE and MENSU- RATION. MEASURE OF VELOCITY, in mechanics, the space passed over by a moving body in any given time. To measure a velocity, therefore, the Space must be divided into as many equal parts as the time is conceived to be divided into. The quantity of space answering to such an interval of time, is the measure of the velocity. MEASURE, Universal and Perpetual, a kind of mea- sure unalterable by time, to which the measures of different nations and ages might be reduced, and by which they might be compared and estimated. Such a measure is very desirable, if it could be at. tained. Huygens, in his Horol. Oscill. proposes, for this purpose, thelength of a pendulum, vibrat- ing seconds, taken from the point of suspension to the point of oscillation. The third part of such a pendulum may be called the horary foot, and serve as a standard to which the measure of all other feet may be referred. Thus, 1). g. the pro- portion of the Paris foot to the horary foot would be that of 864 to 881 ; because the length of three Paris feet is 864 half lines, and the length of a pendulum, vibrating seconds, contains 3 horar feet, or 3 feet 8%.: lines, 1'. e. 88] half lines. But this measure, in order to its being universal, sup- poses, that the action of gravity is every where the same, which is contrary to fact; and, therefore, it would really serve only for places under the same parallel of latitude; and in order to its being perpetual, it supposes that the action of gravity continues always the same in the same place. MEASURE, in a legal, commercial, and popular sense, denotes a certain quantity or proportion of any thing bought, sold, valued, or the like. It denotes also a vessel of capacity employed in MBA measuring grain and other articles: the fourth part of a peck. The regulation of weights and measures ought to be universally the same throughout the kingdom, and should, therefore, be reduced to some fixed rule or standard; the prerogative of fixing which was vested, by our antient law, in the crown. This standard was originally kept at Winchester; and we find, in the laws of King Edgar, cap. 8, neara century before the Conquest, an injunction, that the one measure, which was kept at W in- chester, should be observed throughout the realm. I‘Vith respect to measures of length, our ancient historians (VVil.-Malm. in Vita. Hen. I. Spelm. Hen. I. apucl Wilkins, 999.) informius, that a new standard of longitudinal measure was ascertained by King Henry I. who commanded that the ulna, or ancient ell, which answers to the modern yard, should be made of the exact length of his own arm: and one standard of measures of length being once gained, all others are, easily derived from hence; those of greater length by multi- plying, those of less by subdividing the original standard. Thus, by the statute, called “ Com- positio ulnarum ct perticarum,” 55% yards make a perch; and the yard is subdivided into 3 feet, and each foot into 12 inches; which inches will be each of the length of 3 grains of barley. The standard of weights was originally taken from corns of wheat, whence the lowest denomination of weights which we have is still. expressed by a “grain 5” 32 of which are directed by the statute, called “ Compositio mensurarum,” to compose a pennyweight, of which 20 make an ounce, 12 ounces a pound, and so upwards. Upon these principles the standards were first made; which, being originally so fixed by the crown, their sub- sequent regulations have been generally made by the king in parliament. Thus, under King Richard I. in his parliament liolden at VVest- minster, A.D. 1197, it was ordained that there should be only one weight and one measure throughout the kingdom, and that the custody of the assize or standard of weights and measures should be committed to certain persons, in every city and borough. In King John’s time, this ordi- nance of King Richard was frequently dispensed with for money (Hoved. A.D. 1201); which occa- sioned a provision to be made for enforcing it, in the great charters of King John and his son. Stat. 9 Hen. 111. c. 25. MEA The statute of ZlIagua Charta, cap. 25,.ordains, that there shall be but one measure throughout . England, according to the standard in the Ex- chequer; which standard was formerly kept in the king’s palace; and in all cities, market-towns, and villages, it was kept in the churches. (4~ Inst. 273.) By 16 Car. I. cap. 19, there is to be one weight and measure, and one yard, accord- ing to the king’s standard; and whoever shall keep any other weight or measure, whereby any thing is bought or“ sold, shall forfeit for every offence five shillings. And by 22 Car. II. cap. 8, water measure, (viz. five peeks to the bushel,) as to corn or grain, or salt, is declared to be within the statute 16 Car. I. And if any sell grain or salt, See. by any other bushel, or measure, than what is agreeable to the standard in the Ex- chequer, commonly called Winchester measure, he shall forfeit 403. Sec. (22 Car. II. c. 8. 22 and 23 Car. II. c. 12.) Notwithstanding these sta- tutes, in many places and counties there are different measures of corn and grain; and the bushel in one place is larger than in another; but the lawfulness of it is not well to be accounted for, since custom or prescription is not allowed to be good against a statute. There are three different measures in England, viz. one for wine, one for ale and beer, and one for corn. In the measure of wine, 8 pints make a gallon, 8 gallons a firkin, 16 gallons a kilder- kin, half barrel or rundlet, 4 firkins a barrel, 9 barrels a hogshead, 9 hogsheads a pipe, and '2 pipes a tun. (Stat. 15 R.II. c.4. 11 H. VII. c. 4. 12 H. VII. c. 5.) In a measure of corn, 8 pounds or pints of wheat make the gallon, 4 gallons a peck, 4 pecks a bushel, 4 bushels a sack, and 8 bushels a quarter, 8L0. And in long measure, 3 barley-corns in length make an inch, 12 inches a foot, 3 feet a yard, 3 feet and 9 inches an ell, and 5% yards or 16% feet, make the perch, pole, or rod. (Stat. 72 Edw.III. c. 10). Selling by false measure, being an offence by the common law, may be punished by fine, Ste. upon an indictment at common law, as well as by statute. MEASURES are various, according to the various kinds and dimensions of the things measured. Hence arise lineal or longitudinal measures for lines or lengths: square measures for areas or superficies: and solid or cubic measures for bodies and their capacities. All these again are very different in different countries, and in differs 9.. o ‘2. MBA r em ages, and even many of them for different commodities. Whence arise other divisions of domestic and foreign measures, ancient and modern, dry and liquid measures, 8w. Under this head the reader will find enumerated and exhibited in tables, the various general stand- ing measures, long, square, and cubic, now Or heretofore in use, with their proportions and re- ductions. Tables of dz‘jflrent IlIeasures, according to various Authorities, reduced to English measurement. LONG MEASURES. TABLE I.—-—SCRIPTURE LONG MEASURES. English Ft. In. 1 Digit..= o 0.912 4 Digits..= 1Palm....................= o 3.648 3 Palms”: 1Span*................... = 0 10,944 2 Spans-- = 1Cubittun-..-..........- = 1 9.888 4. CllbltS" = 1Fath0m- ....... .c.....-.o = 7 3,552 11 Fathoms = 1 Reed (Ezekiel’s) ------ .... =2 10 11.328 13‘; Reeds~~ = 1 Pole(Arabian)-u-n-u-a- = 14 7.104 10 Poles... = 1 Seasons, orMeasuring 1ine--- = 145 1.104 * The Orientals used another span, equal to one-fourth of a cubit. 'I' See Table II. TABLE II.——JEWISH LONG, OR ITINERARY s . English MEA URES Miles.Paces.Feet. 1cubit‘D"""""""""""""“ = 0 O 1_824, 400 Cubits-v-u-n- = lstadium ...... = 0145 4.6 5Stadii.......... = 1 Sabbath day’s } = 0 729 30 Journey - - - 2 Sab. days’journ. = 1 Eastern Mile. .. = 1 403 1.0 3 Eastern miles. . . == 1 Parasang ..... . = 4 153 3.0 8 Parasangs - - . . . . = 1 Day’s journey . -' = 33 172 4.0 "‘ Dr. Hutton reckons the Hebrew cubit as follow: Eng. feet. COInmoncubit....oguuollcunoiucoc-ovio = 1.817 Sacred cubit........................... = 2.002 Great cubit = 6 common cubits ......... = 10.902 The Hebrew foot, according to Dr. Hutton, was equal to 1.212 English foot. TABLE III.—-GREC1AN LONG MEASURES. English Pa. F. Inches. 1 Dactylus, or Digit- - .. r - - - ~ - -» - - . ----- = 0 0 0.7554% 4 Dactyli-uu-u- = 1 Doron, or g Dochme, or = 0 0 30218;,- Palesta 27:- Palestm, &C.I 0 o o u = 1 LlChaS """" =: 0 0 7.554637- 1—% Lichas . . .. . .. . . = 1 Orthodoron- - _-.= O 0 8.31013?6 11% Orthodoron . . . . . =—. 1 Spithame- - » - =-. 0 0 9.065631 1%. Spithame - o o a - n o z: 1 P0115, 01' F00t* = 0 1 0.0875 11' P0u5,0 n o n a u o n a - u = 1 Pygme,0r cubit: O 1 1.5984»; 1; Pygmetonest-uvo= 1%yg0n-000-o= 013-109;;- 11P on..........= 1 cous,or __ a r b yg Larger cubit; “ O 1 6'1012" 4 Pecus........... .-=-_ 1 Orgya,orPace= 0 6 0.525 100 Orgya, or Paces. . . = 1 Stadium,‘Au- ; = 100 4 4-5 lus. or Purl. 1 Million, orMile=u 805 5 0 Eng. jbot. 8 Stadll, &COOcoooIo " The Greek foot is variously estimated; thus: I] ByDr.Hutt0n+...--o.ov-..u.-...... = 1.009 By Folks, who reckons it equal to 17‘; g __ g 1.006 Romanfoot UIIOCDIIaoooII-I'otltso — 1.007 ByCavallo....-.-.o--P-.-1.............= 1.007 hy eterian foot ~ - - = 1.167 't Dr.Huttonreckonsthe Macedonian foot--- = 1.160 28.4 MEA N.B. Two sorts of long measures were used in Greece, viz. the Olympzc and the Pythic: the former in I’eloponnesus, Attica, Si- cily, and the Greek cities in Italy; Illyria, Phocis, Thrace, The Olympic foot, (properly called Greek,) contains, according to The Pythic foot (called also natural foot.) contains, according to Hence it appears, that The Olympic stadium is 201% English yards, nearly. The Pythic or Delphic stadium, 162;:— yards, nearly. And the other measures in proportion. The Phyleteriau foot is the Pythic cubit, or 1% Pythic foot. The Macedonian foot was 13.92 English inches. The Sicilian foot of Archimedes, 8.76 English inches. Dr. Hut the latter in Thessaly. and at Marseilles in Gaul. Eng. In. ton 12 . 108 Folkes 12.072 Cavallo 12.084 Dr. Hutton 9.768 g Paucton 9.731 TABLE IV.—ROMAN LONG MEASURES. English Paces. Ft. Inches. 6 Scrupula - ~ - 8 Scrupula - . . 1% Duellum - - - 1 Sicilicum. 1 Duellnm. 1 Seminaria. 18 Scrupula . . . =2 1 Digitustransversus = 0 0 0.725% 1%— Digiti - - ... = 1 Uncia, or Inch -- = 0 0 0.967 3 Uncize - . - - . = 1 Palma Minor - . - - = 0 O 2.901 4 Palmaa-uu = 1 Pes, or Foot“ ... = 0 0 11.604 1% Pes, or Foot = 1 Palmipes = 0 1 2.505 1% Palmipes... :x: 1Cubit.......... = 0 1 5.406 1% CubitSH-o- =1Gradus..-...... = 0 2 5.01 2 Gradus---- =1Passus----n---- = 0 4: 10.02 2 Passus - - . - . = 1 Decempeda - - - - - = 1 4 8.04: 125 Passus-nu = IStadium........ = 120 4 4.5 8 Stadii. . . . . . = 1 Milliare, or Mile 1‘ = 967 0 O "' The length of the Roman foot, in English inches, is stated by various writers, as follows: Eng. In. By Bernard no.ucocoousooouoa-o.o-uoc-IloouuaI-a' 11.640 ByPicard andHutton ....... .o..-...-.---.u..-..... 11.604 ByFOlkes ..... o .......... onllooouoclotoo-o-OOIOII 11.592 By Rape]- (before Titus) . . . . . . ....... . n n ‘ . ...... .. . 11.640 By the same (afler Titus) ....... . . . a . . . . .-o . ........ 11 .580 By Schuckburgh, fr01n rules 0 .......... u n o u o . . o . u - . . 11.6064 Bythesame,frombuildings-nu-nun-u----~-11.6172 By the same, from a tomb-stone - ~ - - - - - - - 11 .6352 Hence, 11.6 English inches seem to be a medium 5 and, therefore, the Roman mile = 1611 English yards, being 149 yards less than the English mile. Colo-0.....- Its Proportion to the English Foot is thus stated :— Befnre Titus .970 By Bernard - - . - - - -970 By Rape” 3 After Titus- - .965 . From Rules .9672 ByGiffé‘: and S .976 By Shuckburgh From Build. .9681 ' ' ‘ ' From a Stone .9696 ByFolkeS l '32? ByDr. Huncn.............. .967 + The Roman mile of Pliny (according to Cavallo) contained 4840.5. English feet; and that of Straho 4903. TABLE V.-—-ANCIENT LONG MEASURES, ACCORDING TO DR. HU.TTON. E71g.Feet. ‘ArabianfootsnoI-ooouucntaoauocoyote-Oeooe-oe= 1_095 . __ 1.144. Babylonianfoot ....... .............. ........ _§l.135 Drusianfoot”..u.n.u...o..-................. = 1.090 Egyptianfoot-............................. = 1491 ______5tadium..-.... ....... .........-....= 7508 Naturztlfoot...... ..... ........-.. ...... H. a .814, Ptolemaic = the Greek foot (see Table III.) Sicilian foot of Archimedes ...... .............. =: .730 M EA 2 LI! MEA EM TABLE Vl.—-ENGLISH LONG MEASURES. 3 Barleycorns...u.-........... 111161,. 2% Inches...o---u-.-.....oun.. lNail. 3 Inchesunu.........-...... IPahn. 4. Inches....-......A.o-..uo.n. IHand. 7.92Incheso-uu-u'............ 1Link. 9 Inches -- 5 Quarters.............. 1 Quarter (of a Yard.) 1 Ell. ll ll ll ll II II ll ll ll ll ll ll II II II ll ll 3 Palms................nu... 1Span. 1% Spans (or 12 Inches) . . ~ - - .. - . - 1 Fbot. 1.2. Foot u-. ...... ............. 1011b“. 2 Cubits(or3Feet)~------~--u 1Yard. 13311311113... ...... .n-u..-..-.... lPace, 22 Yards...o...o......o-..--n.. 1Chaiu. 11 Paces (or2Yards)---------~-- 11"athom. 2,,— Fathoms (or 16% Feet)--------- IRod,Pole, or Perch. 40 Poles,&c.--------- ..... ....o- lFurlong. 8 Furlongs.no.n'c-~o-uqu-cuoal lMlle. TABLE VII.——SCOTTISII LONG MEASURES. Eng. Inches. AnE”......-..oo. ............ .......-.....= 37,2 AFallo-u .............. s...-.......o...o-.-= 223,2 AFurlong....'..-.ouao.. ......... ...... ..... =: 8928. Ahlile ..... onloontnlln-il ----- IOIOOOOIIOQO;=71424I ALink-ao ........... ooooI-Iottnot'O-I-ooolo= 8.928 Achain’ orshortnpod .......... ..-.--...---u = 892.8 ALongRood......o...oo-....ou....n..a.-..- = 1339.2 TABLE VIlI.—-FRENCII LONG MEASURES, BEFORE THE REVOLUTION. Eng. Inches. APointu-n-on-uu = .0148025, ornearly 7%. A Line ----- .......... = .088815, or nearly 5%. An Inch, or POUCe . - . . - = 1 .06578, 01', 33—575, 01-13%. A Foot ............... = 12 , 78933 An E“, or Aune“ ----- . = 46.8947, or 44 French Inches; or, according to Vega, 43.9 63.9967, or 5 French feet, about; English fathom. 76.7360, or 6 French feet. 1' 230.2080, or 18 French feet. 22 French feet. 2282 toises, or 2L5 of a . degree * The aune, or ell, of Paris varies, being for silk stufi's 527.5 lines, or 46% English inches; for woollens. 526.4 French lines, or 463— English inches; for linens, 524 French lines, or 46% English inches; and it varies still more in other parts of France. 1‘ Formerly 76.7], Phil. Trans. for 1742. ASOnde---.~...u... A Toise, or Fathomo . -. . APerche ...... ...... A Perch, mesure royale ALeague....-. one... = TABLE IX.—FRENOH LONG MEASURES, ACCORDING TO THE NEW SYSTEM. Eng. Inches. Millimetre - . . . = .03937 Centimetre - - - - = .39371 Decimetre - - - - = 3. 93710 Metre - - . . . - . - = 39.37100, or3.281 feet, or 1.09364yards, or nearly 1 yard 1% nail, or 443.2959 French . lines, or .513074 toise. 393.71000, or 10 yards, 2 feet, 9.7 inches. = 3937 .10000, or 100 yards, 1 foot, 1 inch. =39371 .00000, or 4 furlcngs, 213 yards, 1 foot 10. 2 inches: so that 8 chiliometres are nearly 5 miles. =393710.0000, or 6 miles, 1 furlong, 136 yards, 0 feet, 6 inches. NB. Artinch is .0354 metres; 2441 inches 62 metres; 1000 (cat nearly 305 metres. In order to express decimal proportions in this new system, the followmg terms have been adopted. The term Deca prefixed dc- notes 10'times; Heca, 100 times; Chitin, 1000 times; and Myrio, 10,000 times. On the other hand, Deci expresses the tenth part; Centt, the hundredth part; and Milli, the thousandth part; so that Dccametre signifies 10 metres; and a Decimetre, the tenth Decametre - . - . Hecatometre . - Chiliometre .. - Myriometre- - - part ofa metre, &c. &c. The Metre is the element of long mea- sures; Are, that of square measures; Stere, that of solid measures; tlte‘Litre is the element of all measures of capacity; and the Gramme, which is the weight of a cubic centimetre of distilled water, is the element for all weights. TABLE X.——PROPORTIONS or SEVERAL LONG MEASURES TO EACH OTHER, BY M. PICARD. Parts. The Rhinland, or Leyden foot (12 whereof make the Rhin- land perclt)snpposed............................. 696 The English foot ......... . . .. ......... . . . . . . ...... . 675% TheParisfoot.....-o... .............. ............. 720 The Amsterdam foot. from that of Leyden, by SnelliuSc . - - 629 The Danish foot (two whereofmake the Danish ell)- - . . - - 701736 TheSwedisthOt............. ...... ....... ..... .... 658* The Brussels foot ........ . . ........... . . . . ...... . . . 609% The Dantzic foot, from Havelius’s Seleuographia - . - - . - - - 636 The Lyons foot, by M. Auzout ------ . - ------ - - - - - - - - - 757g- The Bologna foot, by the same - - . - - - - - ~ - . ------------ 843 The braccio ofFlorence, by the same, and father Mersenne 1290 The palm of the architects at Rome, according to the ob. servations of Messrs. Picard and Auzout ---------- - . - - 494% The Roman foot; in the Capitol, examined by Messrs. Picard and Auzout ............... o u ......... 653 or 653711: The same from the Greek foot- - . . - - - ‘ - ---------- . . - - - 652 Fromthe vineyard Matteln..........-......-....... 657.}: From the palm . . . . ..... . . .......... . .......... . - . . 6582,? From the pavement Of the Pantheon. supposed to contain 10 Roman feet ............ . . . . . . ................. 653 From a slip of marble'ln the same pavement, supposed to contain 3 Roman feet ..... . ...................... . 650 From the pyramid ofCestius, supposed to contain 95 Roman feet ........... . .............. .... ....... ....... 6537:. From the diameters of the columns in the arch Of Septimins Severus-onso....: .......... ......o. ............. 653%. From a slip of porphyry in the pavement of the Pantheon 6534;- TABLE XI.—PR0PORTIONS OF THE LONG MEASURES OF SEVERAL NATIONS TO THE ENGLISH FOOT, TAKEN FROM GREAVES, AUZOUT, PICARI), AND EISENCHMID. The English standard foot being divided into 1000 equal parts, the other measures will have the proportions to it which follow: . Parts- Inches. Englishfoot...”.o..-.-..no.o.o--u..-.... 1000 12 Parisfoot....n. .......... ......--.-o...... 1068 12,816 'Venetianfootuu-n.........--on........... 1162 13.944. Rhinlandfoot.u............. ...... "A“... 1033 12,395 Strasburghfoot.-nou.n..o-oooo-.....oao.-o.. 952 11.424. Nurembergfoot ..... ....n.........o....... 1000 12. Dantzicfoot------.u----u---o---- ...... 944. 11.328 Danishfoot ....... ----......oa..onu.- ...... a 104.2 12,504. Swedishfoot...a.nu.Eucouns...o-o.......... '977%11.733 DerahorcubitofCairo-o-u-u-uu ------ .... 1824 21.888 Persianafish ...... u..-..-.........-ouaoaono 3197 38.364 GreaterTurkish pike ----- . --------- ........ 2200 26.4 LesserTurkish pike ------ ..................- 2131 25.572 BraccioatFlorence-nonu--------.-u-uu- 1913 22.956 Braccio for woollen at Sienna-u-u-u-n-un 1242 14.904 Braccio for linenat Sienna-u-n-u-u- ------ - 1974 23.688 CanuaatNaples-uncon-u-uu”-2-” -- 6880 82.56 Vera,at Almeira and Gibraltar - ----------- 2760 33-12 PalmodiArchtettiatRome .................. 7320 87.84 Fanna diArchtelti .............”nun”... 7320 87.84 Palmo di braccio di mercantiao- - - - - - - - - ~ . ..... 695% 8.346 GCHOH.pall’fl--'--"""""" ..... . ......... 815 9.78 Bologmanfoot..uaso. ..... ..-.-....... ..... 1250 15. Antwerpell-u ---------- 2283 27.396 Amsterdame” .n..---.-.---.-. ..... :...--;o 2268 27,216 Leydene]]....-...... ..... ................. 2260 97,12 Parisdraper’s ell..............,..........-. 3929 47-.148 Parismerccr’s ('11........................... 3937 47.24-1- M EA 286 M EA :— r‘ 1 . 'lABLE XlI.—-——M0DERN LONG MEASURES or I _ . 11 Eng. Ft.’ Authorities. . ‘ , .eipzlg, e . . . . . . . . . . . . . . 1 .833 Dr. Hutton, Journ. R. I. SEVERAL COUNTRIES COMPARED WITH LfiydennfOOt............. 1.023 ditto ENGLISH FEET. fiebge,f1oot ..... .944 ditto ' . ._ is on, oot.............. .. ‘ Compiled by Dr. Young, from ogrzous Autlzorztzes. Lucca, braccio . . .. 1.3212; (Elfin. Al Eng. Ft. Authorities. Lyons : Dauplnné l D l tdorf, foot . . . . . . . . . . . .. .775 Dr. Hutton , ' -9 5 f- I utton .927 ditto Madrid, foot. . . . . . . ...... 3 .918 Howard Amsterdam, foot .......... .930 Cavallo Madrid. vara - - . . ------ .. 3-263 Cavallo .931 Howard Maestricht, foot .......... .916 Dr. Hutton Amsterdam, ell. , . . . . . . . . . 2. 233 Cavallo Malta, palm ........... . . .915 ditto Ancona, foot. . ..... . . . . . . 1 .282 Dr. Hutton Mantua, brasso --------- - . 1-521 ditto Antwerp, foot ........ . . . . .940 ditto Mantuan, braccioz Brescian Cavallo Aquileia, foot . . .......... 1, 123 ditto Marseilles, foot . . ........ .814 Dr. Hutton ArleS, foot” ........ . .888 ditto Mechlin, foot ...... . . . . . . .753 ditto Augsburg, foot , , , ,,,,,,,, .972 ditto Mentz, foot. . . ...... . . . . . .988 ditto Avignon_ -- Aries, see Arles ll'Iilan, decimal foot ..... . . .855 ditto Barcelona, foot ..... . , . , , . .992 ditto Blilan, aliprand foot ....... 1 .426 ditto Basie, foot. . . . . . . . . , , . . . , .944 ditto Milanese, braccio ......... 1 .725 Cavallo Bavarian, foot. . . . . . . . . . . . .968 Beigel. See Munich. Modena, f°°t ------------ 2-081 DT- Hutton Bergamo, foot. . . . . . . . . . . . 1.431 Dr. Hutton MOMCO: fOOtc ---------- - - -771 ditto Berlin, foot... . . ...... . . . .992 ditto Montpelier. pan . - - . . - . - . . .777 ditto Bern, foot ..... . . . . . . . . . . .962 Howard Moravian, fOOt ----------- . -971 Vega. Besancon, foot . . . . . . . . . . 1.015 Dr. Hutton leioravian, ell ----- . ------ 2-594 59 a 1,244. ditto oscow, foot ..... . ..... . .928 r. Button 30108“, foot ' - ' - - ' - - - ' - ' 31 .250 Cavallo Munich, foot. . . . ........ . .947 ditto Bourg en Bresse, foot. . . . . . 1 .030 Dr. Hutton T .861 ditto Brabant, ell, in Germany. . . 2.268 Vega. A aples, palm ' ' ' ' ' ° """ ' i .859 Cavallo Bremen, foot . . . . . . . . . . . . . .955 Dr. Hutton Naples, canna. . . ------- - - 6-908 Him) Brescia, foot . . . . . . . . . . . . . 1 .560 ditto T -996 utton Brescian, braccio. . . . . . . . . . 2.092 Cavallo l\uremberg, town fOOt ' ' ' ' ' -997 Vega. Breslau, foot ............. 1 . 125 Dr. Hutton Nuremberg, country fOOt- - - -907 Dr. Hutton Bruges, foot . . . . . . . . . . . . , .749 ditto Nuremberg, artillery foot . . .961 Vega. Brussels foot .902 ditto Nuremberg, ell ..... . ..... 2.166 ditto ’ ' ' ° ' ' ' ' ' ' ' ' ' ' .954 Vega, Padua, foot ...... . ....... 1.406 Dr. Hutton Brussels, greater ell . . . . . . . 2.278 ditto Palermo, fOOt ----------- . .747 ditto Brussels, lesser ell ..... . . . 2.245 ditto Paris: fOOt - ------------- 1 -066 ditto CaStilian, vara...... ,..., , 2.74.6 Cavallo Paris, metre ......u.... 3.281 Dr. Young Chambery, foot. . . . . . . . . . . 1.107 Dr. Hutton Parma, foot . - - . - - - - - - 1 -869 Dr. Hutton China, mathematical foot. . . 1 .127 ditto garmesan, braccio - - . - - - . - 2-242 (311711110 . . . 1 .051 ditto avia, foot .............. 1 . 540 r. Hutton ., China, imperial foot. ' ' ' ' ‘ ’ g 1 .050 Cavallo Placentia : Parma . . . . . . . Cavallo Chinese,li. . . . . . . . . . . - . .606. ditto .987 Dr. Hutton Cologne, foot . .- . . . . . . . .903 Dr. Hutton :rague, fig” ' ' ' ' ' ' ' ' ' ' ' 3 ~972 3933' . . 2.195 ditto ra ue,e 1.948 ea. Constantmop 1e, fOOt‘ ' ' ' ' ' ' 3 1 . 165 ditto Progence : Marseilles. Dr.g Hutton Co enha en, foot . . . . . . . . . 1.049 ditto - 1.023 Ditto Crzicau, fiot. . . . . . . . . . . . . . 1.169 ditto Rhmland, foot.. ' ' ‘ ' ' ’ ' ' ' ' $1.030 Vega. Eytelweia Cracau, greater e1] . . . . . . . . 2 .024 Vega. Riga :Hamburgh. . . . . . . . Cracau, smaller e11 . . . . . . . . 1 .855 ditto , Rome, palm ............. .733 Dr. Hutton Dantzic, foot. ..... . . . . . . . .923 Dr. Hutton Rome, foot . . . . . . . ....... .966 Folkes Dauphinéfioot. . . . . . . . . . . 1. 119 ditto Rome, deto, 3’3 f00t- - - - . - . . ~0604' ditto Delft, foot. . . . . . . . . . . . . . . .547 ditto Rome, oncia, 7 foot. . . . . . .0805 ditto Denmark, foot. . . . . . . . . . . . 1.047 ditto Rome,palmo ............. .2515 ditto Dijon, foot . . . . . . . . . . . . . . 1.030 ditto Rome, palmo di architettura. .7325 ditto Dordrecht, foot. . . . . . . . . . . .771 ditto Rome, canna di architettura 7. 325 ditto Dresden, foot . . . . . . . . . . . .929 Wolfe. P11.Tr. 1769. Vega. Rome. staiolo. . . ......... 4. 212 ditto Dresden, ell : 2 feet . . . . . 1 .857 Vega Rome, canna dei mercanti . 6.5365 ditto, 8 palms Ferraro, foot. ..... . . . . . . . 1.317 Dr. ‘Hutton - - - 2 .7876 ditto, 1. 1211mm Florence, foot. . . . . . . . . . . . .995 ditto Rome, braccro def mercanti. i 2.856 Cavallo 1 Florence, braccio . . . . . . . . . g 132% 3:31“ 32:11:, braccro d1 tessuor ‘dl 2.0868 Folkes Franche Comté, foot . . . . . . 1 .172 Dr. Hutton Rome, braccio di architet- ‘ Frankfort: Hamburgh. . . . ditto tura ......... . . . . . . . . . g 2'56!” Cavallo .812 ditto Rouen :: Paris . . . . . . . . . . Dr. Hutton Genoa, palm . . . . . . . . . . . . . .800 Cavallo Russian, arcliine. . . . . . . . . . 2.3625 Cavallo , .817 ditto Russian, arschin. . . . - - ~ 3333 Ph. M. XIX. Genoa. canna . . . .. . . . . . . . 7.300 ditto Russian. verschock, 1- arschi112.1458 Geneva, foot ......... . . . . 1 ~919 Dr. Hutton Savoy“— ._ Chamberyl.6 . . . . . . Dr. Hutton Grenoble : Dauphiué. . . . . ditto Seville: Barcelona... . . . . . ditto Haarlem, foot. . . . . . . . . . . . .937 ditto Seville, vara . . . . . . . . . . . . . 2.760 Cavallo Halle, foot . . . . . . . . . . . . . . .977 ditto Sienna, foot . . . . . . . . . . . . . 1.239 Dr. Hutton Hamburgh, foot . . . . . . . . . . .933 ditto Stettin, foot. . . . . . . ...... . 1.224 ditto Heidelberg, foot. . . . . . . . . . .903 ditto Stockholm, foot. . . . . . . . . . . 1 .073 ditto Inspruck, foot. . . . . . . . . . . 1.101 ditto Stockholm. foot. - . . . . . . . . . (.974 Celsius Ph. Tr.) Leghorn, foot . . . . . . . . . . . . .992 ditto Strasburgh, town foot. . . . . . .956 Dr. Hutton Leipzig, foot . . . . . . . . . . . . . 1 .034 ditto Strasburgh, country foot . . . .969 ditto M EA 87 M EA Number of Length of a each equal Eng. F t. Authorities. Toledo :2 Madrid . . . . . . . . Dr. Hutton Trent, foot ....... . . . . . . . . 1 . 201 d1tto Trieste, ell for woollens. . . . _ 2.220 ditto Trieste, ell for silk . . . . . . . . 2 . 107 d1tt0 ' i 1 . 676 ditto Turin,foot............... 1.681 Cavallo Turin. ras ....... . . . . . . . . . 1 .958 ditto Turin, trabuco. . . ...... . . 10.085 ditto Ty rol, foot ............. . . 1 .096 Vega. Tyrol, ell .............. . . 2 . 639 ditto 1 alladolid. foot ....... . . . .908 Dr. Hutton 1 .137 ditto Venice, foot . . . . . . . . . . . . . 1 . 140 Bernard. Howard. Vega 1 . 167 Cavallo Venice, liraccio of silk. . . . . 2. 108 ditto Venice, ell .............. 2.089 Vega Venice, braccio of cloth. . . . 2.250 Cavallo Verona, foot . . . . . . . . . . . . . 1 . 117 Dr. Hutton Vicenza, foot ............ 1 . 136 ditto .. ) . 1.036 ditto \ louna, foot ............. 3 1 .037 Howard. Cavallo. Vega Vienna, ell .............. 2.557 Vega Vienna, post mile ...... 24888. ditto Vienna in Dauphiné, foot . . 1.058 Dr. Hutton Ulm, foot ................ .826 ditto Urbino, foot . . . . ...... . . . 1 .162 ditto Utrecht, foot. . . . . . . . . . . . .741 ditto “'arsaw, foot ............ 1.169 ditto Wesel :: Dordreclrt ....... ditto . .979 ditto Zurich, foot ............. 3 .984 Ph. M. VIII. 289. TABLE XIII.—A COMPARISON OF THE FOOT, AND OTHER MEASURES OF LENGTH, IN m FFERL‘NT COUNTRIES. Number of Length Qf‘a each equal single Mea- to 100 Eng- sure of each lish Feet. sort. E. Inches. Aix la Chapelle Feet................. 105.18 .- 11.41 Amsterdam - - - - ditto ................ 107.62 . . 11.15 Anspach- . - - - - - ditto . .- ... ........... 102.38 .. . 11.72 Ancona ....... Feet ............... . 78.02 . - 15.38 Antwerp ..‘..... ditto ............. ,.. 106.76 .. 11.24 Aquileia ...... ditto ................ 88.69 . - 13.53 Augsburgli .-.- ditto ................ 103. -- 11.65 Basil ...-...-. ditto ................ 102.22 -- 11.74 Bavaria ....... ditto ................ 105.08 . - 11.42 Btrgamo ...... ditto .. .............. 69.89 .. 17.17 Berlin ....... . ditto . .............. . 98.44 . . 12.19 Bern .... ..... ditto ....... . ..... .... 103.98 -- 11.54 Bologna ..... . ditto .. ....... ....... 80.05 .. 14.99 Bremen ...... . ditto ......... . ...... 105.45 . - 11.38 Brescia ...... . Bracci ............... 64.10 .. 18.72 Breslaw ...... . Feet .............. .. 107.24 . . 11.19 Brunswick ..... ditto . .' .............. 106.85 . - 11.23 Brussels ... ..... ditto ................ 104.80 .. 11.45 Cadiz . . .. ..... (See Spain) Cagliari ....... Palmi ............... 150.52 . . 7.97 Calemberg .... Feet ...... ......... . 104.34 .. 11.50 Carrara - . . .. . .. Palmi ................ 125. . . 9.60 Castille- . . . . . . . (See Spain) Chambery .... Feet ................ 90.36 .. 13.28 Mathematical feet ..... 91.46 . . 13.12 China Builder’s ditto......... 94.41 .. 12.71 ' " ' " ‘ Tradesmen’s ditto . .. .. 90.08 . . 13.32 Land Surveyor’s ditto .. 95.39 .. 12.58 Cleves ...... .. Feet -.... ........... 103.18 .. 11.63 Cologne . .. . ditto ........ . ....... 110.80 .. 10.83 Legal Feet .......... 97.17 .. 1235 Copenhagen g Fathoms ............. 16.20 c . 74.10 Ruthes ...... . ....... 9.71 . . 123.50 Cracow .....-. Feet ..... .......... . 85.53 .. 14.03 ditto ................ 106.28 .. 11.29 ill a...- Dan M: Ruthes-In-I-ll-nnu-' 7'08 '- 169.35 to 100 Eng. lish Feet. Dordrecllt..." Feet................. 84.74 .. Dresden ....... ditto .............-- 107.62 .. Embden....... ditto ..... ........... 102.92 .- ditto ................ 100. - . England .... Yards... ......... .... 33.33 .- Poles ................ 6.06 . - - Feet ........ . ...... . 75.95 . . Ferraro. ""' Pertichi ......... ..... 11.11 .. Florence . .. .. . Builders’ Bracci . ..... 55.55 .- Pieds du Roi ......... 93.89 .. France . .. . . Toises ................ 15.65 . . Metres .............. 30.48 . .. Francfort -...... Feet-... ............. 106.48 .. Geneva ....... ditto ................ 62.50 . . Genoa. ........ Palmi ................ 123.45 . . Gottingen ..... Feet ................ 104.80 . .. Gotha ......... ditto ........ . ....... 106. . . Groningen ..... ditto - ............... 104.44 .. r ditto. ................ 106.28 - - (ljihinland ditto ........ 97.17 .. . ~ lafters .............. 17.71 . . Hamburgh. ' 1 Masch Ruthes ......... 7.59 . . l Geest ditto ..... ...-.. 6.64 .. L Rhinland ditto ........ 8.10 . . Feet ................ 104.80 - . Hanover ' " ' i Rutlies ............... 6.50 . - Haerlem ....... Feet ................. 106.67 . . Heidelberg - . . . ditto ................ 109.48 . . Hildeslieim . .. . ditto .. ............... 108.60 . . Holstein ...... (See Copenhagen) Inspruck ...... Feet ................. 96. . . Konigsberg . . . - ditto ................ 99.09 . . Leghorn ...... (See Florence) ~ . Common feet .......... 108.01 - . Laps” """ Builders’ ditto ........ 107.81 . . Leyden ....... ditto ................ 97.24 . . Liege ......... ditto ................ 106. . . . Common feet .......... 105.26 . - Lmdau """ i Long ditto ............ 96.77 - . . Feet ................. 92.78 . . Lisbon """ 3 Palmi ................ 139.17 . . Lorraine -..... Feet ............... . 106.20 -- ditto ................ 104.80 . . Lubec """3 Ruthes..... .......... 6.55 .. Luneburg ..... Feet ................. 104.80 . . Madrid ....... (See Spain) Magdeberg . .. . Feet ................. 107.52 . . IVIalta ......... ditto ............ .... 107.43 .. lVIanheim. ..... ditto ..... ......... ... 105.39 .. Mantua . . . .. . . Bracci . . . ............ 65.75 - . LIaestricht----. Feet. ........ ........ 108.60 .. Mecklenberg. .. (See Hanover) Mentz ........ Feet . .- . . ........... 101. 26 . . Middleburglt.. ditto ......... mm"... 101 61 .. Milan 3 ditto._ ................ 76.82 . . """" Bracc1..........-.... 62.34 .. Monaco ....... Feet .............. .. 129.73 .. iMoscownu-.. ditto... ......... ..... 91.12 .. Naples ...... . Palmi ............ ...- 115.62 .. Neufchatel .-.. Feet... ..... . ........ 101.61 .. Nuremberg . . . . ditto ................ . 100.34 - . Oldenburg ..... ditto .......... ...... 103. .. Osnaburg ...... ditto ................. 109.09 . . Padna........ ditto.......... ....... 86.15 .. Palermo ....... Palmi ............ .... 125.93 .. Paris 3. ....... (See France) Parma . ....... Surveyors’ Bracci ..... 56.23 .. Pavia........- ditto ............ ..... 65.57 __ Persia ....... . Arish................ 31.36 .. Pomerania .... Feet ........ . ....... . 104.34 .. Portugal ....... .(See Lisbon) Prague ....... Feet ......... ........ 101. .. Ratisbon ...... (See Bavaria) Rdtzburgh...” Feet-IIIIl-Illl-II'II 104-80 .- single Mea- surcqfeach sort. E. Inches. 14.16 11.14 11.66 12. 36. 198. 15.80 108. 21.60 12.78 76.68 39.37 11.27 19.20 9.72 11.45 11.32 11.49 11.29 12.35 67.74 158.06 180.64 148.20 11.45 183.20 11.25 10.96 11.05 12.50 12.11 11.11 11.13 12.34 11.32 11.40 12.40 12.96 8.64 11.30 11.45 183.20 11.45 11.16 11.17 11.41 18.25 11.05 11.85 11.81 15.62 19.25 9.25 13.17 10.38 11.81 11.96 11.65 11. 13.93 9.53 21.34 18.30 38.27 11.50 11.88 11.45 MEA 4-,) pl 8 8 M EA Number of each equal to 100 Eng- lish Feet. Revel ......... ditto ................ 113.96 Reggie .. . . . . .. Bracci .. .......... . . 57.55 Rhinland ...... Feet .......... _ ...... 97. 17 Riga .......... ditto ................. 1 1 1.21 Rimini ........ Bracci ............... 56.10 Feet ............ .... 10345 Rome ...... Builders’ Canne ....... 13.65 Palmi . .-. ............. 136.49 Rostock . . . . . . . Feet ................. 105.45 Rotterdam . .. - (See Rhinland) Arsheens .......... ... 42.86 Russia ...... Sashes. .. ............ 1428 Feet . . . ..... . ....... 87.27 Sardinia . . . . . . Palmi ................ 1:28.70 Savoy . . ...u . (See Chambery)‘ Sienna.. ..-.. . Feet ................. 80.75 Sicily ........ (See Palermo)‘ Silesia ........ Ruthes ............... 7.06 ' Feet --..-........... 107.91 Spain ....... 3 Toesas ..... ......... 17 98 ' Palmos-.... ........ _. 143.88 Stade ..- - . . . . Feet ................. 104.80 Steltin ........ ditto ................. 107.91 Stockholm . . . . (See.Sweden) Feet..... ..... ...... 105.35 Strasburgh. . . Land ditto ............ 103428 (See also France) Stutgard ...... (See Wurtemberg) ‘ Feet ................ 102.66 Sweden..... Fathoms ........-.... 17.11 Rods ............... . 6.43 Trent. ........ Feet ...... . . ........ 83.28 Turin .... .... ditto . ............... 94.34 Ulni ......... ditto ................ 105.35 Utrecht ....... ditto -... ........ -.-.. 111.82 Venice. . . .- . . . ditto ................ 87.72 Verona -...... ditto ................ 89.55 Vicenza ...... ditto ................ 88.04 ' Vienna ........ ditto ................ 96.39 Warsaw ...... ditto ................ 85.53 \Vismar - . ..... ditto ................ 103.63 VVurtemberg... ditto -. ...... ........ 104.80 ch1 .......... (See Hanover) Ziriczee ....... Feet ................. 98.28 ditto ................ 101.60 Zurich . . . . . . Rnthes .............. . 10.16 Fathoms. . . . .......... 16.32 TABLE XIV.—-A COMPARISON or TRIES. on Long Ch of a single Mea- sure of each sort. E. Inches. 10.53 2085 19.35 10.79 21.39 11.60 87.92 8:79 11.38 28. 84. 13.75 9.78 14.86 170 111.12 66.72 8.34 11.45 11.12 11.39 11.69 11:69 70.14 187.04 14.41 12.72 11.39 10.74 13.40 13.68 13.63 19.45 14.03 11.58 11.45 12.91 11.81 118.10 73.50 THE ITI- NERABY MEASURES OF DIFFERENT COUN- Numbcr of Length. of a each equal to 100 Eng- lish. Miles. Aral)ifl....... DIileSUCOQOIDvIIIoIOnooo 81.93 Bohemia .... ditto ...... .......... 17.36 Brabant .... ditto .......... ....... . 28.93 Burgundy .. ditto .................. 28.46 China......Lis............ ....... .279.80 Denmark.... Miles.................. 21.35 . ditto ......oIo-u..-..-u 100. England ’ ditto, Geographical- ..... . 86.91 Flanders Miles ........ 25.62 Leagues, Astronomical. . . . 36.21 France. . . . ditto, Marine ..... .. . . . . . 28.97 ditto, legal, of 2000 Toises 41.98 Miles, Geographical. . . . . . 21.72 “Germany“ ditto, Long.............. 17.38 ditlo'Short'CC‘OIlQIIIIII 25.66 single Mea- sure Qf each sorL Eng. Yds. 2148 10137 6082 6183 6‘29 8244 1760 9625 6869 4860 6075 4963 8101 Hamburgh . . Hanover . . . . Hesse . . . . . . Holland . Hungary . . . . Ireland . . . . Italy ...... Lithuania Oldenburgh - Poland. . . .3 Portugal . . . . Prussia ...... Rome ....3 Russia ...... Saxony . . . . Scotland . . . . _ Silesia . ..... Spain Swahia ...... Sweden . . . . Switzerland . . Turkey . . . . \Vestphalia . . Number of‘ each equal to 100 Eng- lish. .‘lfilca'. Miles............ ...... 21.35 ditto .................. 15. Q3 ditto .......... . ....... 16 .68 ditto ................ . . 27.52 ditto .......... , ...... . 19.31 ditto .................. 57.93 ditto .................. 36.91 ditto ...... . ......... . . 18. ditto ........ . . . . ..... . 16.26 Miles, Short ............ 28.97 ditto, Long .............. . 21.72 Legoas ........ . . ...... 26.03 Miles .................. 20.78 Ancient Miles of 8 Stadia 109. 18 Modern Miles ......... . 86.91 Versts .................. 150.81 Miles ............... . . . 17.76 ditto ...... 88.70 ditto .............. . 27. 67 Le‘guras, common, of 8000 23.73 , aras . . ......... ditto, Legal, of 5000 Varas 37. 97 Miles . . ................ 17.38 ditto .................. 15.01 ditto .................. 19.23 Berries ................ 96.38 Miles.................. 14.56 Length of a single .Mea- surc qfcack. sort. Eng .Yds. . 8244 . 11559 10547 6395 . 9113 . . 3038 . . 2025 9781 10820 . . 6075 . . 8101 . . 6760 . . 8468 . . 1612 . . 2025 . 1 167 . 9905 1984 7083 7416 .. 4635 10126 11700 .. 9153 1826 12151 SUPERFICIAL, 0a SQUARE MEASURES. TABLE XV.—-ANCIENT GREEK SCPERFICIAL 36 Olympic square feet nu”... 6 Hexapoda.................. 2 Hemihecti 6 Modii-on- ollICIIoua MEASURES. Olympic Land Measure. ...-o... II II II ll 05-...lIII‘CO'II. 1 Hexapodon. 1 Hemihectos. 1 Hectos or Modius. 1 Medimnus or Jugerum. Hence it appears, that the Olympic jugerum was equal to 103 English perches, or nearly five-eighths of an acre. 1.666% Square Cubitsl-eloo-tnnao- 2 Hemihecti............... 6 Modii Pythic Land Measure. =1 Modius. 1 Hemihectos. 1 Medimnus orJugerum. Hence the Pythic jugerum appears to have been equal to 109 English perches, or nearly fiths of an acre. NB. The plethron, or acre, is said by some to contain 1444. by others 10,000 square feet ; and aroura, the half of the plethron. The aroura of the Egyptians was the square of 100 cubits. TABLE XVI.—ANCIENT ROMAN LAND 100 SquareRoman feet-u-u-u-u. 4 Scrupulau....... 1% Sextulu3c-........ 6 Sextuli, or 5Actus -- - Unciaann 2 Square Actus - ~- 2 Jugera...-............... 100 Heredia- . 6 MEASURES. ones-nave...- toilllcooool «...-nus... Cootletlnolooolulioc .OQOIII‘OQOOQOO sun-- ..OOOOOQIOIOQOOIIOOC. llll ll ll ll II II ll 1 Scrupulum ofland 1 Sextulus 1 Actus“ 1 Uncia of land 1 Square Actus 1 Jugerumf 1 Heredium 1 Centuria. " The actus was a slip of ground four Roman feet broad, and 120 long. 1' The jugerum, 01- acre, was considered as an integer, and divided, like the libra, or as, in the following manner :g MBA 89 MEA Jugerum contained Roman. English. r----"—-\ r- A—“x Uncioz Sq. Ft. Scrap. Rds. Pol. 80.12. “is”... = 12 = ‘28800 288 = 2 18 250.05 .3 Deunx - . - - = 11 = 26400 $264 = 2 10 183.85 Dextans - - - = 10 = 24000 240 = 2 2 117 .64 ¢ Dodran5u. = 9 = 21600 216 = 1 34 51.42 '1' Bes ----- ~ - = 8 = 19200 192 -_-= 1 25 257.46 1 Septunx - - - = 7 = 16800 168 = 1 17 191 .25 2 Semis - - . - - == 6 = 14400 144: = 1 9 125.03 35. Quincunx' - = 5 = 12000 1‘20 = 1 1 58 .82 1 Triens --- = 4 = 9600 96 = o 32 264.85 E Quadrans- . = 3 a 7200 72 = 0 24 198. 64 1 Sexlans ..- = 2 = 4800 48 = o 16 132.43 11‘; Uncia- . - -- = 1 .1 2400 24 o 8 66.21 NJ}. If we take the Roman foot at 11.6 English inches (see TABLE V.) the Roman jugerum was = 5980 English square yards, or 1 acre 37% perches. TABLE XVII.—-ENGLISH SQUARE MEASURES. 14.4 Inches .u....c.-...aoan.--aonsnuoooo-nu =1F00t. 9 Feet noon-u... ooooooo oacoo-np-aosoo-noo =1Yal‘d. 9% Yards~-~---------~~~---~----‘--------‘ =1Pace, 1089 Paces ..... on...on-ouosa.o-oso-~uoooc-u = IPOIe. 40 Poles ................................. = 1Rood. 4 I{oods -.-......-o-....-o.....u.o....s =1Acl‘e. NB. English square or superficial measures are raised from the yard 06.36 inches, multiplied into itself; and this producing 1296 square inches in the square yard, the divisions of this are square feet and inches; and the multiples, poles, mods, and ncres, as in the Table. The Scottish acre is 55353.6 square feet English, or 1.27 English acres. MEASURES USED BY DIFFERENT ARTIFICERS. 144 Square inches. . . . . . . . . . . . . : 1 Square foot 9 Square feet ........ . ...... : 1 Square yard 63 Square feet : 7 square yards .: 1 Rood 100 Square feet .......... . . . . . :: 1 Square of work 272% Square feet : 30i- sq. yards : 1 Rod, perch, or square pole. TABLE XVIII.-—FRENCH SQUARE MEASURES, BEFORE THE REVOLUTION. A Square inch - - - - An Arpent . . . . nun-unc- a 1-13582 English sq. inches. 100 Square perches, French, about-g acre English, used near Paris. about 1% English acre. * The perch, (see Table VIII.) which determines the measure of the acre,varies in different parts of the country: but the arpent Of wood-land is every where the same, the perch being 22 feet long; and this arpent contains 48,400 French square feet, or 6108 English square yards, or one acre, one rood, one perch. The arpent for cultivated land, in the vicinity of Paris, contains 900 square toises, or 4088 English yards; so that 43 such arpents are equal to 58 English acres nearly. a An Arpent, mesure royale" TABLE XIX.—FEENCH SQUARE MEASURES, ACCORDING TO THE NEw SYSTEM. Are, a square decametre . . - Decare ‘I-oooolulcalvooi Hecatare-.. H g 3.95 English perches,or 119.6046 Square yds. 1196.0460 Square yards. 11960. 4600 Square yards, or 2 acres, 1 road, 35.41 perches. oo-Iooo...... VOL. II. 2 Xestes................... TABLE XX.-—CONTENTs OF A SQUARE F001- OF DIFFERENT COUNTRIES Eng. Square. Inches. A Square Foot of Amsterdam contains- - - . - ~ - - . . - - - 124.32 Antwerp ..... .o...~..oo..-...-n 126.34 Ber]iu......... ..... . ..... u... 148 59 Berne.....n...u.. ...... ....- 133,23 Bologna-vnus-scoiouoooooooon1- 224.70 Bremen....oo..--..o-.ooo..... 129.50 Denmark or Rhinlaud ------ ----- 152.52 Dantzi‘c....................... 127.46 Dresden....................... 124.10 Eng]and...u........-.........- 144.00 Franceo..............o..,-.-.. 163.32 Hamburgh..n.o.a. ...... ....... 127.46 }[anover ........ . ...... . . . . . o . . 131. 10 1(onigsberg... ...... ........--. 146.65 Leipsic....ac.....-..........-o 123.43 Lisbon-c...--a.n.o.o ........ .. 167.96 NIH-gnu}...................... 234,98 Nuremberg......... ....... .... 134_()4 Osnaburgh .u........ ....... ... 121_00 Rome.............-........ .. 134,56 Spain .................. ....... 123,65 Sweden....................... 135.55 Turin-u ..... .. ........ ....... 161.80 Venice..... ..... o ..... ... o... 187.13 Vienna........... . . . ...... . 155,00 Zurich......................... 139_4g AFrenchSquare men-e.......-..---............ 1550.00 MEASURES OF CAPACITY. TABLE XXL—JEWISH DRY MEASURES, REDUCED TO ENGLISH. English ‘ Pks. Gall. Pts: Sol. In. 1 Gachal...................... : O 0 1% 0.031 20 Gachals : 1 Cab ........ . : 0 0 2% 0.073 1% Cabs... : 1 Gomer......- : 0 0 53% 1.211 351 Gomers : 1 Seah ...... . . . : 1 0 1 4.036 3 Seahs . . : 1 Epha ...... . . 2 3 0 3 12.107 5 Ephas. . = 1 Leteeh ...... I: 16 0 0 26.500 _ Chomer, or _ 2 Leteehs ._ 13 Comm; __ 32 o 1 18.969 TABLE XXII.—JEWISH MEASURES OF CAPA- CITY FOR LIQUIDS, REDUCED TO ENGLISH WINE MEASURE. English Gall. Pts. 801.173. 1 Caph................... .. .. .. : 0 0 0.177 131Caphs....... : 1Log. .. .. 2: 0 0% 0.211 4 Logs........ : 1Cab .. : 0 3.} 0.844 3 Cabs........ : lllin ......... -__— 1 2 2.533 2 Hius........ : 1Seah ...... .. : 2 4 5.067 3 Seahs....... —__—_ 1 Bath, Epha... : 7 4 15.002 10 Baths,orEphas 2 iggffigérm; :75 5 7.625. TABLE XXIII.—-ANCIENT GREEK CORN MEASURES. 1 Chtenix 4 Chenices ..... . . . . . . . . . . . : 1 Hernihectos 1% Hemihectos . . . . . . . . . . . . . . :— 1 Tetarlon 2 Hemihecti............... : lModius 6 Modii . . . . ..... . . . . . . . . . . z: 1 Medimnus,‘ or Achana. *Paucton states the medimuus to have been 3% French bois~ seaux: 1.27 English bushels, and the inferior measures in proportion. ‘ 2P MBA 290 M EA —. ——7 TABLE XXIV.——ATTIC DRY MEASURES RE- DUCED TO ENGLISH. English. Pee/cs. Gall. Pints. Solid In. 1 Cochl-iarion................... =0 0 0 0.276276 10 Cochliaria .. . = 1 Cyathus. . .. == 0 O 0 2.763% 1% Cyathus ..... = 1 Oxylmphon. == 0 0 0 4.114% 4 Oxybaphi. . .. = 1 Cotyle , . . . = 0 0 0 16.579 2 Cotylae...... -= 1 Xestes ..... = O 0 0 33.158 1% Xestes . . .. . . = 1 Choenix . . . . = 0 0 1 1537053,; .48 Choenix . . . . . = 1 g Nfifféigfigig = 4 0 6 3.501 * Besides this, there was also a Medimnus Georgicus, equal to six Roman Modii TABLE XXV.—ATTIC MEASURES OF CAPA- CITY FOR LIQUIDS. English Wine Measure. Gall. Pints. Solid In. 1 Cochliarion . . . . ....... . . . . . . . . . = 0 03156 0.35671 2 Cochliaria. = 1 Cheme. . . . . . . = 0 Ogd 0.712% 1% Cheme . . . = 1 Myston . . . . . . = O 03% 0.89% 2 Myston. . . = 1 Concha ...... = 0 0%: 0.178%% 2 Conchae. . . = 1 Kyathus ..... = 0 (>712 0.356% 1% Kyathus . . = 1 Oxybaphon. . . = 0 03‘,- 0.535% 4 Oxybaphi . = 1 Cotyla . . . . . . = 0 0% 2 441% 2 Cotylze = 1 Xestes....... = 0 1 4.283 6 Xesles. . . . = 1 Chous, congius = 0 6 25.698 . - Metretes, or 12 Chm = 1 i Amphoreusi = 10 2 19.626 6 Choi. . . . = 1 Amphorens. N'B' Some reckon i2 Amphorei = 1 Keramion, or Metretes. Paucton states the Keramion as equal to 35 French pints, or 8% English gallons ; and the rest of these measures in proportion. TABLE XXVI.——ROMAN DRY MEASURES RE- DUCED TO ENGLISH. English Pks.Gal. Pts. Sol. In. 1 Ligula....... .. ......... : 0 0 3L8. 0.01 4 Ligulze : 1 Cyathus . . . . . . . : 0 0 0112 0.04 1% Cyathus . . : 1 Acetabulum. . . . . L: 0 0 0% 0.06 4 Acetabula : 1 Hemina, or Trutta : 0 0 0% 0.24 2 Heminze . . :: 1 Sextarius . . . . . . . : 0 0 1 0.48 8 Sextarii. . . = 1 Semiiuodius . . . . . : 0 1 O 3. 84 2 Semiinodii : 1 Modius . . . . . . . . 2: 1 0 0 7.68 TABLE XXVII.——ROMAN MEASURES OF CAPACITY FOR LIQUIDS. English Wine Measure. Galls. P63. Sol. In. 1 Ligula....................-.... : 0 03% 0.11773 4 Ligulae. . . . . :2 1 Cyathus. . . . . '5: 0 052 0.469% 1% Cyathus. . . . = 1 Acetabuluni . = 0 0% 0.704% 2 Acetabula . . 2 1 Quartarius . . : O 0% 1 .409 2 Quartarii. . . 2 1 Hemina . . . . . I 0 0% 2.818 :3 Heminae . . . = 1 Sextarius . . . . 2 0 1 5.636 6 Sextarii. . . . : 1 Congius . . . . . : O 7 4.942 4 Congii ..... 2 1 Urna. . ...... 2 3 4% 5 .33 2 Urnze ..... 2 1 Amphora . . . ' Z 7 1 10.66 20 Amphorze. . 2 1 Culeus . . . . . . :- 143 3 11.095 TABLE XXVlIl.—ANCIENT ROMAN LIQUID MEASURES. ssextarii = ICongius 4Congii.... ....... ............ '33 lUrna 2Urme........ ...... 2 1Amphora 20 Amphorae.... ....... ......... =3 1 D0511!“ NB. The sextarius and its divisions were used as in the preced- ing table. If the sextarius be, as above supposed, 236.94 English cubic inches, the amphora will be 2 7% English gal- lons, and the dolium : 153% English gallons. l “ ...—.- TABLE XXIX.-—ENGLISH DRY, OR CORN M E A s U R E . Solid I riches. 1 PInt.....-n........ ...... o o ........ n —— 343312 2 Pints ........ : 1 Quart . ........... : 68 2 Quarts . . . . . . : 1 Pottle ........ . . . . : 136‘ 2 Pottles . . . . . . Z 1 Gallon“ . . .......... __ 272% 2 Gallons ..... Z 1 Peck. . . . . .......... ~ 544% 4 Peeks . . . . . . 2 1 Bushel (Winchester) . — 2178 2 Bushels ..... : 1 Strike . ............. I 4356 2 Strikes ...... : 1' Como, 0r Carnock . . . : 8712 2 Cooms . . . . . . = 1 Quarter, or Scam ..... :2 1742-1 6 Quarters . . . Z 1 Weigh f . . . . . . . ..... — 10451-1 1%— lVeighs ..... Z 1 Last ...... ......... I 174240 * But if the Corn gallon contain only 268.8 solid inches, the measures will be as follow : Solid Inches. 1 Pint ........ . ............ . ..... . ...... 2 33.6 2 Pints ....... : 1 Quart .............. _ 67.2 2 Quarts ..... : 1 Pottle . . . . . . . ...... : 134.4 2 Pottles..... Z 1 Gallon ...... ...... : 268.8 2 Gallons ..... : 1 Peck .............. 2 537.6 4 Peeks ...... Z 1 Bushel (\Vinchesterfi 2 2150.42 8 Bushels..... '_ 1 Quarter............ :2 17203.36 1 A heaped bushel is one-third more. 'l‘ Some make five quarters a weigh or load, and two weighs a last of wheat; and others reckon ten quarters to the weigh, and twelve weighs to the last. A bushel of wheat, at a mean, weighs 60 pounds, of barley 50, of oats 38. A chaldron of coals is 36 heaped bushels, weighing about 2988 pounds. English dry or corn measures are raised from the \Vinchester gal— lon, which contains 272% solid inches, and is to hold of pure running or rain water, nine pounds thirteen ounces. This seems tO stand on the foot of the old wine gallon, of 224 cubic inches; 12 being to 14%, as 224 to 272%. Yet, by act of parliament, made 1697, it is decreed, that a round bushel, eighteen inches and a half wide, and eight deep, is a legal Winchester bushel. But such a vessel will only hold 2150.42 cubic inches: and’ consequently the gallon will contain 268% cubic inches. TABLE XXX.—ENGLlsH MEASURES OF CAPACITY FOR LIQUIDS. WINE MEASURES. Solid I arches. 1 Pint................... ..... : 28.875 2 Pints.......... _ 1Quart........ : 57.750 4 Quarts........ :: IGallon........ :- 2‘31. 18 Gallons . . . . . . . : 1 Rundelet ...... = 4158. 1% Rundelets 2 1 Barrel ........ 2 7276.5 10 Barrels ...... . . Z 1 Tierce ...... . . : 9702. 1% Tierces ...... . : 1 Hogshead . . . . . = 14.553. 1% Hogsheads . . . . I: ‘1 Puucheon . . . . . : 19104. 1% Pnncheons . . . . 2 1 Butt, or Pipe . . = 99106. 2 Butts, or Pipes. : 1 Tun .......... 2 58212. A 1'" b1 MEASURES. Solid Inches. 1 Pint................Q........... ..... : 35.25 2 Pints ..... I lQuart ': 70.50 4 Quarts ......... . : 1 Gallon . ...... 2 282. 8 Gallons I 1 Firkin ........ = 9256. 2 Firkins.... = 1 Kilderkin...... 1‘ 4512. 2 Kilderkins ...... = 1 Barrel ..... Z 9024. 1% Barrels . ........ = 1 Hogshead ..... . : 13.336. M EA BEER MEASURES. Solid Inches. 1 Pint..............-... ....... o. : 35-25 2 Pints .......... . 2 1 Quart ....... . . : 70.50 4 Quarts .......... 2 1 Gallon ....... . : 282. 9 Gallons . ....... . :2 1' Firkin . ..... . . . :: 2538 . 2 Firkins ......... . = 1 Kilderkin . . . . . . :2 5076. 2 Kilderkins ..... . Z 1 Barrel ..... . . . . = 10152. 1E Barrels . . ....... Z 1 Hogshead . . . . . . = 15228. 2 Hogshcads ...... = 1 Butt ...... . . . . . = 30456. English liquid measures were originally raised from troy weight; it being enacted by several statutes that eight pounds troy of wheat, gathered from the middle of the ear, and well dried, should weigh a gallon of wine measure, the divisions and mul- tiples whereof were to term the other measures. at the same time it was also ordered, that there should be but one liquid measure in the kingdom , yet custom has prevailed , and there having been introduced a new weight, viz. the avoirdupois, we have now a second standard gallon adjusted thereto, and therefore exceeding the former in the proportion of the avoir— dupois Weight to troy weight. From this latter standard are raised two several measures, the one for ale, the other for beer. The sealed gallon at Guildhall, which is the standard for wines, spirits, oils, Sic. is supposed to contain 231 cubic inches , and, on this supposition, the other measures raised therefrom will contain as in the preceding tables; yet, by actual experiment made in 1688, before the lord mayor and the commissioners of excise, this gallon was found to contain only 224 cubic inches; it was however agreed to continue the common supposed con- tents of 231 cubic inches; so that all computations stand on their old footing. Hence, 12: 231: :1413: 2811, the cubic inches in the ale gallon: but in effect the2 Gale quart contains 70% cubic inches; on which principle the ale and beer gallon will be 282 cubic inches. The several divisions and multiples of these measures and their proportions are exhibited in the preceding tables. It 13 conjectured, that some centuries before the Conquest, a cubic foot of water weighing 1000 ounces, 32 cubic feet, weighed 2000 pounds, or a ton; that the same quantity was a ton of liquids; and a hogshead eight cubic feet, or 13824 cubic inches, one sixty—third of which was 219.4 inches, or a gallon. A quarter of wheat was a quarter of a ton, weighing about 500 pounds, a. bushel one-eighth of this, equivalent to a cubic foot of water. A chaldron of coals was a ton, and weighed 2000 pounds. At present 12 wine gallons of distilled water weigh exactly 100 pounds avoirdupois. TABLE XXXI.—SCOTTISH MEASURES OF CAPACITY, REDUCED TO ENGLISH. English Solid Inches. AGill..... ..... .. ...... ..... .......... = 6.462 A Mutchkin . . ........ . .............. . . . . 2 25.85 AChOppin. ......... . :2 51.7 APint .......................... ........ = 103.4 ALippie, or Feed.... ............ ........ : 200.345 A Quart ...... . ................ . ....... . : 206.8 A Gallon ......... . .................... . . : 827. 23 A Hogshead ....... . . — 16 Gallons ..... : 13235.7 By the Act of Union, twelve Scottish gallons are reckoned equal to an English barrel, or 9588 cubic inches, instead of 9927. TABLE XXXII.——~FBENCH MEASURES OF CAPACITY BEFORE THE REVOLUTION. ACubic inch... 1.21063 Cubic inches English ALitron........ : 65.34 A Boisseau ..... . =1 1045 44, or 16 Litrons A Minot. . . . = 2090. 875, or 3 Boisseaux, nearly an English bushel A Mine . . . . . . . . : 4181 .75. or 2 Minots A Septier. . . . . . . : 8363.5, or 2 Mines, or 6912 inches French ............ .............. double for oats A Maid ........ 100362, or 12 Septiers A Ton ofshipping 42 Cubic feet. 91‘ M EA ‘- *4 5-: TABLE XXXIII.-—FRENCH MEASURES or CA- PACITY, ACCORDING TO THE NEW SYSTEM. English solid inches. Millilitre : .06103 Centilitre............ : .61028 Decilitre ........ . . . . :: 6.10280 Litre, a cubic decimetre :: 61 .02800. or 2 . 113 wine pints Decalitre ...... . . . . . . : 610.28000, or 2.64 wine galls. Hacatolitre . . ........ :, 6102.80000, or 3.5317 cubic feet, or 26.4 wine gallons :: 61028.00000, or 3.5.3170 cubic Cliiliolitre . . . . . . . . . ~ feet, or 1 tun. 12 wine galls. Myriolitre . . 610280.00000, or 353.1700 cubic H feet. SOLID NIEASURE. English Cubic Feet. Decistre, for fire wood . . ...... . ........ . . . . : 3.5317 Stere, a cubic metre. ....................... : 35. 3170 Decastere ....................... . ...... . : 353.1700 For an explanation of the proportions, see Table IX. TABLE XXXIV.——CONTENTS or A CUBIC FOOT OF DIFFERENT COUNTRIES, IN ENG- LlSH CUBIC INCHES. English solid Inches. Amsterdam..........-.................. __ 1386.2 Antwerp................................ : 1420.03 Berlin..... ..... . ..... .................. 2 1811.39 Berne ..... -.. .......... . ........ ....... :— 1536.80 Bologne ..... .. ..... ..... ...... ... ...... : 3368.25 Bremen .............. . ........ ........ : 1473376 Denmark, or Rhinland ..... ..... = 1883.65 Dantzic ............. ...... ...... ....... 2 1439.07 Dresden ...... . ........ ................. : 1382.50 England ............... ........... ..... 2 1728.00 France ............. . ................. . : 2087.34- Hamburgh. ...... .......-............ .. = 1439.07 Hanover ..... .... ........ .............. 2 1501.12 Konigsberg ....... ........... ........... : 1775.96 leipsic............ ..... ........... . 2 1371.33 Lisbon.. ...... ......... ......... ...... : 2177.80 Milan ......... ... ....... . ............. . :2 3812.98 Nuremberg ............ ..... . ..... .. = 1710.76 Osnaburgh...... .............. ..... ..... : 1331.00 Rome ................. ..... . : 1560.90 Spain ............... . ........ ......... = 1375.04 Sweden.......................... = 1597.52 Turin..... ..... ...... .. . 2 2058.07 Venice..... ...... .. . .. .......... : 2560.10 Vienna......... ........................ : 1929.78 Zurich .............. . ............ ...... : 1617.20 FrenchCubicmetre...................... : 61023.50 MEASURING, or MENSURATION,defined geome- trically, is the assuming any certain quantity, and expressing the proportion of other similar quanti- ties to the same. MEASURING, defined popularly, is the using of a certain known measure, and determining thereby the precise extent, quantity, or capacity, of any thing. In general, it constitutes the practical part' of geometry. See MENSURATION. MEASURING or LINES, or quantities ofonedimen- sion, is called longimetry; and when thoselines are 2 P 2 - u.— MEA Q not extended parallel to the horizon, altimetry. When the different altitudes of the two extremes Of the lines are alone regarded, it is termed Ze- vellz'nrr. MEASURING or SUPERFICIES,Ol'quantities oftwo dimensions, is variously denominated, according to its subjects: when lands are the subject, it is called geodesia, or surveying; in other cases, simply measuring. The instruments used are the ten-foot rod, chain, compass, circumferentor, Ste. MEASURING 0F SOLIDS, or quantities of three di- mensions, is called stereometry; but where it relates to the capacities of vessels, or the liquors they contain particularly, gauging. Theinstruments for this art are the gauging-rod, sliding-rule, Ste. From the definition of measuring, where the mea- sure is expressed tO be similar or homogeneous to, d. e. of the same kind with, the thing measured, it is evident, that in the first case, or in quantities of one dimension, the measure must bea line; in the second, a superficies; and in the third, 21 solid. For example, a line cannot measure a surface; the art of measuring being no more than the ap- plication of a known quantity to the unknown, till the two become equal. Now a surface has breadth, and a line has none: and if one line have no breadth, two or a hundred have none. Aline, therefore, can never be applied so often to a sur- face, as to be equal to it, 2'. e. to measure it. And from the like reasoning it is evident, a su- perficies, which has no depth, cannot become equal to, i. e. cannot measure, a solid, which has. While a line continues such, it may be measured by any part of itself: but when the line begins to flow, and to generate a new dimension, the measure must keep pace, and flow too ; i. e. as the one com- mences superficie-s, the othermust do so too. Thus we come to have square measures, and cubic mea- sures. Hence we see why the measure of a circle is an are or part of the circle, for a right line can only touch a circle in one point, but the periphery of a circle consists of infinite points. The right line, therefore, to measure the circle, must be applied infinite times, which is impossible. Again, the right line only touches the circle in a mathematical point; which has no parts nor dimensions, and has consequently no magnitude; but a thing that has neither magnitude nor dimensions bears no pro- portion to another, that has 5 and cannot therefore 92 M EC W measure it. Hence we see the reason of the divi- sron of Circles into 360 parts or arcs, called degrees. See Alto, CIRCLE, and MENSURATION. MECHANICS (from the Greek pmxam, art) that branch of practical mathematics which treats of motion and moving powers, their nature, laws, effects, See. This term, in a popular sense, is ap- plied equally to the doctrine of the equilibrium of powers, more properly called statics, and to that science which treats of the generation and com- munication of motion, which constitutes dyna- mics, or mechanics strictly so called. See FORCE, MOTION, POWER, and STATICS. This science is divided by Newton into practice? and rationalmechanics, the former of which relates to the mechanical powers, viz. the lever, balance, wheel and axis, pulley, wedge, screw, and inclined plane; and the latter, or rational mechanics, to the theory of motion; shewing, when the forces or powers are given, how to determine the motion that will result from them; and, conversely, when the circumstances of the motion are given, how to trace the forces or powers from which they arise. Mechanics, according to the ancient sense of the word, considers only the energy of organs, or ma- chines. The authors who have treatedthe subject of mechanics systematically have observed, that all machines derive their efficacy from a few simple forms and dispositions, which may be given to organs, interposed between the agent and the re- sistance to be overcome; and to those simple forms they have given the name of mechanical powers, simple powers, or simple machines. The practical uses of the several mechanical powers were undoubtedly known to the ancients, but they were almost wholly unacquainted with the theore- tical principles ofthis science till a very late period; and it is therefore not a little surprising that the construction of machines, or the instruments of mechanics, should have been pursued with such industry, and carried by them to such perfection. Vitruvius, in his 10tl1l)ook, enumerates several in- genious machines,which had then been in use from time immemorial. We find, that for raising or transporting heavy bodies, they employed most of the means which are at present commonly used for that purpose, such as the crane, the inclined plane, the pulley, Sec. : but with the theory or true principles of equilibrium they seem to have been unacquainted till the time of Archimedes. This celebrated mathematician, in his book of Equie ”—— M EC 293 m ‘_—,-— M EC" Jun—1 I w ponderants, considers a balance supported on a fulcrum, and having a weight in each scale; and taking as a fundamental principle, that when the two arms of the balance are equal, the two weights supposed to be in equilibrio are also of necessity equal, he shews, that if one of the arms be in- creased, the weight applied to it must be propor- tionally diminished. Hence he deduces the general conclusion, that two weights suspended to the arms of a balance of unequal length, and remaining in equilibrio, must be reciprocally proportional to the arms of the balance; and this is the firsttrace any where to be met with of any theoretical investiga- tion of mechanical science. Archimedes also far— ther observed, that the two weights exert the same pressure on the fulcrum of the balance, as if they were directly applied to it; and he afterwards ex- tended the same idea to two other weights sus- pended from other points of the balance, then to two others, and so on,and hence, step by step, ad- vanced towards the general idea of the centre of gravity, a point whichhe proved to belong to every assemblage of small bodies, and consequently to every large body, which might be considered as formed of such an assemblage. This theory he applied to particular cases, and determined the si- tuation ofthe centre ofgravity in the parallelogram, triangle, trapezium, parabola, parabolic trapezium, 8tc. 81c. To him we are also indebted for the theoryof the inclined plane, the pulley, and the screw, besides the invention of a multitude of com- pound machines, of which, however, he has left us no description, and thereforelittle more than their names remain. \Vc may judge ofthe very imperfect state in which the theory of mechanics was at that time, by the astonishment expressed by king Hiero, when Ar‘ chimedes exclaimed, “ Give me a place to stand on, and I will move the earth,” a proposition which could have excited no surprise in any person pos- sessing a knowledge of the simple property of the lever. Of the theory of motion, however, it does not appear that even Archimedes possessed any adequate idea; the properties of uniform motion seem only to have engaged the attention of the ancients, and with those of accelerated and varia- ble motion they were totally unacquainted: these were subjects to which their geometry could not be applied, the modern analysis being necessary to bring this branch of the science to perfection. From the time of Archimedes till the commence- n ment of the sixteenth century, the theory of me- chanics appears to have remained in the same state in which it was left by this prince of Grecian science, little or no additions having been made to it during so many ages; but about this time, Stevinus, a Flemish mathematician, made known directly, without the introduction of the lever, the laws of equilibrium of abody placed on an inclined plane: he also investigated, with the same success, many other questions on statics, and determined the conditions of equilibrium between several forces concurring in a common point, which comes, in fact, to the celebrated proposition relating to the parallelogram offorces: but it does not appear, however, that he was at all aware of its conse- quences and application. In 1592, Galileo com- posed a treatise on statics, which he reduced to this single principle, viz. it requires an equal power to raise two different bodies to heights having the inverse ratio of their weights; that is, whatever power will raise abody of two pounds to the height of one foot, will raise a body of one pound to the height of two feet. 011 this simple principle he investigated the theory of the inclined plane, the screw, and all themechanical powers, and Descartes afterwards employed it in considering the statical equilibriums of machines in general, but without quoting Galileo, to whom he had been indebted for the first idea. See FORCE. MECHANICAL CARPENTRY, that part of the art of construction in timber, which treats of the proper disposition of framing, so as to enable it to resist its own weight, or any additional load or pressure that may be casually laid upon it. MECHANICAL CARPENTRY is so called from the principles of mechanics being employed in the construction of truss—framing, or other parts of the art; while CONSTRUCTIVE CARPENTRY shews the rules for cutting and framing the tim- bers according to the proposed design; (see that article.) The mechanical principles of a piece ofcarpentry are therefore first to be considered; because they must in some measure regulate the disposition and size of the timbers in the design, after which they are to be prepared or formed according to the rules of constructive carpentry. We shall here state a few of the elementary pro- positions, with the principles of trussing, and offer some observations on the best forms of bodies constructed of timber work, to be used MEC 294 under various circumstances. And as it is impos- sible, in complex parts, to give all the minutiae with mathematical precision, this deficiency will in a great measure be compensated by general in— formation. The application of mechanical principles to car- pentry was first introduced in this country by Professor Robinson, of Edinburgh, in the Ency- clopedia Britannica, and it is to be hopedthat his laudable exertions will be followed up by men of ability; for though much has been done by this gentleman, much more remains to be done; as, in relation to mechanical science, carpentry can as yet be only considered in its infancy: the investigation of its complex parts being still at- tended with considerable uncertainty. It is now (A.D. 1814) about ten years since the Author drew up a complete article in every de— partment of carpentry, for that celebrated work Rees’s Encyclopedia; where this branch of the art, as depending upon the principles of mechanics, was particularly inculcated; and though several of the plates have been engraved and published some years ago, the manuscript relative to this particular branch has been retained for the article ROOF, to which indeed it chiefly pertains. In this application of mechanical science we are also indebted to Alexander Nimmo, Esq. F.R.S.E. civil engineer, for a very neat and well-connected theory of mechanical carpentry, published under the article CA RP ENTRY in the Edinburgh Ency- clopaadz'a. Under the article CURB ROOF, of the present Work, the reader will find an investigation of the best forms for a roof, restricted to certain data. With regard to the STRENGTH or TIMBER, the Author has reserved his observations for that arti- cle; but the practical rules derived therefrom will be here introduced preparatory to the general de- sign Ofmechanical carpentry ; and as these will be chiefly applicable to practice, we shall shew the rules under their most simple form; discarding such as, though accurate, would be too complex for common use. TO FIND THE COMPARATIVE STRENGTH OF TIMBER. DEFINITION.-—The depth of a piece of timber is its dimension in the direction of the pressure. PROPOSITION I.——Tojind the comparative strength of difi'erent timbers. RUL13.——Multiplyv the square of the depth of each piece into its thickness; and each product being M EC divided by its respective lengths, will give the proportional strength of each. Example—Suppose three pieces of timber of the following dimensions: The first, 6 inches deep, 3 inches thick, and 12 feet long. The second, 5 inches deep, 4 inches thick, and 8 feet long. The third, 9 inches deep, 8 inches thick, and 15 feet long. The comparative weight that will break each piece is required. OPERATIONS. First. Second. 6 deep 5 deep 6 p 5 36 25 3 thick 4 thick —_ Length 12 ) 108 Length 8) 100 ——_. 9 7; and a half. Third. 9 deep 9 .__.. 81 8 thick Length 15 )Ei§(43 and a fifth. 60 48 45 .— o O Therefore the weights that will break each are nearly in proportion to the numbers 9, 1‘2, and 43, leaving out the fractions; in which it is to be observed, that the number 43 is almost five times the number 9; therefore the third piece of timber will bear almost five times as much weight as the first; and the second piece nearly once and a third the weight of the first piece; because the number 12 is one and a third greater than the number 9. The timber is supposed to be every where of the same texture, otherwise these calculations cannot hold true. PROPOSITION II.— Given the length, breadth, and depth qfa piece (j timber; tofind the depth ofan- other piece, whose length and breadth are given, so that it shall bear the same weight as the first piece, or any number of times more. RULE.—)Iultiply the square of the dcpthof the “up: MEC — V- first piece into its breadth, and divide that pro- duct by its length: multiply the quotient by the number of times you would have the other piece to carry more weight than the first; and multiply the product by the length of the last piece, and divide the product by its width; out of this last quotient extract the square root, which is the depth required. Example 1.—Suppose a piece of timber 12 feet long, 6 inches deep, 4 inches thick; another piece 20 feet long, 5 inches thick; requireth its depth, so that it shall bear twice the weight of the first piece. Proof. 6 deep 9.7 6 9.7 so 67.9 J 873 12)144 9409 ’7}; 1.91 remainder added 2 times 96.00 a: .2 fl length 20) 480 5)}80 24 97319.7, or 9.8 nearlnyor the depth. 81 187i7355 1309 191 Example 2.—Suppose a piece of timber 14 feet long, 8 inches deep, 3 inches thick; required the depth of another piece, 18 feet long, 4 inches thick, so that the last piece shall bear five times as much weight as the first. 8 As thelengths of both pieces 8 of timber are divisible by the 732 number 2, therefore half the 3 length of each is used instead of the whole; the answer. will Half7) 199 be the same. Q7A,&c. 5 times 13 7 9 half the length 4)1233 —308.25( 17.5 the depth nearly 1 Q7)208( 189 345) 1925,&e. $29 U! MEC — —-—— PRO posiTrou [IL—Given the length, breadth, and depth of a piece (f timber; to find the breadth of another piece, whose length and depth are given, so that the last piece shall bear the same weight as the first piece, or any number of times more. RULE.——Multiply the square of the depth of the first piece into its thickness; the product divide by its length; multiply the quotient by the number of times it is required to have the last piece support more than the first; that product multiplied by the length of the last piece, and divided by the square of its depth, gives the breadth required. Example 1.—-Given a piece of timber 12 feet long, 6 inches deep, 4 inchesthick; and another piece 16 feet long, 8 inches deep; required the thick- ness, so that it shall bear twice as much weight as the first. Or, thus, at full length. 6 6 depth of the first piece 6 6 '36 E6 4 4 thickness of the first piece 3)14—4 Length12)1E 23 'ié 2 2 the number of times E)- ;Z stronger 4 16 length of the last piece 8)駥 iii 8)_Z§ Ea; 6fhickness. 8)~‘_38_4‘ — s) 48 6thickness. Example 2.—Given apiece of timber 12 feet long, 5 inches deep, 3 inches thick; and another piece 14 feet long, 6 inches deep; required the thick- ness, so that the last piece may bear four times as much weight as the first piece 6j§36 6) 58333 9:22 M EC 296 M EC PROPOSITION IV.——Ifa piece of timber sustain a force placed unequally between the extremes on which it is supported, the strength in the middle will be to the strength in that part of the timber so divided, as one divided by the square of half the length is to one divided by the rectangle of the two unequal segments; that is, in the reciprocal ratio of their products. Example 1.——Suppose a piece of timber 20 feet long, the depth and width immaterial; suppose the stress or weight to lie five feet distant from one Of its ends, consequently from the other end 15 feet, then the above proportion will be 1 _ 1 . 1 _ L RTE—fifr 5x15_'75 five feet from the end is to the strength at the middle, or 10 feet, or as 5 x 15 : 10 x 10: 100_ ll 33—— " Hence it appears, that a piece of timber 20 feet long is one-third stronger at 5 feet distance from the bearing, than it is in the middle, which is 10 feet, when out in the above proportion. as the strength at Example 2.-— Suppose a piece of timber 30 feet long; let the weight be applied 4 feet distant from one end, or more properly from the place where it takes its bearing, then from the other end it will be 26 feet, and the middle is 1.5 feet; 1 1 l 1 the“ 15x15_2—25“4 x eo‘frfii 17 Or as 4 x 9.6 : 15 x 15 : Q. 10—4, ornearly 2-}. Hence it appears, that a piece of timber 30 feet long will bear double the weight, and one-sixth more, at four feet distance from one end, than it will do in the middle, which is 15 feet dis- tant. Example 3.—Allowing that 266 pounds will break a beam 26 inches long, required the weight that will break the same beam when it lies at 5 inches from either end; then the distance to the other end is 21 inches; 21 x 5 = 105, the half of 26 inches is 13 ; therefore 13 x 13 = 169; consequently the strength at the middle of the piece is to the _ , 169 169_ strength at 0 inches from the end, as —l_6§ .: m3, 169 Ol'aSl:m' The proportion is stated thus: 1 : —— z: 266 to the weight required. - 169 2394- 1596 266 105) 44954 (428 420 299 210 894 840 .—__. 54- From this calculation it appears, that rather more than 428 pounds will break the beam at 5 inches distance from one Ofits ends, if 266 pounds will break the same beam in the middle. By similar propositions, the scantlings of any tim- ber may be computed, so that they shall sustain any given weight; for if the weight that one piece will sustain be known, with its dimensions, the weight that another piece will sustain, Of any given dimensions, may also be computed. The reader must observe, that although the foregoing rules are mathematically true, yet it is impossible to account for knots, cross-grained wood, Ste. such pieces being not so strong as those which have straight fibres; and if care be not taken in choosing the timber for a building, so that the fibres be disposed in parallel straight lines, all rules which can be laid down will be useless. It will be impossible, however, to estimate the strength of timber fit for any building, or to have any true knowledge of its proportions, without some rule; as otherwise every thing must be done by mere conjecture. Timber is much weakened by its own weight, ex- cept it stand perpendicular to the horizon. The bending of timber will be nearly in propor- tion to the weight laid on it; no beam ought to be trusted for any long time with above one~third or one-fourth part of the weight it will absolutely carry; for experiment proves, that a far less weight will break a piece of timber when hung to it for any considerable time, than what is suffi- cient to break it when first applied. PROBLEM I.—Having the length and weight of a beam that can just support a given weight in the MEC 9. W middle, tofind the length of another beam of the same scantling, that shall just break with its own treight. Let Z: the length of the first beam; L = the length of the second; a = the weight of the first beam ; w_ - the additional weight that will break it. Q a) + a Then to +a ——= -————-—g break the lesser beam. Again, let W be the weight of the beam that breaks with its own weight; and because the weights that will break beams of the same scant- ling are reciprocally as their lengths: .220 +a 2n) + a L: l: . l .2. VV. 2 2 L But the weights of beams of the same scantlings are to each other as their lengths; —, half the weight of the is the weight that will greater beam. Now a beam supported at both ends cannot break with its own weight, unless half the weight of the beam be equal to the weight that will break it; a L 2 w + a therefore,—— 2 l... ::———-l 2 L , consequently, a L2 = 1" (2w + a) _ 2 w + a and, L -— l (T). PROBLEM Il.—Having the weight of a beam that can just support a given weight in the middle; to find the depth of another beam similar to the fbrmer, so that it shall just support its own weight. Let (I : the depth of the first beam; at : the depth of the second beam; a = the weight of the first beam; 70 : the additional weight that will break the first beam. Then will a) + a 2w a . 5’ or 2+ : thewholewelght that will break the lesser beam. And because the weights that will break similar; beams are as the squares of their lengths, , ,, ‘Zw a 9 Q l d~:a'~:_: + :Q—-—-——-r w-l-x a:W. I 2 2 d2 ' Then because the weights of similar beams are as the LUbC‘S of their corresponding sides . VOL. 11. 9'7 MEC a ax3 d3 :ar’ :: :2— : a; = ; ax3 ‘2J v Figure 26—3. The strain on any section, B, ofa beam, A B, resting freely on two props, A and B, is A D x D B A B 4. The strain on the middle point, by a force ap- plied there, is one—fourth of the strain which the same force would produce, if applied to one end ofa beam of the same length, having the other and fixed. 5. The strain of any section, C, of a beam rest- ing on two props, A and B, occasioned by a force applied perpendicularly to another point, D, is proportional to the rectangle of the exterior seg- . AC x DB ments, or ls equal to an X T. There- wX fore the strain at C, occasioned by the pressure on 1), is the same-with the strain at D, occasioned by the same pressure on C. 6. The strain on any section, D, occasioned by a load uniformly diffused over any part, EF, is the same as if the two parts, ED, DF, of the load were collected at their middle points, eandf. Therefore the strain on any part, I), occasioned by a load uniformly distributed over the whole beam, is one—half of the strain that is produced when the same load is laid on at D ; and the strain on the middle point, C, occasioned by a load uni- formly distributed over the whole beam, is the same which half that load would produce if laid on at C. Figure 24.—7. A beam supported at both ends on two props, B and C, will carry twice as much when the ends beyond the props are kept from rising, as it will carry when it rests loosely on the props. 8. Lastly, the transverse strain on any section, occasioned by a force applied obliquely, is dimi— nished in the proportion of the sine of the angle which the direction of the force makes with the beam. Thus, if it be inclined to it in an angle of thirty degrees,.the strain is one—half of the strain occasioned by the same force acting perpendicu- larly. On the other hand, the relative strength of a beam, or its power in any particular section to resist any 'transverse strain, is proportional to the absolute cohesion of the section directly, to the distance of its centre of effort from the axis of fracture directly, and to the distance from the strained point inversely. Thus, in a rectangular section of the beam, of which I) is the breadth, d the depth (that is, the dimension in the direction of the straining force), measured in inches, andfthe number of pounds which one square inch will just support without being torn asunder, we must havefx b x d“, proportional to w x C B. Or, f X b X (11, mul- tiplied by some number, 712, depending on the nature of the timber, must be equal to m X CB. Or, in the case of the section, C, of Figure 46, that is strained by the force, to, applied at D, we C DB 753—. Thus, if the beam is of sound oak, m is very nearly 2 2%. Therefore wehavef bd : w A_C_x_9_1_3 9 A B Hence we can tell the precise force, zv, which any section, C, can just resist when that force is applied in any way whatever. For the above- 2 9C5 represented by Figure 25. But the case repre- sented in Figure 26 having the straining force applied at I), gives the strain at C (: w) b d2 x A B =f X QACXCB' Example—Let an oak beam, four inches square, rest freely on the props A and B, seven feet apart, or 84- inches. What weight will it just support at its middle point, C, on the supposition that a square inch rod will just carry 16,000 pounds, pulling it asunder? 16000 x 4 x16 x 84. 9 x 42 x 42 ’ must have m xfb d“: w x mentioned formula gives w = ) for the case The formula becomes to = or w = 86016000 15876 near what was employed in Buffon’s experiment, which was 5312. Had the straining force acted on a point, D, half way between C and B, the force sufficient to break the beam at C would be equal to 16000 X 4 X 16 X 84 9 X 42 X 21 Had the beam been sound red fir, we must have taken f = 10,000 nearly, and m nearly 8; for al- though fir be less cohesive than oak in the pro- portion of 5 to 8 nearly, it is less compressible, = 5418 pounds. This is very = 10836 lbs. EIE C 3&sz ,1 CAL CARP E N T R37, PLATE 121. fig. 20. * men by Mifl'dfiob'on. london,flzblz§rhed byflVL‘des'on & JBar/ield fihrdouro‘treetho‘. Jillnw' Du m “val/[2. M EC 3 r W MEC T and its axis of fracture is therefore nearer to the concave side. Having considered at sufficient length the strains of different kinds which arise from the form of the parts of a frame of carpentry, and the direction of the external forces which act on it, whether con- sidered as impelling or as supporting its different parts, we must now proceed to consider the means by which this form is to be secured, and the con- nections by which those strains are excited and communicated. 'l‘he joinings practised in carpentry are almostin- finitely various, and each has advantages which make it preferable in some circumstances. Many varieties are employed merely to please the eye. We do not concern ourselves with these: nor shall we consider those which are only employed in connecting small works, and can never appear on a great scale; yet, even in some of these, the skill of the carpenter may be discovered by his choice; for, in all cases, it is wise to make every, even the smallest, part of his work as strong as the materials will admit. He will be particularly attentive to the changes which will necessarily happen by the shrinking of timber as it dries, and will consider what dimensions of his framings will be affected by this, and what will not; and will then dispose the pieces which are less essential to the strength of the whole, in: such a manner that their tendency to shrink shall be in the same di- reetion with the shrinking of the whole framing. If he do otherwise, the seams will widen, and parts will be split asunder. He will dispose his boardings in such a manner as to contribute to the stiffness of the whole, avoiding at the same time the giving them positions which will produce lateral strains on truss-beams which bear great pressures; rceollecting, that although a single board has little force, yet many united have a great deal, and may frequently perform the office of very powerful struts. Uur limits confine us to the joinings which are most essential for connecting the parts ofa single piece of a frame when it cannot be formed of one beam, either for want of the necessary thickness or length; and thcjoints for connecting the dif- ferent sides of a trussed frame. M ueh ingenuity and contrivance has been be- stowed on the manner of building up a great beam of many thicknesses, and many singular methods 3‘“ Praetised, as great nostrums, by different ar- tists: but when we consider the manner in which the cohesion of the fibres performs its oflice, we will clearly see that the simplest are equally effec- tual with the most refined, and that they are less apt to lead us into false notions of the strength of the assemblage. Thus, were it required to build up a beam for a great lever, or a girder, so that it may act nearly as abeam of the same size of one log; it may either be done by plain joggling, as in Figure 27, A, or by searfing, as at B or C. If it is to act as a lever, having the gudgeon on the lower side at C, we believe that most artists will prefer the form B and C; at least this has been the case with nine-tenths of those to whom we have proposed the question. The best informed only hesitated; but the ordinary artists were all confident in its superiority; and we found their views of the matter very coincident. They con-- sidered the upper piece as grasping the lower in its books; and several imagined that, by driving the one very tight on the other, the beam would be stronger than an entire log: but if we attend carefully to the internal procedure in the loaded lever, we shall find the upper one clearly the strongest. If they are formed of equal logs, the upper one is thicker than the other by the depth of thejoggling or searfing, which we suppose to be the same in both; consequently, if the cohe- sion of the fibres in the intervals is able to bring the uppermost filaments into full action, the form A is stronger than B, in the proportion of the greater distance of the upper filaments from the axis of the fracture: this may be greater than the difference of the thickness, if the wood is very compressible. If the gudgeon be in the middle, the effect, both of the joggles and the scarfings, is considerably diminished; and if it is on the upper side, the scarfings act in a very different way. In this situation, if the loads on the arms are also applied to the upper side, the joggled beam is still more superior to the scarfed one. This will be best understood by resolving it in imagination into a trussed frame. But when a gudgeon is thus put on that side of the lever which grows convex by the strain, it is usual to connect it with the rest by a powerful strap, which embraces the beam, and causes the opposite point to become the resisting point. This greatly changes the internal actions of the filaments, and. in some measure, brings it into the same state as Qs’z MEC’ S M EC the first, with the gudgeon below. Were it pos- sible to have the gudgeon on the upper side, and to bring the whole into action without a strap, it would be the strongest of all; because, in gene- ral, the resistance to compression is greater than to extension. In every situation thejoggled beam has the advantage; and it is the easiest executed. “7e may frequently gain a considerable accession of strength by this building up of a beam; espe- cially if the part which is stretched by the strain be of oak, and the other part of fir. Fir being so much superior to oak as a pillar (if Musschen- broek’s experiments may be confided in), and oak so much preferable as a tie, this construction seems to unite both advantages. But we shall see much better methods of making powerful levers, girders, 8L0. by trussing. Observe, that the efficacy of both methods de- pends entirely on the difficulty of causing the piece between the crossjoints to slide along the timber to which it adheres. Therefore, if this be moderate, it is wrong to make the notches deep; for as soon as they are so deep that their ends have a force sufficient to push the slice along the line ofjunction, nothing is gained by making them deeper; and this requires a greater expert—e diture of timber. Scarfings are frequently made oblique, as in Fi- gure 28, but we imagine that this is a bad prac- tice. It begins to yield at the point, where the wood is crippled and splintered off, or at least bruised out a little: as the pressure increases, this part, by squeezing broader, causes the solid parts to rise a little upwards, and gives them tome tendency, not only to push their antagonists along the base, but even to tear them up a little. For similar reasons, we disapprove of the favourite practice of many artists, to make the angles of their scarfings acute, as in Figure 29. This often causes the two pieces to tear each other up. The abutments should always be perpendicular to the directions of the pressures. Lest it should be for- gotten in its proper place, we may extend this injunction also to the abutments of different pieces of a frame, and recommend it to the artist even to attend to the shrinking of the timbers by dryintr. When two timbers abut obliquely, the joint should be most full at the obtuse angle of the end; because, by drying, that angle grows more obtuse, and the beam would then be in danger of splintering off at the acute angle. It is evident, that the nicest work is indispensably necessary in building up a beam. The parts must abut on each other completely, and the smallest play, or void, takes away the whole efficacy. It is usual to give the butting joints a small taper to one side of the beam, so that they may require moderate blows of a maul to force them'in, and thejoints may be perfectly close when the exter- nal surfaces are even on each side of the beam. But we must not exceed in the least degree; for a very taper wedge has great force; and if we have driven the pieces together by very heavy blows, we leave the whole in a state of violent strain, and the abutments are perhaps ready to splinter off by a small addition of pressure. The most general reason for piecing a beam is to increase its length. vThis is frequently necessary, in order to procure tie-beams for very wide roofs‘. Two pieCes must be scarfed together. Number- less are the modes of doing this; and almost every master carpenter has his favourite nostrum. Some of them are very ingenious: but here, as in other cases, the most simple are commonly the strongest. We do not imagine that any, the most ingenious, is equally strong with a tie consisting of two pieces of the same scantling laid over each other for a certain length, and firmly bolted to- gether. We acknowledge that this will appear an artless and clumsy tie-beam; but we only say thatit will be stronger than any that is more arti- ficially made up of the same thickness of timber. This, we imagine, will appear sufficiently certian. The simplest and most obvious scarfing (after the one now mentioned) is that represented in Figure 30, No. land 2. 1f considered merely as two pieces of woodjoined, it is plain that, as a tie, it has but half the strength of an entire piece, sup- posing that the bolts (which are the only connec- tions) are fast in their holes. No. 2 requires a bolt in the middle of the scarf to give it that strength; and, in every other part, is weaker on one side or the other. But the bolts are very apt to bend by the violent strain, and require to be strengthened by uniting their ends by iron plates; in which case it is no longer a wooden tie. The form of No. l is better adapted to the office ofa pillar than No. 2; espe- cially if its ends be formed in the manner shewn in the elevation, No. 3. By the sally given to the ends, the scarf resists an effort to bend it in that direction. Besides, the form of No. ‘2. is une MECHAN ICAL CARPE N T RY. PMTEIV. 11:0. 29. F1313”. 2W]. F137. 30. N? 2. F131. 30. 2V." 3. 113,, 33. 51/ MANidleon. Engraved by [Dan/111‘. [ombml‘ublithal by 1’. Nit/whorl, @- IBarf-‘ield, Wardour Jtreet, 1816. km 2.4; . _..; A MEC 317 MEC M suitable for a post; because the pieces, by sliding on each other by the pressure, are apt to splinter off the tongue which confines their extremity. Figures 31 and 82, exhibit the most approved form ofa scarf, whether for a tie or a post. The key represented in the middle is not essentially necessary; the two pieces might simply meet square there. This form, without a key, needs no bolts (although they strengthen it greatly); but, if worked very true and close, and with square abutments, will hold together, and will resist bending in any direction. But the key is an ingenious and a very great improvement, and will force the parts together with perfect tight- ness. The same precaution must be observed that we mentioned on another occasion, not to produce a constant internal strain on the parts by over driving the key. The form of Figure 31 is by far the best; because the triangle of 32 is much easier splintered off by the strain, or by the key, than the square wood of 31. It is far preferable for a post, for the reason given when speaking of Figure 30, No. l and 2. Both may he formed with a sally at the ends equal to the breadth of the key. In this shape Figure 3] is vastly well suited forjoining the parts of the long corner posts of spires and other wooden towers. Figure 31, No. 2, differs from No. 1 only by having three keys. The principle and longitu- dinal strength are the same. The long scarf of No. 2, tightened by the three keys, enables it to resist a bending much better. None of these scarfed tie-beams can have more than one-third of the strength of an entire piece, unless with the assistance of iron plates; for if the key be made thinner than one-third, it has less than one-third of the fibres to pull by. We are confident, therefore, that when the heads of the bolts are connected by plates, the simple form of Figure 30, No. l, is stronger than those more ingenious scarfings. It may be strengthen- ed against lateral bendings by a little tongue, or by a sally; but it cannot have both. The strongest of all methods of piecing a tie- beam would be to set the parts end to end, and grasp them between other pieces on each side, as in Figure 33. This is what the ship~carpenter calls fishing a beam; and is a frequent practice for occasional repairs. M. Perronet used it for the tie-beams, or stretchers, by which he con- nected the opposite feet of a centre, which was yielding to its load, and had pushed aside one of the piers above four inches. Six of these not only withstood a strain of 1800 tons, but, by wedging behind them, he brought the feet of the truss 2% inches nearer. The stretchers were 14 inches by 11, of sound oak, and could have withstood three times that strain. M. Perronet, fearing that the great length of the bolts employed to connect the beams of these stretchers would expose them to the risk of bending, scarfed the’two side pieces into the middle piece. The scarfing was of the triangular kind (trait de Jupiter), and only an inch deep, each face being two feet long, and the bolt passed through close to the angle. In piecing the pump rods, and other wooden stretchers of great engines, no dependence is bad on scarfing; and the engineer connects every thing by iron straps. But we doubt the propriety of this, at least in cases where,the bulk of the wooden connection is not inconvenient. These observations must suffice for the methods em ployed. for connecting the parts ofabeam ;. and we now proceed to consider what aremor-e usually called thejoim‘s ofa piece of carpentry. ' Where the beams stand square with each other, and the strains are also square with the beams, and in the plane of the frame, the common mor- rise and tenon is the most perfect junction. A pin is generally put through both, in order to keep the pieces united, in opposition to any force which tends to part them. Every carpenter knows how to bore the hole for this pin, so that it shall draw the tenon tight into the mortise, and cause the shoulder to butt close, and make neat work; and he knows the risk of tearing out the bit of the tenon beyond the pin, ifhe draw it too much. We mayjust observe, that square holes and pins are much preferable to round ones for this pur- pose, bringing more of the wood into action, with less tendency to split it. The ship-carpen- ters have an ingenious method of making'long wooden bolts, which do not pass completely through, take a very fast hold, though not nicely fitted to their holes, which they must not be, lest they should be crippled in driving. They call it foxtail wedging. They stick into the point of the bolt a very thin wedge of hard wood, so as to project a proper distance: when this reaches the bottom of the hole by drivingthe bolt, it splits the end of it, and squeezes it hard to the side. This may be practised with advantage in car- MEC S 18 L - __ ‘__. pentry. If the ends of the mortise are widened inwards, and a thin wedge be put into the head of the tenon, it will have the same effect, and make the joint equal to a dovetail. But this risks the splitting of the piece beyond the shoulder of the tenon, which would be unsightly. This may be avoided as follows: Let the tenon, T, Figure 34, have two very thin wedges, a and c, stuck in near its angles, projecting equally: at a very small distance within these put in two shorter wedges, b, d, and more within these, if necessary. In driving this tenon, the wedges a and c will take first, and split off a thin slice, which will easily bend, without breaking. The wedges b, d, will act next, and have a similar effect, and the others in succession. The thickness of all the wedges taken together must be equal to the enlargement of the mortice toward the bottom. The mortise in a girder for receiving the tenon of a binding joist of a floor should be as near the upper side as possible, because the girder becomes concave on that side by the strain. But as this exposes the tenon of the binding-joist to the risk of being. torn off, we are obliged to mortise far— ther down. The form (Figure 35), generally given to this joint is extremelyjudicious. The sloping part, a I), gives a very firm support to the additional bearing, 0 (1, without much weakening of the girder. This form should be copied in every case where the strain has a similar direction. Thejoint that most of all demands the careful at- tention of the artist, is that which connects the ends of beams, one of, which pushes the other very obliquely, putting it into a state of exten- sion. The most familiar instance of this is the foot of a rafter pressing on the tie-beam, and thereby drawing it away from the other wall. When the direction is very oblique (in which case the extending strain is the greatest), it is difficult to give the foot of the rafter such a hold of the tie-beam as to bring many of its fibres into the proper action. There would be little difficulty if we could allow the end of the tie-beam to pro- ject to a small distance beyond the foot of the rafter: but, indeed, the dimensions which are given to tie-beams, for other reasons, are always sufficient to give enough of abutment whenjudi- ciously employed. Unfortunately, this joint is much exposed to failure by the effects of the weather. It is much exposed, and frequently perishes by rot, or becomes so soft and friable, M EC w ———‘ that a very small force is sufficient, either for pulling the filaments out of the tie-beam, or for crushing them together. We are therefore obliged to secure it with particular attention, and to avail ourselves of every circumstance of construction. One is naturally disposed to give the rafter adeep hold by a long tenon; but it has been frequently observed, in old roofs, that such tenons break off. Frequently they are observed to tear up the wood that is above them, and push their way through the end of the tie-beam. This in all probability arises from the first sagging of the roof, by the compression of the rafters and of the head of the king-post. The head of the rafter descends, the angle with the tie-beam is diminished by the rafter revolving round its step in the tie-beam. By this motion the heel, or inner angle of the rafter becomes a fulcrum to a very long and pow- erful lever much loaded. The tenon is the other arm, very short, and being still fresh, it is there- fore very powerful. It therefore forces up the wood that is above it, tearing itout from between the cheeks of the mortise, and then pushes it along. Carpenters have therefore given up long tenons, and give to the toe of the tenon a shape which abuts firmly, in the direction of the thrust, on the solid bottom of the mortise, which is well supported on the under side by the wall-plate. This form has the farther advantage of having no tendency to tear up the end of the mortise; and is represented in Figure 36. The tenon has a small portion, a I), cut perpendicular to the surface of the tie-beam, and the rest, b c, is perpendicular to the rafter. But if the tenon be not sufiiciently strong, (and it is not so strong as the rafter, which is thought not to be stronger than is necessary), it will be crushed, and then the rafter will slide out along the surface of the beam. It is therefore neces- sary to call in the assistance of the whole rafter. It is in this distribution of the strain, among the various abutting parts, that the varieties ofjoints and their merits chiefly consist. It would be endless to describe every nostrum, and we shall only mention a few, that are most generally ap- proved of. The aim, in Figure 37, is to make the abutments exactly perpendicular to the thrusts. It does this very precisely; and the share which the tenon and the shoulder have of the whole, may be what we please, by the portion of the beam that we W M EC 5 19 MEC notch down. If the wall plate lie duly before the heel of the rafter, there is no risk of straining the tie across, or breaking it, because the thrust is made direct to that point where the beam is sup- ported. The action is the same as against the joggle on the head or foot of a king-post. We have no doubt but that this is a very efl'ectual joint. It is not, however, much practised. It is said that the sloping seam at the shoulder lodges water; but the great reason seems to be a secret notion that it weakens the tie-beam. If we con- sider the direction in which it acts as a tie, we must acknowledge that this form takes the best method for bringing the whole of it into action. Figure 38 exhibits a form that is more general, but certainly worse. The part of the thrust that is not borne by the tenon acts obliquely on the joint of the shoulder, and gives the whole a ten— dency to rise up and slide outward. The shoulder joint is sometimes formed like the dotted line, a b c d efg, of Figure 38. This is much more agreeable to the true principle, and would be a very perfect method, were it not that the intervals, I) dand df, are so short that the little wooden triangles, b c d, d ef, will be easily pushed off their bases, 1) (1, df. Figure 39 seems to have the most general appro— bation. It is the joint recommended by Price, (p. 7), and copied into all books of carpentry, as the true joint for a rafter foot. The visible shoulder-joint is flush with the upper surface of the tie-beam. The angle of the tenon at the tie nearly bisects the obtuse angle formed by the rafter and the beam, and is therefore somewhat oblique to the thrust. The inner shoulder, a c, is nearly perpendicular to b d. The lower angle of the tenon is cut off horizontally, as at e (1. Figure 40 is a section of the beam and rafter foot, shewing the different shoulders. We do not perceive the peculiar merit of this joint. The effect of the three oblique abutments, a I), a 0, ed, is undoubtedly to make the whole bear on the outer end of the mortise, and there is no other part of the tie-beam that makes imme- diate resistance. Its only advantage over a tenon extending in the direction of the thrust, is, that it will not tear up the wood above it. Had the inner shoulder had the form e c 1', having its face, 1e, perpendicular, it certainly would have acted more powerfully in stretching many filaments of the tie-beam, and would have had much less ten- _~u dency to force out the end of the mortise. The little bit, c i, would have prevented the sliding upwards along e c. At any rate, the joint, a I), being flush with the beam, prevents any sensible abutment on the shoulder, a c. Figure 39, No.2, is a simpler, and, in our opinion, a preferable joint. We observe it practised by the most eminent carpenters, for all oblique thrusts; but it Surely employs less of the cohe- sion of the tie-beam than might be used without weakening it, at least when it is supported on the other side by the wall-plate. Figure 39, No. 3, is also much practised by the first carpenters. Figure 41 is proposed by Mr. Nicholson, (p. 65), as preferable to Figure 39, No. 3, because the abut- ment of the inner part is better supported. This is certainly the case; but it supposes the whole rafter to go to the bottom of the socket, and the beam to be thicker than the rafter. Some may think that this will weaken the beam too much, when it is no broader than the rafter is thick; in which case they think that it requires a deeper socket than Nicholson has given it. Perhaps the advantages of Nicholson’s construction may be had by ajoint like Figure 41, No. 2. Whatever be the form of these butting joints, great care should be taken that all parts bear alike, and the artist will attend to the magnitude of the different surfaces. In the general com pres- sion, the greater surfaces will be less compressed, and the smaller will therefore change most. When all has settled, every part should be equally close. Because great logs are moved with difficulty, it is very troublesome to try thejoint frequently to see how the parts fit; therefore we must expect less accuracy in the interior parts. This should make us prefer those joints whose efficacy depends chiefly on the visible joint. It appears, from all that we have said on this sub- ject, that a very small part of the cohesion of the tie-beams is suflicient for withstanding the hori- zontal thrust of a roof, even though very lOw pitched. If therefore no other use he made of the tie-beam, one much slenderer may be used, and blocks may be firmly fixed to the ends, on which the rafters might abut, as they do on the joggles on the head and foot of a king-post. Although a tie-beam has commonly floors or ceilings to carry, and sometimes the workshops and store- rooms of a theatre, and therefore requires a great M EC- 320 M EC scantling, yet there frequently occur in machines and engines very oblique stretchers, which have no other oflice, and are generally made of dimen- sions quite inadequate to their situation, often containing ten times the necessary quantity of timber. It is therefore of importance to ascertain the most perfect manner of executing such a joint. We have directed the attention to the principles that are really concerned in the effect. In all hazardous cases, the carpenter calls in the assistance of iron straps; and they are frequently necessary, even in roofs, notwithstanding this superabundant strength of the tie-beams. But this is generally owing to the bad construction of the wooden joint, or to the failure of it by time. Straps will be considered in their place. There need but little to be said of thejoints at a joggle worked out of solid timber; they are not near so difficult as the last. When the size of a log will allow the joggle to receive the whole breadth of the abutting brace, it ought certainly to be made with a square shoulder; or, which is still better, an arch of acircle, having the other end of the brace for its centre. Indeed, this in general will not sensibly differ from a straight line perpendicular to the brace. By this circular form, the settling of the roof makes no change in the abutment; but when there is not sufficient stuff for this, we must avoid bevel joints at the shoul- ders, because these always tend to make the brace slide ofi“. The brace, in Figure 41, must not be joined as at a, but as at I), or some equivalent manner. Observe the joints at the head of the main posts of Drury—lane theatre. See ROOF. When the very oblique action of one side of a frame of carpentry does not extend, but compress the piece on which it abuts, as in Figure 21, there is no difficulty in thejoint. Indeed, a joining is unnecessary, and it is enough that the pieces abut on each other; and we have only to take care that the mutual pressure be equally borne by all the parts, and that it do not produce lateral pressures, which may cause one of the pieces to slide on the butting joint. A very slight mortise and tenon is sufficient at the joggle of a king- post, with a rafter or straining beam. It is best, in general, to make the butting plain, bisecting the angle formed by the sides, or else perpendi- cular to one of the pieces. In Figure 42, No. ‘2, where the straining beam, a I), cannot slip away from the pressure, the joint a is preferable to I), or indeed to any uneven joint, which never fails to produce very unequal pressures on the difl'erent parts, by which some are crippled, others are splintered off, 8L0. When it is necessary to employ iron straps for strengthening ajoint, a considerable attention is necessary, that we may place them properly. The first thing to be determined is the direction of the strain. \Ve must then resolve this strain into a. strain parallel to each piece, and another perpen- dicular to it. Then the strap, which is to be made fast to any of the pieces, must be so fixed, that it shall resist in the direction parallel to the piece. Frequently this cannot be done; but we must come as near to it as we can. In such cases, we must suppose that the assemblage yields a little to the pressures which act on it. We must exa- mine what change of shape a small yielding will produce. We must now see how this will affect the iron strap, which we have already supposed attached to the joint in some manner that we thought suitable. This settling will perhaps draw the pieces away from it, leaving it loose and un- serviceable; (this frequently happens to the plates which are put to secure the obtuse angles of but- ' ting timbers, when their bolts are at Some distance from the angles, especially when these plates are laid on the inside of the angles); or it may cause it to compress the pieces harder than before; in which case it is answering our intention. But it may be producing cross strains, which may break them; or it maybe crippling them. We can hardly give any general rules; be will see the nature of the strap or stirrup, by which the king post carries the tie-beam. The strap that we ob- serve most generally ill-placed is that which con- nects the foot of the rafter with the beam. It only binds down the rafter, but does not act against its horizontal thrust. It should be placed farther back on the beam, with a bolt through it, which will allow it to turn round. It should em- brace the rafter almost horizontally near the foot, and should be notched square with the back of the rafter. Such a construction is represented in Figure 43. By moving round the eye-bolt, it follows the rafter, and cannot pinch and cripple it, which it always does in its ordinary form. We are of opinion that straps which have eye-bolts in the very angles, and allow all motion round them, are, of all, the most perfect. A branched strap, such as may at once bind the king-post and the )iiit‘iiiir’iir wi‘ MW 'll‘i Hus" W”, Mill]! 2%: 'iiiiifi'“ * / m 53/ MA.NlMalron. MEQHANECAL CARPENTRY. mm” F159. 35. r“ _ I it“ 1 WI Fig. 40. f £31.41. TM» [WWI/lbw by RNz'deam, & JBaI-fi'dd, Wardour 5M1616. Engraved by 10m. MEC 34 —:, ~77 two braces which butt on its foot, will be more serviceable if it have ajoint. When a roof warps, ' those branched straps frequently break the tenons, by affording a fulcrum in one of their bolts. An attentive and judicious artist will consider how the beams will act on such occasions, and will avoid giving rise to these great strains by levers. A skilful carpenter never employs many straps, considering them as auxiliaries foreign to his art, and subject to imperfections in workmanship, which he cannot discern nor amend—Supplement to the article Carpentry, oftlte Encyclopedia Bri- tannica, by Professor Robinson. The following part was written by the Author for the Edinburgh Cyclopedia, and is here inserted by permission of the editor. A circular roof may be executed with timbers disposed in vertical planes, whether the ribs or rafters are convex, concave, or straight, without any tie between the rafters or ribs, even though the wall were ever so thin; provided that it be only sufiicient to sustain the weight of the roof pressing vertically, by joining the wall-plate so as to form a complete ring, and by strutting the rafters in one or more horizontal courses, without danger of lateral pressure, or of the timbers being bent by the weight of the covering. The same cannot be done with the roof of a rectan- gular building, for single parallel rafters would not only obtain a concave curvature, but would thrust the walls outwards: hence the means of ex- ecuting circular roofs with safety are simple, but those for straight-sided buildings are complex, and require much skill in contriving, according to the use that is to be made of the space be- tween the rafters, which may be found necessary in rendering more lofty, or more elegant apart- ments, as in Concave or coved ceilings. A polygonal roof, with a great number of sides, approaching very nearly to a circle, is stronger than one of fewer sides; the less the number of sides, the weaker will the roof be, and more liable to get out of order. A roof executed upon an eqvilateral and equiangular polygonal plan, is - much stronger than one that is elongated. All circular roofs, for the same reason, are stronger than elliptical ones; the pressure in the former case being equally distributed round the wall- plate, which is therefore kept in an equal state of tension. ‘Trusses are strong frames of carpentry, resolved VOL. 11. MEC into two, or a series of triangles, so as to make the truss act as a solid body, and thereby support certain weights, each at a given immoveable point, the truss itself being suspended from two such immoveable points. The trusses of roofs are constructed generally of a triangular form, and disposed ‘equidistantly on the wall-plates in parallel vertical planes, at right angles to the walls; the top of the opposite walls are the two points of suspension, and the weights supported by the truss at the immoveable points are hori- zontal pieces of timber, running transversely to the planes of the trusses: these horizontal pieces of timber support other equidistant pieces paral- lel to the upper sides of the trusses, and these last timbers support the covering, or the covering and timber-work, to which the covering is fixed. In a truss, some pieces of timber are in a state of tension, and some are in a state of compression; but a piece of timber, which is neither extended nor compressed, is useless. A quadrilateral frame, so constructed that each two adjoining timbers made moveable round a point at their intersection may be put into an infinite number of forms, be- cause the whole frame will be revolvable about the angles; but if any one of the angles be. immove- able, the whole frame will also be so. Two pieces of timber forming an angle, and revolving round a point at their intersection, may be made im- moveable by fastening each end of a bar to each leg, or by taking any two points in the bar, and fastening each point to each leg: now if a force be applied at any of the three angular points, the frame will be immoveable, but of the two legs which form the angle, the one will be in a state of tension, and the other in a state of compression, provided that the direction of the force applied does not fall within the angle if produced: but if the line of direction of the force applied fall within the angle of the triangle, then both legs are either in a state of tension, or in a state of compression, according as the force applied is pulling or pressing; if one of the sides of the tri- angle be lengthened without the boundary, and a force be applied transversely to the-part so lengthened, this force will bend the side of the figure which is in the straight line with the side to which the force is applied: therefore suppose again a quadrangle, or quadrilateral, revolvable about the angles, and a bar be fixed to any two sides forming an angle, viz. a point in the bar to ‘2. '1‘ m M EC 3 fl a pointin one of the legs, and another point in the bar to a point in the other leg, and suppose the two points not to be in two of the angles, or one of the points to be’in the side, at some distance from either end, the figure will be divided into two parts, one will always be a triangle; then if it be supported at two of its angles, and a force be applied to the angle opposite, the angle which has the bar fixed to its legs, so that the direction of the force thus applied does not tend to the fixed point, which is the farther extremity ofthe one leg, where the force is applied to the angular point at the other extremity. All the sides of this figure will be bent, and the bar thus fixed will occasion trans- verse strains to the sides; but if the bar be fixed to two opposite angles, and if the frame be held immoveable at one of the angular points where the bar is fixed, and also at one of the other angles at the extremity of one of the legs of the said an- gle, and a force in any direction in the plane of the figure be applied to the angle where the frame is unsupported, and where the bar is not fixed, the frame will be by this means rendered immoveable, and the force by this disposition will not occa- sion any transverse strain on the sides of the frame. Suppose the frame to be pentagonal, and a bar fixed in like manner to two angles at the ends of two adjoining sides, these two adjoining sides and the bar will form a triangular compart- ment in the figure; if the frame be suspended by two of the angles of the triangle, the three re- maining sides will be moveable at the extre- mities of the bar, and at the remaining angles; but if another bar be fixed to any one of the three angles of the triangle at one end, to one of the angles of the other three sides, to form another triangle, three of the sides of the pentagonal frame will be made immovable, and the two remaining sides will be so likewise. In like manner,in what- ever number of sides the frame consists, by first forming a triangle of two of the sides, and fixing a second bar from any angle of the triangle to one of the other angles of the figure, at the remote ends of two adjoining sides of this frame, will form another immoveable side, and give another immoveable point at the next angle of the frame; if from this fixed point, or any of the other three points, which are the angles of the triangle, the end of a third bar be fixed, and the other end of the bar to one of the remaining angles of the frame, so as to form a triangle with the second 22 M EC m m bar and one of the adjoining moveable sides of the frame, or a triangle with one of the fixed sides of the frame and the adjoining moveable side; and by proceeding in this manner succes- sively, until all the sides are fixed, the frame will be made immoveable; so that if any two angles of this frame be supported, and? a force or forces be applied at one, or each of the angles in the plane of the figure, the whole figure will be im- moveable. Frames of a triangular form, which have to resist only a single force, or support one weight, are most simply and best constructed of three sides; the frame being suspended from two angles, and the force, or weight, from the other. A triangular frame, supporting only one weight, has no occa-a sion for any subdivisions to compart the internal space, provided the compressed timber or timbers were inflexible, so as to support their own weight without bending, and the tensile timbers inca- pable of extension. Though a frame should have to support several weights, the external figure may be of any form whatever, provided that the points from which the weights are hung, and the two points from which the frame is suspended, be all immoveably supported by comparting the figure with timber divisions, and thereby forming a succession of adjoining triangles, of which each two contiguous have a common side; that is, when two of the angles of each of the adjacent triangles are coincident. It may be proper to ob- serve here, that though it may not be at all times eligible to divide a frame, so that all the com- partments will be triangles, yet the succession must not by any means be discontinued by the in. tervention of quadrilateral or polygonal figures, for these compartments may adjoin without in- jury to the truss. The triangle is the most simple of all rectilenear figures, it is also easier con- structed, and better adapted to the discharge of rain or moisture in a roof, than any other figure; but, in its adoption to large buildings, as several weights must be supported, and-as there is only one point from which this weight car. he sus- pended, it becomes necessary to take other equi- distant points in the sides, in order to support the covering equally : these points maybe made stationary, by the former means of dividing the interior space into asuccession of triangular com- partments. But if the two upper sides of the frame be of equal lengths, and equally inclined to MEG the horizon, the opposite points may be made to counteract each other without a concatination of triangles, by introducing timbers from point to point, parallel to the horizon; in this the com- partments will all be trapezoids, except the upper one, which will be a triangle. These beams may be supported by vertical bolts passing transversely through them from the points where the weights are supported, and the bolts may be nutted below the beams. This mode of securing the points of support depends entirely upon the doctrine of equilibrium, and thus a very little difference from the equality of forces might easily occasion a change of figure, to which the other method by a series of triangles is.not liable. The securing of the points of support by beams is not confined to triangular frames, but may be applied to roofs having two or several rafters upon each side, so that their lengths and inclinations are equal, and their junctions on the same level. The beauty of every truss is to dispose the timbers in positions as direct to each other as possible: oblique direc- tions require timbers of large scantlings, and exert prodigious thrusts on the abutments, so as to compress the joggle-pieces, and render the truss in danger of sagging. ' Trusses are variously con- structed, according to the width of the building, the contour of the roof, and the circumstances of walling below. The general principle of construction is a series of triangles, of which every two are connected by a common side. Figure 44.——Let A B C D E F G, be the curve of the arch which requires a centre. Let the points, A B C, 8L0. be connected, so as to form the equi- lateral polygon A B C D E F G, and join A C, C E, and E G; the timbers thus disposed will form three triangles, which may be looked upon as so many solids revolvable about the angu- lar points, A, C, E, G; suppose now these to be in equilibrium, the smallest force on either side would throw it down ; and therefore, without otherconnec‘ing timbers, it would be unfit for the purpose or a centre. Figure 45.-—Let A B C D E F G, be the curve of an arch which requires a centre. First, form the equilateral polygon, A B C D E F G, with the tim- bers AB, C D, G D, Ste. and fix the timbers AC, C E, EG,»as before, which will form three trian- gles, moveable round A C EG; let the timbers B D and D F be fastened, and thus the whole will 3 3 MEC be immutable, so that, if supported at the points A and G, and a force be applied at any other of the angles, B, C, D, or F, the timbers will be all in a state of tension, or in a state of compression, and the whole may be looked upon as a solid body. . For since the sides and angular points of a trian- gle are fixed, when the triangle is supported at two of the angles, and a force applied to the other, let us suppose the triangle, A B C, to be sup- ported at the points A and B, and the point C, and the other two sides, B C, C A, will be fixed; and because B C D is a triangle, and the points B and C are fixed; the point D, and consequently the sides C D and D B are fixed. In like man- ner, sinée C D E is a triangle, and the points C and D fixed, the point E will also be fixed, and also the sides I) E and EC. The same may be shewn in like manner for the points F and G. b‘up- pose, then, two equal and opposite forces applied at the points A and G, in the plane of the figure, the figure can neither be extended out nor com- pressed together. The pieces A H, H B, and G I, IF, are of no other use than to make the centre stand firmly on its base. This disposition of the timbers will cause them to occupy the least possible space. If the timbers are fixed at the points 1:, l, m, n, o, p, the same immutability of figure may be demonstrated; for suppose the points A and H to be fixed, the point K will also be fixed; the points Aand K being fixed, the point B, of the triangle A k B, will likewise be fixed; again, the points B and K being fixed, the point I will also be fixed: in the same manner all the remaining points, C, m, D, n, o, F, p, G, L, may be proved to be stationary in respect of the points A, H; and the whole figure being kept in equilibrio by any three forces, acting in the plane of the figure at any three angles, the action of the forces will only tend to compress or extend the timbers in the direction of their length. In the construction of this truss, the triangular parts may be constructed all in the same plane, and the pieces, B D and D F, may be halfcd upon the pieces C A and E G; but the utmost care must be taken to secure the several pieces concurring at each of the angles, by bolting, or iron straps, as no dependence can be put in any such joint with- out iron: but perhaps the best method of any is to halve the thicknesses of the pieces A C,*C F, EG, at the points C and E, and also the pieces 2 T ‘2. M EC ' 3 A M AB, BC, CD, DE, EF, FG, at the points B, D, F: then bolting the ends, A and C, of the pieces BA, B C, the end, C and E, of the pieces D C and D E, and the ends E and G ofthe pieces F E and PG, and then fixing double braces, B D, DF; that is, fixing BD upon side of the truss, and another upon the other side of the truss, op- posite to it; also fixing DF upon one side, and another opposite to it. p ‘ Figure 46 represents the manner of constructing a centre according to the principles of Perronet, the celebrated French engineer; but the disposi- tion of the timbers, forming only a series of qua- drilaterals, gives nothing but immutability of figure; and can, therefore, only derive its stiffness from the resistance of thejoints. Having thus giving a general account of the prin- ciples of centering, as connected with the article Carpentry, we must refer our readers to the article STONE BRIDGE for its application, and other practical remarks in the construction. MECHANICAL POWERS, such machines as are used for raising greater weights, or overcoming greater resistances than could be effected by the natural strength without them; the power of strength being applied to one part of the machine, and another part of the machine applied to the weight or resistance. In treating of each of which, two principal problems ought to be resolved. The first is, to determine the proportion which the power andweight ought to have to each other, thatthey may just sustain one another, or be in equilibrio. The second is, to determine what ought to be the proportion of the power and weight to each other in a given machine, that it may produce the greatest effect possible, in a given time. As to the first problem, this general rule. holds in all powers; suppose the engine to move, and re- duce the velocities of the power and weight to the respective directions in which they act; find the proportions of those velocities; then if the power he to the weight as the velocity ofthe weight is to the velocity of the power; or, which amounts to the same thing, if the power multiplied by its velocity, gives the same product as the weight multiplied by its velocity, this is the case wherein the power and weight sustain each other, and are in equilibrio; so that in this case the one would not prevail over the other, if the engine were at rest; and if in motion, it would continue to 4 MEL proceed uniformly, were it not for the friction of its parts, and other resistances. The Second general problem in machanics is, to determine the proportion which the power and weight ought to bear to each other, that when the power prevails, and the machine is in motion, the greatest effect possible may be produced by it in a given time. It is manifest, that thisis an inquiry of the greatestimportance, though few have treated of it. When the power is only a little greater than that which is sufficient to sustain the weight, the motion is too slow; and though a greater weight is raised in this case, it is not sufficient to com- pensate the loss of time. \Vhen the weight is much less than that which the power is able to sus- tain, it is raised in less time; and this may happen not to be sufficient to compensate the loss arising from the smallness of the load. It ought, there- fore, to be determined when the product of the weight, multiplied by its velocity, is the greatest possible; for this product measures the effect of the engine in a given time, which is always the greater in proportion as the weight which is raised is greater, and as the velocity with which it is raised is greater. The simple machines by which power is- gained, are six in number, viz. the lever, the wheel and axle, or axis in peritrochio, the pulley (or rather system of pulleys) the inclined plane, the wedge, and the screw. Of these, all sorts of mechanical engines consist; and in treating of them, so as to settle their them'y, we must consider them as me- chanically exact, and moving without friction. For the properties and applications of the mecha- nical powers, see LEVER, PLANE (INCLINED,) PULLEY, \VEDG E, and \VHEEL. MEDALLION (from the French) in architecture, a. circular tablet, on which are embossed figures, bustos, or other ornaments. MEDIANHS, in Vitruvius, the columns in the middle of the portico, where the intercolumniation is en- larged. MELROSE ABBEY, a monastic structure in the parish of Melrose and shire of RoxbuI-g'i. This is one ofthe most remarkable monastic structuresin Scotland. Its original foundation probably tocl’ place towards the close of the sixth century. In the works of the Venerable Bede, we have an ac- count of the situation of the more ancient edifice, on the bank of the Tweed,as likewise of its abbots. This place was a celebrated school t‘orlearned and MEL 'MEN W7 religious men, and seems to have continued to flourish till the reign of king David, by whom the new abbey was founded, in the year 1136. The former establishment was at Old Melrose, the name of which still serves to remind the inhabi- tants that they tread on ground rendered sacred by the piety of their ancestors. The foundation of the wall, which enclosed the ancient monastery and its precincts, can still be discovered, stretching across a sort of promontory, formed by a curva- ture of the Tweed; but all vestiges of the build- ings are entirely lost. It seems probable, therefore, that they were of little comparative magnitude, and might. perhaps have been constructed only of wood, or other perishable materials, as most of the churches of that age undoubtedly were. Of a similar description was the edifice erected by king David, which was rebuilt, first in the thirteenth century, and again after the accession of Robert Bruce, who granted a revenue for its restoration. This last appears, from its ruins, to have been a truly magnificent and spacious structure. Indeed the size and workmanship of its columns, its sym- metrical proportions, aud the quality of the stone of which it is constructed, entitle it to rank among the most superb edifices which devotion or super- stition has reared in Great Britain. From the charters granted to this monastery by different Scottish monarchs, its inmates appear to have been monks of the Cistercian order, and to have en- joyed a pre-eminence or species of jurisdiction over all their brethren in Scotland. Among the more distinguished of these monks was the celebrated St. Cuthbert, who entered as a monk under Boisil, about the year 60], and had the honour of found- ing the bishopric of Durham. The church belonging to this abbey constitutes the most entire part of its ruins. It was built in the form of St. John’s cross, and is dedicated to the Virgin Mary. The present extent of this building is 258 feet in length, and 137% in breadth; its circumference measuring 943. That these are not the original dimensions, however, are evident from the state of the western division, the greater part of which has been destroyed, and that so com- pletely, that it is impossible to determine to what distance it reached. Both the exterior and the interior of this edifice were formerly adorned with a variety, of sculptured figures of men and animals. Many of the former, in particular, were destroyed in the reigns of Henry VIII. Edward VI. and Elizabeth, whose stateSmen and warriors were no less egregious fanatics than the infuriated Scottish reformer John Knox,in whose time, likewise, this building sustained much additional injury. The niches in which they stood display much curious and beautiful workmanship. The tower, which rose from the middle of the cross or transept, was a noble piece of architecture. Part of it still re- mains, but the spire is entirely gone. The east window is most magnificent, and consists of four mullions with tracery, variously ornamented. On each side appear several elegant. niches, and on the top is the figure of an old man, with a globe in his left hand, resting on his knee; and another of a‘ young man on his right; both in sitting postures, ‘ with an open crown over their heads. Under- neath this window, in the inside, stood the altar- piece. A great number of. piscinas, niches, 8L0. excellently sculptured, are dispersed throughout the church. Many of the pillars are perfect and beautiful,and the embellishments upon them still seem as if newly executed; a decisive evidence of the excellence both of the stone and of the workmanship. Part of this church continues to be used for divine service. The ruins yet standing, besides the church, con- sist chiefly of a part of the walls of the Cloisters; the other buildings,of which there were many,be- ing almost entirely levelled with the ground. All of these, together with the gardens, and other conve- niences, were enclosed within a lofty wall, which extended about a mile in circuit. A large and ele- gant chapel formerly occupied the site of the present manse; and to the north of this house there has been lately discovered the foundation ofa cu- rious oratory, or private chapel, from which was dug up a large cistern, formed from one stone, having a leaden pipe appended to it, for the con- veyance of water. MEMBER (from the French) any partof an edifice; or an moulding in a collection. y n MENSURATION (from the Latin mensura, mea- surement) that branch of mathematics which is employed in ascertaining the extension, solidities, and capacities of bodies; and in consequence of its very extensive appplication to the various pur- poses of life, it may be considered as one of the most useful and important of all the mathematical sciences: in fact, mensuration, or geometry, which were anciently nearlysynonimous terms, seem to have been the root whence all the other exact MEN 326 Ill sciences, with the exception of arithmetic, have derived their origin. As soon as men began to form themselves into _ society, and direct their attention towards the cul- tivation of the earth, it became as necessary to have some means of distinguishing one person’s allot- ment from another, both as to position and quan- tity, as it did to enumerate the number of their flocks and herds; and hence, in all probability, the former gave rise to the science of mensuration, as the latter did to that of arithmetic; and though we may easily imagine that each of them remained for ages in arude uncultivated state,yet it is from this period that we must date their commence- ment; and therefore, to state the precise time when they were discovered, or by whom they were first introduced, would be to trace out the origin of society itself: on this head, therefore, we shall barely observe that in all probability they first arose from the humblest efforts of unassisted genius, called forth by the great mother of invention, ne- cessity; and that they have since grown up by slow and imperceptible degrees, till they have it length acquired the dignity of the most perfect sciences; as the acorn which is first accidentally sown in a field, is in due course of time converted into the majestic oak. But notwithstanding we cannot attribute the in- vention ofthe science ofmensuration to any parti- cular person, or nation, yet we may discover it in an infant state, rising as it were into a scientific form amongst the ancient Egyptians; and hence the honour of the discovery has frequently been given to this people, and to the circumstance of the overflowing of the Nile, which takes place about the middle of June, and ends in September. It is, however, to the Greeks that we must con- sider ourselves indebted for having first embodied the leading principles of this art into aregular system, Euclid’s Elements of Geometry were pro- bably first wholly directed to this subject, and many of those beautiful and elegant geometrical properties, which are so much and so justly ad- mired, it is not unlikely, arose out of simple inves- tigations directed solely to the theory and prac- tical application of mensuration. These collateral properties, when once discovered, soon gave rise to others ofa similar kind, and thus geometry, which was first instituted for a particular and limited purpose, became itself an independent and impor— tant science, which has perhaps done more towards MEN harmonizing and expanding the human faculties, than all the other sciences united. But notwithstanding the perfection which Euclid attained in geometry, the theory of mensuration was not in his time advanced beyond what related to right-lined figures, and this, so far as regards surfaces, might all be reduced to that of measuring a triangle; for as all right-lined figures may be re- duced to a number of trilaterals, it was only ne- cessary to know how to measure these, in order to find the surface of any other figure whatever bounded only by rightlines. The mensuration of solid bodies, however, was of a more varied and complex nature, and gave this celebrated geome- trician a greater scope for the exercise of his su periors talents, and still confining himselfto bodies bounded by the right—lined plane superficies, he was able to perform all that can be done even at this day. With regard to curvilinear figures, he attempted only the circle and the sphere,and if he did not succeed in those, he failed only where there was no possibility of success; but the ratio that such surfaces and solids have to each other he ac- curately determined. After Euclid, Archimedes took up the theory of mensuration, and carried it to a much greater ex- tent. He first found the area ofa curvilinear space, unless indeed we except the lunules of Hippo- crates, which required no otheraid than that of the geometrical elements. Archimedes found the area of the parabola to be two-thirds ofits circumscrib- ing rectangle, which, with the exception above stated, was the firstinstance of the quadrature of a curvilinear space. The conic sections were at this time but lately introduced into geometry, and they did not fail to attract the particular attention of this celebrated mathematician, who discovered many of their very curious properties and analo- gies. He likewise determined the ratio ofspheres, spheroids, and conoids, to their circumscribing cylinders, and has left us his attempt at the qua- drature of the circle. He demonstrated that the area of a circle is equal to the area of a right- angled triangle, of which one ofits sides about the right angle is equal to the radius, and the other equal to the circumference, and thus reduced the quadrature of the circle to that of determining the ratio of the circumference to the diameter, a pro- blem which has engaged the particular attention ofthe most celebrated mathematicians of all ages, but which remains at present, and in all probability MEN 3” I W -’__— ever will remain, the desideratum ofgeometricians, and at the same time a convincing and humiliat- ingproofof the limited powers of the human mind. But notwithstanding Archimedes failed in es- tablishing the real quadrature of the circle, it is to him we are indebted for the first approxrmatron towards it. He found the ratio between the dia- meter of a circle, and the periphery of a circum- scribed polygon of 96 sides, to be less than 7 to 2%, or less than 1 to 371%; but the ratio between the diameter, and periphery of an inscribed polygon of the same number of sides, he found to be greater than 1 t031‘,-%; whence, dfortiori, the diameter of a circle is to its circumference in a less ratio than 1 to 3%, or less than 7 to Q9. Having thusestab- lished this approximate ratio between the Circum- ference and diameter, that of the area of the circle to its circumscribed square, is found to be nearly as 11 to 14. Archimedes, however, makes the latter the leading proposition. These, it is true, are but rude approximations, compared with those that have been since discovered; but, con- sidering the state of science at this period, parti- cularly of arithmetic, we cannot but admire the genius and perseverance of the man, who, not- withstanding the difficulties that were opposed to him, succeeded in deducing this result, which may be considered as having led the way to the other more accurate approximations which fol- lowed, most of which, till the invention of fluxions, were obtained upon similar principles to those employed by this eminent geometrician. Archimedes also determined the relation between the circle and ellipsis, as well as that of their similar parts; besides which figures, he has left us a treatise on the spiral, a description of which will be given under that article. See SPIRAL. Some advances were successively made in geo- metry and mensuration, though but little novelty was introduced into the mode of investigation till the time of Cavalerius. Till his time the re- gular figures circumscribed about the circle, as well as those inscribed, were always considered as being limited, both as to the number of their sides, and the length of each. He first introduced the idea ofa circle being a polygon of an infinite number of sides, each of which was of course in- definitely small; solids were supposed to be made up of an indefinite number of sections indefinitely thin, 8L0. This was called the doctrine of indivi- sibles, which was very general in its application MEN _ '!! to a variety of difficult problems, and by means of it many new and interesting properties were discovered ; but it unfortunately wanted that dis- tinguishing characteristic which places geometry so pre-eminent amongst the other exact sciences. In pure elementary geometry, we proceed from step to step, with such order and logical preci- sion, that not the slightest doubt can rest upon the mind with regard to any result deduced from those principles; but in the new method of con- sidering the subject, the greatest possible care was necessary in order to avoid error, and fre» quently this was not sufficient to guard against erroneous conclusions. But the facility and gene'- rality which it possessed, when compared with any other method then discovered, led many emi- nent mathematicians to adopt its principles, and of these, Huygens, Dr. Wallis, and James Gre- gory, were the most conspicuous, being all very fortunate in their application of the theory of in- divisibles. Huygens, in particular, must always be admired for his solid, accurate, and masterly performances in this branch of geometry. The theory of indivisibles was however disapproved of by many mathematicians, and particularly by Newton, who, amongst his numerous and bril- liant discoveries, has given us that of the method of fluxions, the excellency and generality of which immediately superseded that of indivi- sibles, and revived some hopes of squaring the circle, and accordingly its quadrature was again attempted with the greatest eagerness. The qua~ drature of a space and the rectification of a curve, was now reduced to that of finding the fluent of a given fluxion; but still the problem was found to be incapable of a general solution in finite- terms. The fluxion of every fluent was found to be always assignable, but the converse proposi- tion, viz. of finding the fluent of a given fluxion, could only be effected in particular cases, and amongst these exceptions, to the great disap- pointment and regret of geometricians, was in.- cluded the case of the circle, with regard to all the forms of fluxions under which it could be ob- tained. At length, all hopes of accurately squaring the circle and some other curves being abandoned, mathematicians began to apply themselves to finding the most convenient series for approxi- mating towards their true length and quadra- ture; and the theory of mensuration now be- MEN 328 MEN gan to make rapid progress towards perfection. Many of the rules, however, were given in the Transactions of learned societies, or in separate and detached works, till at length Dr. Hutton formed them into a complete treatise, intitled, A Treatise on Mensuration, in which the several rules are all demonstrated, and some new ones introduced. Mr. Bonnyeastle also published a very neat work on this subject, intitled, An Introduction to Mensuration. These may be con— sidered as standard works, and the only ones of importance in our language, though there are. others on the same subject, as Hawney’s and Ro- bertson’s; the latter of which only requires the demonstrations .of the several rules, which are omitted, in order to render it also a very useful and valuable performance. Particular rules for measuring the various kinds of geometrical figures and solids will be found under their respective heads; but as a collection of examples of the mensuration of distances capable of application to the purposes of enginery and architecture is a desideratum in science, the following, which have occurred in the course of the Author’s practice, are here inserted; they were originally intended for separate publication. Llany of the examples, and even some of the rules, are not to be found in any other work pro- fessing to treat on the art of measuring; where the examples generally given are only calculated for the exercise of school-boys, under masters totally uninformed as to the wants of mechanics. The Author, therefore, embraces this opportunity of laying them before the public, to whom, he has reason to suppose, they may be of equal ad- vantage as they have been to himself; without, however, relinquishing the hope of being able hereafter to accomplish his intention of publish- ing a complete practical treatise on all the useful parts of mensuration. I MENSURATION OF LINES. PROBLEM I.-—-Any two sides of a right-angled triangle being given, tofind the third. CASE I.—-VVhen the two legs are given, to find the hypothenuse. RULE.——Add the squares of the two legs together, and the square root of the sum will give the hypothenuse. Example 1.——In the right-angled triangle, A B C, are given the base, A B, equal to 195 feet, and a the perpendicular, B C, : 9.8 feet: what is the length of the hypothenuse, AC? 195 28 195 28 975 224 17.35 .56 195 .___ 784 (A B)‘=38095 (BUY: 784 3,88,09 (197.:AC l ‘29 ) 288 9.6] 387) 2709 2709 Example 2.——If the span, A B, of a roof, be 24 feet, and the height, D C, 5 feet, what should be the length of the rafters AC and C B. This is resolved into two equal and similar right— angled triangles, as follows: 24 -,=- 2 = 12, the half base. (12‘ +58% :: 13, the answer. CASE II.—VVhen the hypothenuse and one of the legs are given, to find the other leg. RULE.—Fl‘0m the square of the hypothenuse take that of the given leg; and the square root of the difference will be the leg required. Example 1.——In the right-angled triangle, A B C, are given the hypothenuse B C, 601, the perpen- dicular AC, 240; required the base. (6012 —— 240g)% : 551, the answer. Erample 2.-—-In a roof, whose span, AB, is 45 feet 6 inches, and the rafters, A C or BC, 25 feet 5 inches, required the height, D C, of the roof. 45 .. (J 95 .. 5 19. 12 Q ) 5—16 Rafter 305 inches. Base ofeachtriangle 9.73 inches. Inches. Feet. Inches. =136 =11 .. 4- the L 2 Then will (3059 -— 2732) answer. Example 3.—-—-ln a roof, whose rafters are each 26 feet, and the perpendicular height 10 feet, what is the sparror distance between the feet of the rafters E (269 — 108% : 24 feet, half the span. Consequently, 48 feet is the distance between the feet of the rafters. MEN 329 W EXAMPLES FOR PRACTICE. 1. Given the hypothehuse, 1625 yards, and the perpendicular, 400; required the base—Answer, 1575 yards. ‘ / ’ g. “’anted to prop a building with raking shores at the height of 9.5 feet from the grOund, having several pieces of wood of equal length, which might be used For the purpose, each 30 feet long; how far tnust the bottom of the shores be placed frOm the base of the building ?—/Inswer, 16.583. As the following is not to be met with in books of mensuration, and may be useful in the practice of constructing roofs, the Author has here in- troduced a rule for the construction of right- angled triangles, the sides of which shall be com- mensurable with each other. RU LE.——Take any two square numbers at pleasure; then their sum, their difference, and the double product of their roots, will give the sides of a right—angled triangle, which shall be commen- surable with each other. Example 1.—-Let the two square numbers 1 and 4 be taken: the roots of which are 1 and 2. Then 4 + 1 = 5, the hypotheuuse. 4- -—- 1 : 3, one ofthe legs, and 2 x 2 x 1 = 4, the other leg, equal to dou- ble the product of the roots; consequently, 3, 4,5, are the numbers required, and are the least num- bers by which a right-angled triangle can be c011- structed. Eramp/e Q.—~Let the two square numbers be 144 and ‘26. Them 144 + 25 : 169, the hypothenuse. H4 -— 25 : 119, one of the legs. 2 X 12 x 5 : 190, the other leg. In this manner an infinite variety of ratios may be found for the sides of right-angled triangles. The above rule may be found in some books of arithmetic; but having obtained the three sides, suppose 169, 119, 120, the following progressive table of ratios, invented by the Author, may be constructed, by adding 10 continually to the fourth column, and the opposite number of the vertical arithmetical progressive column on the left hand to each horizontal number in the second and third columns, which will generate those immediately below. Examples—To generate the numbers 194-, 144, 130: Add 25 to 169, and the sum will be 194, the hypothenuse of the triangle. In like manner, VOL.1L MEN. 25 + 119 = 144, one of the legs; and by adding 10 to "120, we have 130, the other lea. And thus, in every instance, each horizontal number will be generated by adding the number in the vertical left—hand column to each of the two adjacent numbers in the second and third colutnns of the same horizontal line, and by adding 10 to the number expressed in the fourth. 31:11:. Sides of a right-angled triangle, Ratio of mun? expressed by any three of the p the two bers. horizontal numbers. . legs. ‘25 169 119 190 9 1,1, 27 194 .. .. 144 . . . . 130 1g, 29 221 171 140 1g, 31 250 . . . . 200 . . . . 150 1% 33 ‘281 231 160 1,731, 35 314 264 170 y '13.; 57 . 349 .. . . 299 . . . 180 1113 39 386 . . . . 336 . . . . .190 15’; 41 425 . . . . 375 .. . 200 1g 43 466 416 210 1,3,3. 45 509 . . . . 459 . . . 220 9,1,9, 47 551 . . . . 504 . . . . 230 2,2,3; 49 601 . . . . 551 . . . . 240 £573}; 51 650 . . . . 600 . . . . 250 2% 53 701 651 260 egg 55 754 . . . . 704 . . . 270 22,1: .57 809 . . . . 759 . . . . 280 2—33 ' 59 866 . .. . 816 290 21,13 61 925 875 300 9;; 63 986 . . . . 936 . . . . 310 37;? 65 1049 . . .. 999 . . . . 320 3,4220 67 1114 1064 330 3,32; 69 1181 1131 340 3,1,1, 71 1250 1200 350 3; 73 1321 1271 360 3,9 75 1394: . . . . 1344: . . . . 370 , 3% 77 1469 . . . . 1419 . . . . 380 3%; 79 1546 . . . . 1496 . . . . 390 3% 81 1625 .... 1575 4-00 3.1% 83 1706 . . 1656 . . . . 410 4,12; l l PROBLEM II.—-Tofind the length (gfa cylindrical helix. RULE.-—Multiply the circumference of the base by the number of revolutions; to the square of the product add the square of the height of the spiral, or the square of the distance of the axis from the beginning to the end; and the square root of the sum will be the length of the spiral. The form of the cylindric helix is a right-angled triangle, the base of which is the number of re- volutions, and the height that of the spiral; i. e. if the whole were unwound and stretched upon a plane, the developement would be a right-angled triangle. Example 1.—Required the length of a screw twisting round a cylinder 22 inches in circum- ference, 3% times, and extending along the axis 161nches. 9. U MEN 330 MEN WM 22 16 3% 16 66— 96 1 l 16 .7—7—base of the deVelopement. 256 77 —— 539 539 5929 square of the base. 256 square of the altitude. 6185 ( 78.64 inches, the answer. 49 = *— 148)]285 1184- 1566)]0100 9396 15724) 70400 62896 7504 Example 2.——Required the number of feet of handrailing for a semicircular stair, consisting of nine winders, each 6%. inches high, the diameter of the well-hole being 18 inches. PROBLEM III.—-—The chord and versed sine of an are if a circle being given, to find the diameter. RULE 1.—Divide the sum of the squares of the sine and the versed sine by the versed sine itself, and the quotient is the diameter. Example 1. Figure 6.-—Given, the chord, A B : 48 feet, and the versed sine, DE = 18 feet; re- quired the diameter. 438-: 24, the sine, or half chord. 242 +182 “ 18 This arithmetical operation of finding the radius is much preferable to the geometrical construc- tion, the calculation being so easy, and performed in a very small compass; whereas the other mode requires a floor, or flat surface, to decribe it upon, which cannot at all times be obtained; re- course must therefore be had to a temporary floor of rough boarding, which requires an immense time in the preparation, and when done is not much to be depended upon. The = 50, the diameter required. EXAMPLES FOR PRACTICE. A room is to be constructed with a cylindric how, the plan being the segment of a circle, whose chord is 18 feet, and the height of the segment 6 feet; what length of a rod will be necessary to describe the arc? A bridge is to be constructed of a cylindric in- trados, the section of which is to be the segment of a circle, to span 100 feet, and to rise 33 feet; what length of a line, or wire, will be necessary to describe the arc? RULE 2.——As the versed sine is to the half chord, so is the half chord to a fourth proportional; add this fourth proportional to the versed sine, and the sum is the diameter: thus, take the di— mensions in the preceding example; we have a a o - Q4 x 24‘ -—- fi . 18 . 24 .. 24 . —-——18 -—32, then 32 + 18 = 50, the diameter. PROBLEM IV.—In the segment of a circle are given the chord, audits distance from the centre; tofind the radius qf the circle. RULE.—-—Add the square of the half chord to the square of the distance; and the square root of the sum will be the radius of the circle. Example l.———Let the chord,A B, be 8 feet, and the distance of AB from the centre, C D, 3 feet; re- quired the radius of the circle. Here % = 4 the half chord. Then (42 + 32 l : 5, the answer. Or thus, at full length. “I <90) :99 [salute 25 ( 5, the answer. Example ‘2..——In Stewart’s Ruins of Athens, vol. ii. pl. vi. eh. i. are given, in asection of the columns of the portico 0f the temple of Minerva at Athens, the distance between the chords of two opposite equaland parallel flutes, 6 feet 1.8 inches, and the chord of each flute 11.688 inches; required the diameter of the column, which he has omitted. 6 L8 2)]L688 12 5.844 half chord. Q. ) 73.8 diameter reduced —— to inches. 36.9 Inches. (36.99 + 5.844.?)% = 37.36 the radius nearly. M’EN 331 MEN PROBLEM V.--The radius of a circle being given, and the chord of a segment if that circle: to find the versed sine of the lesser segment. RULE.—Method l.—-Subtract the square of the half chord from the square of the radius, and the square root of the difference will be the cosine; subtract the cosine from the radius, and their difference will be the versed sine of the lesser segment; that is, a: r —- (rq — 2)? Example—A weir is to be constructed across a river, in the arc of a circle of 250 feet radius; the span of the river, or chord, to be 200 feet; what is the versed sine of the lesser- segment? 250 —- (250* —— 1009 )i = 20.87122, the versed sine required. N.B. If the versed sine of the greater segment is required, add the cosine to the radius, and the sum will be the versed sine. BIethod Z—When the chord is very small, and the diameter large. As the diameter of the circle is to the half chord, so is the half chord to the versed sine, nearly. Example 1.—-Suppose a bridge is to be executed, 56 feet in diameter, the breadth or chord of each stone on the face and on the intrados of the arch being 19. inches; what is the versed sine, or height of the arc of a single stone? 56 12 672 . 0 : 6 6 679.) 36.000( .053 inches nearly. 33 6O 2 400 2 016 384 Example 2.—-Supposing the diameter of the earth to be 7957 miles, how much does the curvature rise in a chord of 2 miles? We have 7957 : l :: 1 : .000125 ofa mile, which reduced gives 7.92 inches nearly for the rise of the are. This would also be the distance that the curvature of the earth would fall from the tangent in one mile. N.B. The deflection of the are from the level- is as the square of the distance from the point of contact nearly. This proportion would give the same result as the method by which this example is wrought. PROBLEM VI.——Given the distance between the two parallel sides of a trapezoid, and the breadth of the lesser end; to find the breadth cf the greater end, so that the sides may tend to a point-lat any given distance. . . N0te.—The distance from the lesser- end to the given point is here termed the distanceqf the point of convergence. RULE.—-—As the given distance is to the sum of that distance, and the distance to the point of convergence; so is the breadth of the lesser end to that of the greater. Example 1. Figure 7.—Given the distance, EF, between the parallel sides, A B and D C, ofa tra- pezoid, A BC D, equal to 3 feet; the breadth of the lesser end, D C, 2 feet; and the distance, EG, from the lesser end, D C, to the point, G, of the meeting of the inclined sides, A D and B C, 58 feet; required the breadth, A B, of the greater end. 58 : 58 + 3 z: 2 breadth of the greater end. .(58+3)><2 58 = 2.103, the Example 2.—-—A‘ stone weir is to be constructed across a river, in the form of the segment of a circle, with the convex side of the arc towards the stream; the joints of the stones being all to tend to the centre: now the length of each stone in the direction of a radial is 4 feet, the radius 250 feet, and the breadth of the lesser end of the stone 1 foot; required the breadth of the upper end of the stones. Foot. In. Sec. Answer, 1.016 feet, or 1 O 2 This problem is also useful in perspective, in the drawing of two lines towards a vanishing point. Example 3.—-A bridge is to be constructed of a cylindric intrados, the section of which is the segment of a circle of 28 feet radius, the length of the arch-stones are to be 2 feet, and their breadth in front of the arch and on the in— trados 1 foot; required the breadth of the thick end of the stone. ‘28 : 28 +2 :: lto the answer. 9. U 2 MEN , 332 W ~Or',w- 28:30::1 1 28 )36( 1.0714 the breath of the greater end, as 28 required. ———_.. 200 1 96 40 28 Ed 112 ——- 8 _..—— Or, the answer may be reduced to the Workman’s rule for taking his dimensions, thus: 1.0714 12 8 6.8544- 4 3.4176 This gives one foot and very nearly seven-eighths of an inch, the foot being divided into twelve equal parts, called inches, and each inch into eight equal parts ; the workmen seldom regard any thing less than the sixteenth part of an inch. This example corresponds to Problem V. Me. thod 2, which ascertains the versed sine of the arc of the stone of a bridge, weir, or the like, of a given radius and given chord : it likewise ascer— tains the taper that the stones should have in the direction of a radius. The mould of the section of the stones may therefore be found by calcula- tion, and the are described by Problem Lll. of the article GEOMETRY, almost within the com- pass of the section itself, without having recourse to the long distance of a centre, which not only requires an inconvenient degree of space, but occasions great loss of time in the preparation.- PROBLEM VII.———To find any point in the arc 9f the segment ofa circle at the extremity qf an ordi- nate ,- the radius of the circle, the chord qf the are, and the distance of the ordinate from the middle qf the chord, being given. - RU LIL—Find the versed sine by Problem V. sub- tract it from the radius, and the remainder will be MEN ‘_ : ”the cosine;-subtract this cosine from the square root of the difference of the squares of the radius and of the distance from the middle of the chord to the ordinate, and the difference will give'the length of the ordinate. Example. Figure 8.——Suppose the radius, A E, of the segment, G E H, to be 250 feet, the chord, G H, 200 feet, and the distance from the middle, B, of the chord to the ordinate, C D, 50 feet; required the ordinate, C D. The versed sine, I E, will be found to be20.871, by Problem V. consequently, 250 “,- 20.871: 229.129 the cosine; therefore (250’ —— 502% —— 229.129 : 15.820 feet, the answer. In the following examples, the radius and Chord are the same as in the last; but the variation is in the distance of the ordinate from the middle of the chord. EXAMPLES FOR PRACTICE, TO BE ANSWERED. Let the distance from the middle of the chord to the ordinate be 10; required the ordinate.— Answer, Let the distance from the middle of the chord to the ordinate be 20; required the ordinate.—~ Answer, Let the distance from the middle of the chord to the ordinate be 30; required the ordinate.— Answer, Another rule, without finding the versed sine, is as follows : First—Find the cosine of G E, the half arc, thus: from (250)? viz. the square of the radius, subtract(100)"" viz. the square of the sine, or half chord, 200; and the square root, 229.129, of the remainder gives A B, the cosine of the arc G E. Secondly.—— Find the cosine of the arc D E in the same manner, thus; from (250)‘Z viz. the square of the radius, subtract (50)“, viz. the square of the sine, or half chord, of 100, that is, the dis- tance from B to C; and the square root, 244.949, of the remainder gives A I , the cosine of the are D E. Thirdly.—Substract the cosine, A B = 229.129, of the greater are, G E, from the cosine, AI : 244.949, of the lesser arc, D E; and the remain- der, B I : 15.82, is equal to the ordinate C D. PROBLEM V [IL—Given the chord qfa very large segment qfa circle, and the radius ofthc circle; to MEN 333 MEN find any number of points in the arc, and thence to describe it. «Runes—Divide the chord into any number of vconvenient equal parts each way from the middle, and erect ordinates upon the points of division; - calculate the length of each ordinate by the last problem; find the versed sine to a chord not less than the distance between the two most remote adjacent points in the ends of the are; describe an arc to this chord and versed sine by Problem LII. of the article GEOMETRY; then procure a board equal to the length of the chord, and curve its edge to the arc; with the curved edge draw an are between every two points of the ex- tended arc, and the entire are will be formed. N.B. There are several methods of describing segments of circles, as shewn under the article GEOMETRY; but none so eligible, upon a large scale, where accuracy is required, as the aboVe. It will be found convenient to erect the ordinates ten feet apart 011 each side of the middle of the chord, though the last distance at each end, be- tween the extreme ordinate an’d the extreme of the curve should be less than the intermediate 10 feet distances. Boards in general do not exceed 10 or 19 feet; but a twelve-foot board will be sufficient for ten-foot distances on the chord, in most cases, even when the versed sine rises high in proportion to the chord. Example. Figure 9.—-—An engineer intending to construct a stone weir over a river, in the are, A LM, of a circle; the chord, A M, of which being 900 feet, and the radius 250 feet; required the length of the ordinates at 10 feet distance from each other, and the versed sine to a chord of 12 feet, for completing the are. N L, the versed sine . 20.871 Problem V. O K, the first ordinate . 20.671 Problem VII. 1’ I, the second ditto . 20.07 ditto. Q H, the third ditto . 19.065 ditto. R G, the fourth ditto . 17.65] ditto. S F, the fifth ditto . . 15.82 ditto. T E, the sixth ditto . 13.565 ditto. U D, the seventh ditto 10.872 ,d-itto. V C, the eighth ditto . 7.726 ditto. W B, the ninth ditto . 4.11 . ditto. These ordinates are respectively calculated at 10, £20, 30, 40, 50, 60, 70, 80, 90 feet distance from the middle of the chord to each ordinate. It now remains to calculate the versed sine cor- responding to a chord of 19. feet of the same are ' bare measure. as that of the Weh: This will be found, by Pro- blem'V' to' be .072 of a foot, or V"e1y nearly seven- eighths of an inch, being as werkmen say, Cuive‘ the edge of a twelve-fem; board to a versed sine of seVen- eighths of an inch; then lay the curved edge, with the concave side towards the‘chord, successively betV’Veen every two points, A, B, B, C, C, Di'SLCfid‘r‘aWing each part until the whole. are is completed to‘ the cl101d A M. N. B. A boarding IS generally fixed to a" timber giating, or framing, supp01 ted by piles, for the foundation of the stone-wink " PROBLEM IV. -—Ina parabola having two abscissa: and an ordinate to one qfthem, tojind the ordinate ofthe other. RULE .——-As the absciSsa of the given ordinate is to the abscissa of the required ordinate, so is the squaie of the ordinate of the former abscissa to the square of the ordinate of the lattei. Then the root of the fourth term so found Will be the ordinate required. Example. Figure 10. -—In the parabola, A ‘B C A, are given the base, or double eldi'nate, A C, 18 feet, the height, or abscissa, B D," 16 feet, and the ab- scissa, B E, 8 feet; required the ordinate, E F. -— — "9, the ordinate, 2 and92 :81. 81 S 16. 8. 81:72—- _ 40. 5 the square of E F. Therefore 40. 5% _ —6.364 : E F, the ordinate re- quiied. . In this manner any number of ordinates, and con~ sequently of points, may be found in the curve, : so as to construct the figure. . most appropriate for use in the-formation of the curve, when the abscissa is greater" than the ordi- This method is the nate, or equal to it. PROBLEM V.—‘—To find-any point in the curve ofa parabola by means qfanabscissalparallel, or trans- r'verse ordinate; the‘height, or abscissa, the ordinate, and the distance oftheD transverse ordinatefr am the abscissa, being given. , ' ' ' - = Note.—At1ansverse ordinate, or abscissal parallel, is a right line terminated by the curve and by the base parallel to thetabscissa,‘ commonly called a a diameter, in'tliis particular curve. 'RUiLEr—M‘ultiplythe difference of the squares of . the ordinate and of» the-distance of the abseissal parallel, or transverse ordinate, from the abscissa, MEN by the height, djvide the product. by the squa1e {of the 0,1dinate, and the quotient. will give the . , height of the tiansveise ordinate. . , Q1, thus: Take any two numbers, in, the proportion of the ordinate, o1 half base, and the distance be- tween the abscissa and transverse ordinate; call these numbers respectively A andB1 multiply the difi'erence of the squares of A and B by the height, . d1v1de._the product bythe square of A, and the quotient will give the transverse ordinate, Example. Figure 11.-—..—.,In the parabola, A B C, are given the. abscissa, . B D, 8, feet, the ordinate, AD, 40 feet, and the distance” D E, 16 feet; to find the abscissal parallel, or the transverse or- _ dinate,EF , x 2— 1 2 X W: 6.72 feet, the anSwei. " 01, because 5 and 2 are in the same prOpottiOn- as 40 and 1,6 ,we have (.52 ~—— 29) X 8 as before. 5“ ‘ “ This method, as it avoids the square root, willnot only be easier than the/last, of finding a point in the curve of theparabola, but will be much more accurate when the abscissais less than.the ordinate. = 6.72 feet, PROBLEM ~XI.’-—-.-Gz'ven the abscissa and. ordinate of a, parabola, 120. find,‘ (tiny. number .1in equidistant diameters, or abscissal parallels, and‘cpnsegluently points, in the curve, at the extremities. Take the simple arithmetical progression of the ' numerical scale 1, Q, 3, 4, 5, Sec. till the; last contain as many units as the number of equal parts intended tobe contained in the ordinate. Then if the last number represent the ordinate, the preceding numbers, 1, 2, 3, Ste. will represent ‘ the respective distances that each transverse ordi- nate is from the abscissa. Proceed with these numbers as distances, and calculate as in the last Problem, and the several results will give the ordinates. Or thus: Ifa double ordinate be given, and the number of transverse ordinates be even, or the equal parts of the double ordinate odd, take the Odd numbers of the arithmetical.progression l, 3, 5, 7, SLC. and proceed as above: and having found the transverse ordinates, let the real base, or double ordinate, be divided into the equal parts required, and perpendiculars.erected,at the points of division, and made respectivelyequal to the results on each side of the abscissa,.will give the transverse ordinates, and consequently as many points in the curve. q, M EN 1 This method applies to the construction of a pa- rabola of very great extent, as the extrados of a bridge, not for-one'arch only, but for the upper line of a series of arches. The parabolic curve is well adapted to bridges, as it gets quicker to- wards the middle, and therefore, the contrast with , the land is. not so violent as the circular arc, . which hasthe same curvature at the ends as in the middle. The use of transverse ordinates in constructing the curve, is not only more expedi- tions in calculation, but more accurate in ascer- taining the curve at the vertex. SYNOPSIS OF THE PRINCIPAL RULES OF MENSURATION. THEOREM I. RULE 1.—The circumference, c, Of a circle being given, to find the diameter, d. C ‘1‘ 3.1416' THEOREM II. RULE 2. THE RECTIFICATON 0R DEVELOPEMENT OF CURVES. THEOREM I. RULE 1.-—-To rectify or develope the circumference of a circle. I c = 3.1416 (l. THEOREM II. RULE 2. 22 d C: 7 THEOREM III. RULE I.—-To rectify the arc ofa circle, the radius, 7', and the sine, s, of half the are, being given. Let z be the length of the are required, in all the following cases , then 0579 C, Sit. where q = j: , and A,_B, C, the preceding terms. THEOREM IV. RULE _2.——-Let [6 equal the chord of the half are, and 1: equal the chord of the whole are. 81-— Z:-,,—— c, by Huygens. THEOREM V. RULE 3.—The diameter, d, the versed sine, v, and the chord, 1:, being given: 4110 __ th—t‘ ,z:c+ 6d—5v “‘0 (id—5v :Qx fidd— (dv—v‘i) x6 :5d,by theAuthoi, MEN 335 THEOREM VI. RULE 4.—The chord, c, and the versed sine, 1), being given: 8 use ”.1. 10 v” z — 0 + W, °r " W ' Author. THEOREM VII. RULE 5.——The sine, s, and versed sine, v, Of half the are being given: sws 6s2+5fi z: 23 + W,or 23W, by the Author. THEOREM VIII. RULE 6,—The diameter, d, the sine, s, and versed sine, v, of half the are, being given: Qst 2g 3‘2 + '02 ,Or 811394-310” by the = __ . h z 1111—8-11 by te Author. THEOREM IX. RULE 7.—The radius, r, the 1 chord, c, and versed sine, '17, being given: Q z— .. c +'C§— :+——-, by the Autho1. THEOREM X. RULE ].——To rectify the curve of an ellipsis, the major axis, t, and the minor » axis, 0, being given. 3 d 3. 5 d 5 7 d d Z=A-—é-.-2'A—Z;B-— 73—6 C— 178,850. t2 -— where d : t2 ceding terms. THEOREM XI. RULE 2. 23t+9$lc Z:— , by the Author. AREAS OF PLANE SURFACES. In the following theorems, let A be the proposed ‘ area. THEOREM I.-—-To find the area of a parallelo- i gram; the length, l, and the breadth, b, at right j angles to the length, being given. A = l b. THEOREM II. RULE l.——To find the area of a triangle; the base, b, and the perpendicular height, h, from the opposite angle, being given. A _ b h ; — 2 I THEOREM III. RULE 0 .-—-The three sides, (1,?) 0, being given, lets be the half sum of the three sides, then A:(s Xs—axs—b XS—c)’. cg . I ; and A, B, C, 8w. are the pre— THEOREM IV' RULE 3.—-Given, I), the base, and, s, the half sum of the two opposite sides: A :1: z (ET-1,2 x 17:12)! THEOREM V.—To find the area. of a polygon; the side, 3, the number, n, of the sides of the po- lygon, and, the radius, 7‘, of the inscribed circle being'given. ' V ' THEOREM VI. RULE 1.—To find the area of a circle; the diameter, d, and circumference, 8, being given. 0, 1 dc *‘XW",OI'-—-- 2 2 4: THEOREM VII. RULE 2.—-The diameter, d, being given :‘ - ' .7854 (12. . THEOREM VIII. RULE 3.—The circumference, 6, being given: ' 1 ' ' .0796 09.. THEOREM IX. —-To find the area 'Of the sector of a circle; the radius, r, and the arc, a, being given 1' a a V : r — or —-- A _ x 9’ 2 THEOREM X.—To find the area Of a frustum sec- tor, or part of a circular ring, Contained between two radii; the breadth, b, the exterior arc, e, and interior are, a, of the ring, being given. a +e A: b x —-— ; 2 THEOREM XI. RULE 1.—To find the area of the segment ofa circle; the diameter, d, and the versed sine, 11, being given. 1 L 2 '1') '0‘ ‘03 A=2vd“v"x(—-—- .____) 3 5d _28d‘ 72 d3’ Ste. Or thus, RULE 2. 1 ' l ( 2 3 'v 5 v 7.3 O W 1’ x 5—3727 “WE—97;: 95v - 11.8diD’ &°') A, B, C, 8w. being the first, second, third, Ste. terms. C Or thus, RULE 3. V being the supplemental versed sine, and V: d ——'c, therefored: V+v; therefmeA: QvV’t” 3 '1 .w‘. .v - x(LL3+185V+3EJV‘+519W’&°) m “v— MEN 3'36 01: thus, RU1.E ctr—Where A, B, C denote the . ‘ preceding. terms . ._ , _ 1 v 31: .__ t t; ._-.. __ __ A... va+5vVAl 7V§+§VQ 5v , 24;, 1 _ ‘11vD3‘C- THEOREM 'XII. RULE 5.—-—The chord, c, and ve1sed sine, '0, being given: '2 c v A= +~—-,o . A rvfzgcé +: :), by the Author, 2012 v" ’ 12° or A : 3T+§—c——2—0—— 4, still neare1, by the Author. ' THEOREM XII[.. RULE 6.—-The chord, C, of the half arc, and the versed sine, v, of the same, being given :, =(C+:13—cx 1461), orc+ 4dI véxéévfiy Sir Isaac Newton. . THEOREM XlV. RULE 7.——-The radius, r, the sine, s, and the versed sine,.v, of half the arc, - being, given : 2 z , $1.1, by the Author. 11 s‘ + 31) _ THEOREM XV.-——To find the area of an ellipsis; the major axis, M, and the minor, m, being given. -A :, .1854 M m. THEOREM XVI .—-—TO find the area of an elliptic segment; the length, l, and the altitude, a, being given: also the b1eadth, b, of the segment of a circle of the same altitude and of the same dia- meter as the axis of the ellipsis, perpendicula1 to b. A=11rsg 3 A = -Z[;-x (633 a b +-§—E) by the Author. THEOREM XVII.——To find the area of a para- bola; the base, b, and the altitude, a, being given. A— Q a b. 3 THEOREM XVIII. -—-To find the area of the sini— cal curve; the radius, r, and the versed sine, 12,01 the segment, being giv.en A: re. AREAS OF CURVED SURFACES. THEOREM I.——To find, the area of a cylindric sur- face; the axis, a, and the diameter, d, being given. A : 3.1416 (1 a in a right cylinder. Or A = p a in an oblique cylinder, where p is the perimeter. of the segment of a hemisPhere; MEN THEOREM Il.—-To find the .curved surface of a ds—ac cylindric ungula, A = It; wherekis the length‘of the part that is Cut, and v the 'versed srne of the segment which forms the base, and d the diameter. THEOREM III.———To find the area of the curved surface Of‘a right: cone; the side, 8, and the cir- "c'umference, c, of the circumference being giVen. A: L” THEOREM IV .-—To find the area of the segment of a square dome. A: 4 (s + v), or 4 dv, whe1e s is the sine, and v the versed sine of the circu|a1 segment which forms the vertical section, or d the diame- ter of the circle which forms the vertical section. THEOREM V.—To find the area ofa segment ofa. hemisphere; given the radius,.s, of the base, the versed sine, v, and the diameter, id, of the axal p section. A : 3.1416 (3‘ + '0‘“), or 3.1416 (11:. THEOREM VI.——To find the area of the fru'stum the circumfe- rence, c, of the great ciule, and the distance, d, of the parallel planes, being given. A=cd. THEOREM VII. RULE 1.-To find the surface Ofa spheroid; given the axis, a, and the diame- ter, d, of the great circle. - A : .5236 x (4 a d + 9.. (1‘). by the Author. Or, A :1.0472(2 ad + d2). This is a near approximation; by the Author. THEOREM VIII. . z a +9 A: .8809(2ad+d)+——6—‘—‘— to the truth than Rules 1 and 2. RULE 2. , still nearer THEOREM IX. RULE l.~——To find the surface of an ellipsoid ; the length, a,.the breadth, b, and the thickness, c, being given. 2 X .5236(ab +ac + be). This rule is a near approximation; by the Author. THEOREM X. RULE 2. a2 +62 + c” 6‘ »*’Y the Author; it is apnearer approximation than Rule 1. A—8805(ab + ac+bc)+ MEN 337 12:: THEOREM XL—To find the surface of a semi- circular groin ; given the side 6. A : 1.1416 1)“. SOLIDITIES OF BODIES. THEOREM I.——-To find the solidity of a cube. S = 33, where s is the linear dimension. THEOREM IL—To find the solidity Ofa prism. S = all; where a is the area of the base, and It the perpendicular height. This also includes cylinders. T11 EOR E \1 III .——TO find the solidity of a pyramid. (It It S - ,or—EXa, or :xlt; whereaisthe area 3 of the base, and It the perpendicular height. This also includes cones. THEOREM IV. TO find the solidity of a wedge, 01' pyramoid; the two adjoining edges, (1 and I), of the base, the edge, 0, in the same plane with a, and the height, being given. _, 2 a b + c I) S : ————— . 6 It THEOREM V.—To find the solidity of the frustum of a pyramoid. b d 4 S = (L—icTi—f‘f/z; where a and c are the opposite terminations of a plane of one of the sides; 6 and d the Opposite terminations of the plane of one of the adjoining sides, a and I) being adjoining sides of the base, c and d those of the top, e the hall sum ofa and c, andf the half sum of b and d. THEOREM VI ——To find the solidity of a cuneoid. S: 2 a b + c b 0 same as that of Theorem V. except the addi- tional multiplier. 7854; this solid only differing in construction from the py ramoid 111 having ellip- tic sections instead of rectangular ones. x .7854 x k. This formula is the THEOREM VII.—-T0 find the solidity of the frus- tum of a cuneoid. S ~ab+cd+4ef §'——'fi"_—_ c are the two axes of the elliptic base, and c and (l the axes of the elliptic top , c being opposite to a, and dopposite to b. This solid only differs 110111 the trustum of a pyramoid in being cir- culu VOL. IL x .7854 x 71; wherea and MEN THEOREM VIII.-—-TO find the solidity of the seg- ment of a cylinder RULE 1.——S—= a2 (9.3.. versed sine, I) the chord of the base, and Z the length of the cylinder. Invented by the Author. ab+a° I)” RULE 2.—-S’ :2 x (T +— 56 than Rule 1. when the segment is nearly a semi- cylinder. zb a2 . +572), ' where a 15 the —); stillnearer THEOREM IX .—To find the solidity of the seg- ment of a square dome, 3 4x . RULE 1.—S=4r1‘9~—3—; where .r is the height, and r the radius of the circle, Of'which the segment forming the vertical section is apart. See Vol. I. p. 401, of this ‘Vork. 2 23a 3 RULE... 0 .~—S = 2 +~— the square base, and a 3the altitude of the dome. See Vol. I. p. 403, of this Work. THEOREM X.—To find the solidity of the seg~ ment of a hemisphere. —-——; where s is the side of 3 RULE 1.—S’ = p (r or: -—£3 ); where p is equal to 4 x .7854 = 3.1416; and x and r, as in the preceding Theorem. Roma—S: “854(35- +2_: ). This only differs f1om Rule 2. Theorem IX. in the base being circular. It gives the contents independent of the diameter of the great circle. THEOREM XI.-—To find the solidity of a trun- cated square dome, independent of the radius, 01' diameter, of the vertical section. .3 4 z . . S = a $2 —- —3(—-; where a is the altltudre, and s the side, of the square base. THEOREM XII.-—-To find the solidity or the frustum Ofa hemisphere. 3 ~ 0 4a . ‘ i _ S = .7854 (as—“7); belng the Same as 1n 0 the last Theorem, except the multiplier .7854. THEOREM XIII.—To find the solidity of a hollow truncated square dome. v S : a(Dg-—- d9); where J) is the side of the square base, between the Opposite external sur- 2 x MEN 338 MEN J i = m . ivfaces',‘ d the side of the square base between the Opposite internal surfaces, and a the altitude; . supposing the heel to be equally thick. ' THEOREM XIV. -—-TO find the solidity ofa hollow hemispheric frus'.tum .7854 a (Do. -'—- d9) , being. the same as- Theorem XIII. excepting the multiplier ..7854 ‘~ THEOREM XV. -To find the solidity of a para- : boloid. b h S = 2 ' the base ; where h 15 the height, and b the area of THEOREM XVI.-—To find the solidity of the ' . frus‘tum of a paraboloid. a + h S==——2—-- h; where a and I) are the areas of the two ends. THEOREM XVII.——To find the solidity 'of an hyperboloid. S __ a + b + 4772 — 6 of the two ends, and. m the area of the middle section. This theorem will also serve to measure a sphere, spheroid, paraboloid, cone, pyramid, pyramoid, or any segment, or frustum of these bodies. h; where a and b are the areas NOTES ON THE PRECEDING THEOREMS. Many of the preceding theorems have never be- fore appeared in print. Those of the Author’s in— vention are mostly approximations, contrived to expedite business. RECTIFICATION OF CURVES. Rule 2, of Theorem VII. by Huygens, is very 8h— neatly expressed by8 —-———-—— ;but the half chord must either be found geOmetrically, by bisecting the chord by a perpendicular, and drawing the half chord, or by a very operose arithmetical Operation. If d = 2 h —- c, then will c + d +1 0 be the length of the arc: this affords a very easy geometrical construction; viz. if to the chord cf the whole are be added the difference of twice the chord qfthe hatf arc and the chord of the whole - arc, and one-third of the said dzfifiarencc, the sum will be nearly the length 09f the are, for c + d +—=c+(2h—c)+1-————Qh_c =8h—c' 3 Rules“ 0, 4, 5, 6. Theorems VII. VIII. IX. and X. were invented by the Author. The circum- stance which gave rise to them was a stone weir, . or dam, which he had designed and superintended at Denton Holm Head, over the river Caldew, near Carlisle. The form of the weir was that of the segment of a circle, of which the chord was 200 feet, and the versed sine 22 feet; when the work was completed, the contractor for the ma- son’s work was very desirous to have it measured, butat that time, being early in the spring of1810, the river was flooded so high, that the water ran two feet above the top of the weir; now having.‘ the true dimensions, as above, and an exact sec-g tion. of the work, it was only necessary to find: the length of the arc, and then the solid contents were easily computed: but, in order to obtain this end, he found that the calculations by the rule of Huygens would require too much trouble for common business, and therefore, as well for present convenience as for any thing that might happen in future of a like nature, the following formulas were invented: L = c gffi, or L=c +fi%z=c%§i orL=c + $3,166,. The second formula, or Rule 4, is derived fromi the first, by substituting the value Ofd 1n termsi Ofc and v; and Rule 5 is also deiived from RuleS, l by substituting the value of d in terms ofs and‘l '0; so that, being derived from each other, they will all give the very same result; and tO shew how near this is to the truth, the investigation is as follows: 6 d —— v 6 d— 6 d — 5 6 d— quantity 2 (do —— 112))", being the value of c, in terms of d and v: Forc ——-Q.(dv——vg)% X 51) ———-—,the 0 but2(dv—eQ)I=QdI‘v—Ix 1— fi~g§§,&c.) and 6%)?) = %+gg, Sic. Hence ‘2. (do —— v‘lfix H : QdI véx (1—5Zg-d°’&c)x(l+3d+5:;’ 8(a) =2divi x (1 +6d+7—;vd" 810.) :Bdlitl :3Efi9 dEElE=2EEEEEEEE=EEEEEEEEE:=EE====E2EEEEEEEEEEEEEEEEEEEEE2EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE=2EEEEE2:22:2222222522525222225 v 3 v . but 2 dl 19% x <1 + 33+ 2671;: 830-) IS known to express the arc of a circle, whose diameter is d, and its versed sine u; now this last series only differs frbm the former in the third term, in being 1) s - the excess bein ~—-——-—;. 163 , g 45 (1 Now to shew how far these rules may be depended upon in practice, the. Author has calculated the following table, where the numbers found an- swer to segments of different proportions. The results found, both by Huygens’ rule and by that of the Author, are compared with the result found by an infinite series, which is the criterion; be- cause by such an infinite series the answer may be found, which can he depended upon, to any num- ber of figures. The result found by the series in the table is therefore true to the last figure, or to the last but one when the next figure would be above 5: in this case, the last figure of the decimal is augmented by unity. In the table, the first vertical column contains the chords, and is maiked C; the second column contains the versed sines of the several segments, and is marked V; the third column contains the lengths of the arcs according to the dimensions stated in columns C and V in the same horizontal row, and is marked L; and the last column, marked R, shews the ratio, or number of times that the versed sine is contained in the chord. In each cell under L are the three results 3. the upper one being that of Huygens, the middle one that of the series, and the lower one that of the Author. C V' L It 1002.666 936 155 1002.959 6 1002.9 1-1 1.19. ml . 26.666 24 5 26.687 4g 26.69 631 .333 556 136 632.252 4,1 632 . 5 10.666 10.743 370.666 240 119 374.960 2;. 375.24 21.73 14 7 21.991 2 22. LM'EN From this table it appears, that 111 low segments the 1esult is nearly the same by each rule, but that the Author’s is nearer to the series than that of Huygens; and it becomes much more so in proportion as the segment approaches to.- wards a semicircle: thus, in a semicircle,the length of the are found by the series is 21.991, the length found by Huygens is 21.73; the difference .26] ; now the length of the are found by the Author’s rule is 22, which is ultimately the Alchimedean p1oportion, and the difference between this result and that found by the series is only 009. , In the first 1101izontal row, both methods ag1ee with the series to four places of figures; in bthe second they agree in three places; in the third, fourth, and fifth, they agree in two placesgand in the sixth they agree in one. In the fi1st ho1i— zontal column the Autho1’ s method ag1ees in five places with the sexies; in the second, thi1d, and fourth, with three figures of the séries; in the fifth, with two figures of the series; and in the last with one figure of the series; but only differs in five figures from the truth by .009. The length of the are found by the two approxi- mating rules in low segments, is exceedingly near the true value; but when the result is found by Huygens’s rule in high segments, it is very con- siderably below it, and cannot well be employed in la1 ge dimensions. T'D'he1e 1s still another rule to be found 1n books of mensuration, which will give the length of the arc to any exactness, either by finding the num- ber of degrees by means of an instrument, or by trigonometry; the former is not very eligible in practice, and the latter would require too much time to be of real utility amid the hurry of business. The investigation of Rule 6. Theorem X. from the geometrical division of the arc of the circle into equal parts, by the diameter being divided also into equal parts, is as follows: Figure lQ.—-Let AD BC be a circle; A B and CD two diameters, intersecting each other in E at right angles; let the diameter, DC, be pro- duced to F, so that the part, CF, without the ci1cle may be three—quarters of the ladius, E C, .01 tl11ee-eighths of the diameter D C; draw D G parallel to A B ; take any portion, D l, of the are D A; join FI; and produce FI to G: 2 x Q. MEN 340 MEN 3d 11 d Let D C be denoted by d; then will F D— — d+—8~ = T; and FK=FD~KD=M~—v=M—;—8—y Now the triangles. F K I and F D G are similar; therefore F K : F D K I : D G; that is, Mfitfl 3—1; s D G = 17%; which is the value 0: the tangent, Then to shew how nearly this value is to that of the arc, we have ML = 812 . 11 (I - 8‘0 1 “m? _ __ 1 é _ % It __ j: __ buts—(d1: v) .._dv (1 2d 80W ,.8Lc) v 102 8—“ 1- 1 — fl, SEC. 1 3 51’ 39 ’0" ' . therefore 1 __ fl : (15 12% x 2 d 8128 d : (11‘ '0E x (I + m + 973W, 8C0) the value of 11d 1 — 11 d‘ the tangent, which should be equal to of the arc will be 22.16; the‘ proportion of Archi- that of the are; but the series expressed in the same terms for the value of the arc, is If 192x ( 1 +-- 6 yd + 40 ——d,, Ste. ); it therefore ap- pears that the value of the tangent is too great to express the value of the arc. The length of the arc may be ascertained with tolerable exactness by Theorems XII. and X111. '03 c cv+ + 3 'cr’ _. — which are thus. gexpressed; 2 v2 Z . . S or 2 s +6 ——— :———-——+ ,by substituting for r, 32 32+” and 2 s for c, in the first formula. This rule gives the length of the are 10.73, when the chord is 8, and the versed sine 3'; and the series gives 10.724; and in a semicircle, where the chord is 1'4, and the versed sine 7, the length ad 3 medes would give 22. As this rule depends upon the area of the segment, the investigation will be given under that of Rule 7, Theorem XI. of the areas of plane figures, which follows. AREAS OF PLANE FIGURES. Theorem XII. Rule 5, is a very near approxi- mation to the quadrature of the segment of a circle. It is much easier than any other rule yet shewn for the same purpose. It was ill- vented, and first published in the article MEN— SURATION’, of The Principles of Architecture, by the Author; since that time it has been copied into the new edition of Hawney’s ZlIensurutzon. The rule was first given without a demonstration ;. but it is now supplied with the following inves~ tigation.. , . . . Q“ ("0' o . . The expressron for the area 18 T + 7;, where c is the chord, and v the versed Sine. ~l .1 d2 v' A. '0 72-3 — £1, 8L9.) x(1- Now c =Q(dv-——'v’~’)% = 2 Cl}: 73% x ( 1"“3’ )x%==2 therefore 3%? = 4 djfi x (1 v 23:? :21, 8w.) 2 Therefore 5—: *4d1:v% x < l + de + 3—5;, 8m.) 1 l a 3 H-————=< -— x<1 1+Uvd+8 ::»&C-> 171. Ste.) + £7: :22 meter of which is d, and its versed sine 12; then by comparing these two series they will be found to be nearly equal, the former being the greater; . Q . for the first term IS —3— in both, and the second term in\ the approximation only differs from that of the proper series by a quantity less than -v ieod' . 2 3 . From this theorem, ; ”—6, we may derive c v v3 . c + — 3+ c—r’ as in Theorem XI. Rule 7, for the rectification of curves. Figure 13 —— In the sector A D C E A draw the chord A C and E D perpendicular to A C, cutting A C at B; let A U :17, and B D = v; then B E = D E— l) B =r—v; consequently the ‘ . TW 2; c r —- c 1) area of the triangle ACE: xe=———-—. 2 3 ‘2 c v m but the area of the segment A D C is —-3—+ E“; 6 therefore the area of the sector A D C E A is 201,1)? cr—cv cv 2) cr equal to —+——— -———-—= . .-— __ ; ‘2 c 2 O 2 C 2 MEN 341g; MEN M — “1‘ fr l —--- M Now let the last equation be multiplied by di- 0%. I ‘ 5'; 2 ca '03 4 (It) 021:3 v Thendv (3 +20)~——-—*3 x(v—-§7— 78"&C'+) -x(1+ 72+8:——_:’&c') __ 4 (11)2 4 '03 4 1) 8t '03 +04 ‘ 3 0‘ 24d’ (”+75 +8d+32d:’&°' _ 4 deg 5 v3 '0" 8L — 3 12 24 d’ c“ Now let this last equation be divided by (1* u . 3 1 4 alt)e 5 v3 12* d bt .53 3. = _ __ _ an we 0 am + 2 c (1% 0% x < 3 12 04 d’ 8w.) 01.207) 11: __ ] (#11E 4th52 503 v“ & 3 +20—divixdi‘rfi 3 EYE—94¢? c.) .9012 '03 di vi 4dr)” 5'03 '04 0‘ 3 +Qc— dv x( 3 T5 24d’8‘c') 2 CI) '03 l 4.1] 5 112 193 o __ 7. 2 — .—_——— — -——4- r 3 +ec d1” 3 12d 24d2’8‘c') Q01) 1’3 __ g. g (41: 1007‘ 912 or 3 “Lac—d” x 3‘24d‘f (12’3“) 2 6'0 '03 1. L 2 5 v v" — = 2 ’D d2 2 (— -—- —-— -- .) or 3 +26 x ”X 3 24d 48d1’8w But 2 v x (1% 0% x (E __ _v___ 1’ 2’ 8w. ) is and if this area be dwided by” the radius, we 3 5d 28d , c v v3 c 1.0 1:3 known to be the value of the segment, the dia— obtain a + 2 6 75+?” 2 2 +0__ 61' ”2+ —-" rfor the 1:3 half arc, or c+-—+—c-;, for the whole arc. . 4v” . And if c :0” be substituted for r, we obtain Srvz 81)” a f l 0+302+1201 c3+4cv' or thevaueofthe are in terms of c and 'v. Theorem XIV. Rule 7, of the areas of plane 2 2 figures, 11 r s x being the area of the + v 1 l >2 + 3 02’ segment, the sine of the half are of which is s, the versed sine v, and the radius 7', evidently follows from Theorem X. Rule 6, by multiplying half the 1 l s s2 + v2 .2— Yrs—2W, by the radius r. are, x 2111) r13 - 1 Theorem XVI. being 7) x (T 32) will easily be obtained from the following Considera- tion, viz. suppose the ellipsis to be completed, and a circle to be described upon the axis, \\ hich bisects the base of the elliptic segment; then let the base of the elliptic segment, to be continued, if iieCEssary, meet the circumference of the cir- cle on each side; then it will be as the base of 342 ‘M EN m J MEN M i L the circular segment is to the base of the elliptic segment, so is the area of the circular segment to the area: of the elliptic segment; therefore, if the area of the circular segment be known, that of the elliptic segment will follow; now the area a3 ' + 22—]; ; therefore, . . 2 a of the Circular segment 15 3 2017 a3 1 26th a", b=’==T+§z-‘5X(*§'+oo) of the elliptic segment. AREAS OF CURVED SURFACES. Theorem VII. Rule 1, is an approximation; and the following will shew what dependence is to 'be placed in the result obtained by calculation. Let a = the axis of the spheroid; b = the diameter of the great circle; and x = an indefinitely small distance, compared with a or (I. Now .5236 a d1 is the expression for the solidity of the spheroid, being two—thirds of its circumo scribing cylinder; ' then (d+ x)2 x (a +3!) = ad2 + 2 adx + ax2 + dzx+2 dcrz + a3 = ad2 nearly, being in excess; and (d—x) x (a—x) ‘~ad2 _ 2 adx + axz—d‘x + 2 dxz.._.t*3= ad2 nearly, being in defect; therefore 4 a d x the thickness of which is x; therefore 4a d + 2 d2 + 2 a" will be the area. of such a shell, or 4 ad + 2 d’, by leaving out the quantity 2 x1, which is indefinitely small: therefore .5236 (4 ad + 2 d2) is the area ofa Spheroid nearly; it is exactly so when a and d are equal; for then .5236 (4 ad + 2d1) becomes .5236 x 6 dz = 4 x .7854 dz, but the greater the difference between a and d, the more will the error be; beCause the thin shell varies more in its thickness. COROLLARY 1.-—Hence the surface of‘every rectangular prism with a square base is 4 a d + 2 dz. ' COROLLARY 2.—-When a : nothing, then .5236 ' .(4 a d + 2 d‘) becomes .5236 x 2 d2 = 1.0472 d2, instead of .7854 d‘, the area. of the base. Examplefor the oblong spheroid. 50 = a 40 =d 40===d 40 ==tl 2000 -_= ad 1600 = d“ 4 Q 8000 = 4 a d 3200 3200 ———_ 11200=4ad+2dc .6236 1 1200 ~— 1047200 5236 5236 58643200 = .5236 (4 a d + 2 d9) +2de + 2x3 will be the solidity of a thin shell, The true answer is 58826385, the difference is therefore only 18.3185, which is not worth re- garding in so large a number. In a dome which is the half of an oblong spheroid, the error would only be 9.1592 less than the truth. Example for an oblate spheroid. 40 = a . 50 50 —_= d 50 2000 = ad _ 2500--—- J? 4 a 8000 = 4. a d 5000 5000 ——-~ l3000=ad+2dG .5236 13000 15708000 5936 68068000 = .5236 (4 a d + a d?) .— The answer ought to be 6830.4507; the error being about 24 less than the truth, which is very trifling in so great a number. In architecture we very seldom have domes of such large dimensions; and the value of a foot of plaster, or painting, can never be of any great consequence. This rule will therefore be suffi- cient for every practical purpose. The following table contains the areas of the curved surfaces of spheroids of various propor- tions, according to the formula .5236 x (4 a 07+ tie) and to the real series; the comparison of the re- sults will enable us to judge of the truth of the answer as found by the formula. Z'MEN 343 M A D Area. Difference. Series.. 40 40 5026.56 D , Formula 40 40 5026.56 4; none, being equal. Series. . 50 40 5882 . 63 ’ a Formula 50 40 5864.32; 18.31 defective. Series. - 60 40 6867 . Formula 60 40 6702 . 30 . 08; 65.22 defective. Let us now try if any addition can be made to amend the above formula, which always gives the result less than the truth. We know, that the quantity to be added must be equal to nothing when a is equal to d; we also know that the sum of the squares of two quantities is greater than twice their product; and when these quan- tities are equal, that the sum of their squares and twice their product will be equal: therefore a? + d2 is greater than 2 a d; and the greater the difference between a and d, the more the sum of the squares of a and d will exceed twice the pro- duct, 2a (1, of a and (1: thus, when one of the quantities, as d, is nothing in the sum, a" + d2, of the squares, the quantity a2 only remains, and in twice the product Qad, the whole vanishes. Therefore the value of a“+ d9— 2 ad will be greater, as the difference between a and d is greater. But to shew what this difference is, by finding the value of these quantities in the same terms : Let the greater, cl = a + x; then d2 : a2 + 2 ax+ at“; and (12+ d2=2 a2+ 2 ax+ x53. Again, 2ad=2a(a+x)=2a9+2ax: now 2 a2 + Q ax + x9 is greater than 2a9 + 9am by are; that is, the sum of the squares, a9 + (1", of a and (1, is greater than 2 a d by the square of the difference of a and d; therefore the value of 02 + d‘3 — 2 a (1 will be greater, as a is greater than d. But to shew that the square of the dif- ference will not be very great in common cases, let a = 4, and d = 3, then the square of the difference is only 1; that is, when the difference is l, the square of the difference will also be 1. MEN? M Let us now return to the subject, by adding the quantity proposed to .5236 (4 a d + 2:19); it will be found by adding at" + d-2 —- 2 ad to .5236 (4ad+ 2d“) that the sum will be too great; therefore let the quantity a2 + d“ —- Q a d be di- vided by some number: on trial it appears that 2 2 __ the addition of“ + d 6 2 ad to.5236 (4 ad+ 2 d2) will give a result very near to the truth, at the same time that it furnishes avery easy formula for architectural purposes, in the mensuration of domes, as will be seen in the following table. This formula will therefore now stand .5236 2 ‘2_, (4ad+9d3)+w=1.0472(4ad+2d2) 6 2 ‘1 _ o . + 2%, which may again be reduced to a2 + 2 (12 this form .8805 (Q. a d + d”) + 6 Rules. A D Areas. Difference. Series . - 40 40 5026‘ 22 nothing. Formula 40 40 5026. 60 Formula 50 40 5880 . 8 30 Series- . 60 40 6767 . 6768 .74 l l Series” 50 40 5882' £1.83 in defect. l l Fonnula 60 40 1.44 in CXCBSS. This table shews the formula sufficiently exact for any practical purpose, at least in all useful propositions of architecture; and therefore con- firms Theorem VIII. Rule 2. Ifa dome upon an elliptic plan, rising half the minor axis, be re— quired to be measured, then the rule for such a , a‘2 + ’2. d2 dome Will be .4409 (Q a d + d9) + -——-———12 . The approximating formula 2x .5236Ca b + a c+bc), Theorem IX. Rule 1, may be thus confirmed: let the three dimensions of the ellipsoid be a, b, c, and let x be a very small increment to be added to a, b, and c, respectively; also a very small decre- ment to be taken from a, b, and c, respectively; now the solidity of an ellipsoid is .5236 ab 0 ; then abc=(d+1‘) X (b+x)x (c+x)==abc+bcx+acx+cx2+abx+bx2+axe+xfl nearly; and abc=(a—;r) x (b—x) X (c —_ x)=abc—bc.r._ acx+cx2_abx+bxg+a;rQ—x3, nearly; therefore 2 bcx+2acx +2abx +2.1“g is the increment of the solid, or the solidity ofa shell, the thickness of which ism; consequently, if the incre- ment,2 I) cx + Q a c x + Q a I) :r, of the solid be divided by x, we shall then obtain 2 be + 2 a 0+ 2 a b + 9. 13 for the surface of the solid; but the quantity 2x3 is indefinitely small, and appears as nothing in com- parrson ofa bc+2ac + Q ab,- therefore Q [n+2 a c + Q. ab, or 2 ab +2ac+ ch is nearly equal to the surface of the solid; and consequently, .5236 (Q a Z) + 2a 0 'l' ‘3 b c), or 1.0472 (ab + a c + b c) will be nearly equal to the surface of the ellipsoid. M EN 344 MEN W" J COROLLARY 1.—Hem-e 2a b + 2 ac + ch'will‘ be the surface OFa rectangular prism, exactly. COROLLARY 2.-—Let a, b, and c, be each equal to d; then 1.047% (a b + a c + b c) becomes 1.0472 x 3 d? = 3.1416 d9 = 4 x .7854 d2, as it ought to be: but the greater the difference be- tween a, b, and c, the more will the error be. This rule may be corrected in the same manner as Theorem VlI. Rule 1. by adding a2+b2+ c9—-a bV—ac —- bc 6 done, the formula may be reduced to .8805 (ab+ac+bc)+(-1—?——--l:—I:).-——'-l-—CZ rem X. Rule 2. 7; which being , which gives Theo- NOTES ON THE SOLIDITIES OF BODIES. The method of the middle section has never been noticed by any writer in a practical way. There can be little doubt but this method took its rise from that of equidistant ordinates, first given by- Sir Isaac Newton, as we are informed by Shirt— clifl‘e, in his Art of Gauging, in the following wzords “ I shall lay down a proposition for measuring planes or solids by approximation, a thing of the greatest importance to this part Of science, of any that was ever brought for that purpose, since it may be said to contain the whole art of gauging, and that of coppers, stills, tuns, as well as all kinds of casks, whether full or partly empty,either standing or lying. “ 0f measuring curvilinear planes and solids, by approximation. “PROPOSITION.——lf MQ=y’,NR———y”,PS ——y’” Figure 14, represent three equidistant perpendi- cular ordinates to the axis of a curve, M N P, whose equation is 1/: a + bx + cx‘l, where .1" stands for any abscissa, Q T, andy its ordinate, TO; then, calling Q S the distance of the ex— treme ordinates, l, the measure of the space, Q M P S, will be thus expressed: QMPS _______..__ l “THEOREM. = y’+y”’ + 43/” x 6' “ For by the preceding principles, the quadrature- of the curve, whose abscissa is x, and ordinate a+bx+ca€ W111 befounda+ §§€+c§ x 1‘; and this, when x becomes 1, is bl cl2 1 a+§+§-xl:6a+3bl+2c 2 x61=QbIPSn 4 But from the equation of the curve we have these three equations, y'”:a + bl .1. cl“. And by taking the difference of those above, we have ,, _ bl c l2 . 3’, r" a - “2‘ +71 III II____ b l 3 6/2. .9 ‘1’: —-+ 1 And the difference of the last4 gives E cl2 _2 0+ =___' a' a a 2 Whence Q o 1’3 = 4 x y'” -——- 2g” + a; and by the third equation above, b l = y’” —- a — 612; there- foreSbl: 3y”’——3a —-—6 xym—Qf—t—a: —- 33'” + 123/” —— 9a; put these for 2 cl" and 3 b Lin the above expression of the area,and then wehave, QMPS=6 (1+ 3 51+ .3 012 x~6£ I =3/'+41/”+_/”’ +7.- Q.E.D. “ COROLLARY 1.—'l he same method of demon- stration extends to any number of equidistant or- dinates; so ifA denotes the sum of the extreme ordinates, B the sum of those next to them, C the sum of the two next following the last, and so on; then we shall have the foilowing tables of areas, for the several numbers of ordinates prefixed to them, viz. for l Q.A;x-5 am 1. J» + x6, _____ 1. 4..A+3BX-§a ——————.~—————————— 1 5.7A+oQB+lZCX-\-)6; 6.19A+70B+50C XE—bs; 7. 41A+2103+27Q+g72D xii—O; 8. 751 A + 3577B +13230 + 2989]) >< Sac. 8m. “This method was invented by SirIsaac Newton, and published by Mr. Jones in 1711; and since ”T’SO’ MEN _ 345 MEN W proS-ecuted by‘Mr. Coats, Mr. De Moivre, and by Mr. Stirling, in a whole treatise entirely built thereon, where such as desire a farther insrght . into this matter, may find it sufiiciently explained, and applied to some of the most intricate parts of mathematics.” . This table errs in the last term of the areas cor- i responding to the ordinates 3,5,7, Ste. viz. 4B should only be 9. B, and 1% C should only be 6 C, and so of the rest; that is, they are double what they ought to be. , This error has also escaped the notice of that great mathematician, Mr. Emerson, see p. 29 of his Dtflerential JlIetlwd, published With his Conic Sec- tions, 1767, where he has the same table as in Shal'tciifle’s Gauging; but it has been corrected by Dr. Hutton. See his ZlIensurution, large copy, printed in I770. To shew how this rule may be derived in the sim- plest manner, in order to approximate any curvili- near surface, of which the ends are parallel, let AEl) BA, figure 15, be bounded on one side by a parabolic curve, B C D; and let A B and ED be two diameters, or straight lines, parallel to its axis; and let A E be perpendicular toA B and E D; also let AB be bisected in F; and let FC be drawn parallel to AB or ED; and let BD be drawn cutting F C in G; and let A B = q, FC=b, and ED=c; also, AF, orF E=m: now F G will be equal to a o , a+c and the part G C will be b —— g , but the space B C D B is equal to a parabola, of' which the base is AE, or 2m, and the height a + c Qb—a—c G C,or b— T: -——2———; 26 -— a -— c 2 ml to therefore: + GC x AB = x x 2m :97? X (21) —a — c)theareaBCDB; but the area of the trapezoid AB DE is equal% x (a + c) x Qm =(a + b) x 772; there- fore the arca ABC D EA= (a+c) xm + ' 2m ' 4b—Qaw2c WWW . > VOL. II. 3a+30+4b—-2a-—20 Xm= xm 3 =a+c3+4b X m 01'a+436+c>< a +b+c+d,8tc.top+q by I, n multiply each side respectively by n, 22 — l, and then adding, or taking away the common parts; by making the divisor l a multiplier, and the multipliers n, 11—1,divisors; then multiplying the equation I x and the equation 13 x 2—2;? = a + b + c + d, 8&0. to p + q by I, and dividing it by n and 21—], a + q 2 X (It —— l) a+b+c+d,&c. top-l-q ”—7: x (nZ—irfl“ there will arise lx = 1x MEN >347 MEN W WWW Example.—-—Let a = 4, b = 19, c = 16, d: 18, p=19,q=18, andl=10; a+q __ 4+18 __ then1x2_——_mx(n——l)—10x ——~————-2 x(6~1)-2?’ a+b+c+d,8cc,top + g __ andlx nx(n—-l) —le 4+19+16+18+19+18__ _ . ence is therefore 7, the same ‘as between (a+q+b+c+d,8tc.top+q) 2 n—l xl,and a+b+c+d,8tc.top+q x n l. MENSURATION or ARTIFICERS’VVoRKs. All such works, whether superficial or solid, are computed by the rules proper for the figure of them. The most common instruments for taking the measures are, a five-feet rod, divided into feet and quarters of a foot; and a rule, either divided into inches, or twelfth parts, and each twelfth part into twelve others; a fractional part beyond this division, measurers seldom, or never, take any account of. When the dimensions are taken by a rule divided in this manner, the best methods to square the dimensions will then be by duodecimals, by the rule of practice, or by the multiplication of vulgar fractions; but, in the Author’s opinion, the best method of taking dimensions is with a rule, when each foot is divided into ten parts, and each part into ten other parts, orseconds, because the dimen- sions may be then squared by the rules of multi- plication of decimals, which is by far the shortest and readiest method. Those who contend that duodecimals, or cross multiplication,is the easiest method of squaring dimensions, as well as the most exact, are very much mistaken; for if the dimensions are taken in duodecimals, and reduced to decimals, and then squared, the operation, in this case, will certainly be much longer than if it had been done at once by duodecimals, and some- times not so exact: but if the dimensions are taken in feet, tenths, 8L0. the operation will not only be easier and shorter, but in many cases will be much more exact than by duodecimals: the reason is obvious to those who consider that there are many cases in which it will be impossible to express, truly, a decimal scale equal to a duode- cimal one; neither will it, in many cases, be pos- sible to express accurately, a duodecimal scale equal to a decimal one; duodecimals have the same property with regard to twelfth parts, as decimals have to tenth parts; therefore, in many ’ cases, duodecimals will sometimes circulate and run on, ad ilgfinitum, when reduced from deci- mals, as decimals will, when reduced from duode— cimals; and farther, since duodecimals are ex- pressed by a series of twelfth parts, and decimals by a series of tenth parts, in multiplying each of the parts of the former, the trouble of dividing by twelve will then be unavoidable, and more burthensome to the mind than if the operation had been done by the latter, where there is no such division to be made, but merely to multiply, as in common multiplication, and point off the decimal places in the product. This last method is always to be preferred, as the most natural, as well as the most easy of the two. BRICKLAYERS’ WORK. The mensuration of brickwork has already been treated of at considerable length under that head, but in order to complete the article, we shall give a few more problems and examples. PROBLEM I.—To measure the vacuity qfa window. Find the area of the outside of the window, and multiply that by the number of half bricks thick, from the face of the sash-frame on the outside, to the face of the wall on the same side; to the area so found, at half a brick thick, add the area of the inside vacuity multiplied by the number of half bricks thick, from the face of the sash-frame on the outside, to the face of the brick-work within the building; also add therarea of the vacuity of the recess, the height being taken from the bottom of the sash-frame to the floor, and its width the same as the inside vacuity above; multiply this also by the number of half bricks thick, then the sum of these will be the whole vacuity, or void space in the whole win- dow, at half a brick thick; and if required to be reduced to the standard, divide the area so found by 3, and the area of the contents will be reduced to 1%) brick thick. Example—Let Figure 17 be the plan, or hori- zontal section of a window. Figure 18, the elevation as it would appear within the build- ing. Figure If), a vertical section through the middle of the elevation of the window. The height of the outside vacuity is 8 feet, its breadth 4 feet, and halfa brick thick ; the height of .the 2 Y 2 MEN ' ’34s 1 ' m1 MEN 1* j inside vacuity is 8 feet, and its breadth 4 feet 9 inches, and 2 bricks thick, as appears by the plan and section; the recess is 2 feetQ inches high, 4 feet 9 inches wide, and halfa brick thick, which is also marked upon the plan and section; required the area of the whole vacuity, at half a brick thick. Feet. In. 8 0 height of the outside vacuity. 4 0 width of the outside vacuity. ~..—_~—- 32 0 area of the outside vacuity, % abrick thick. ~— 4 9 width of the inside vacuity. 8 0 height of ditto. —— 38 0 4- 0 number of half bricks. 152 0 area of the inside vacuity, éabrick thick. 4 9 width of the inside vacuity. Q. 9 height of the recess from the floor to the side of the sash. 9 6 3 6 9 33 O 9 area at 1% brick thick. 3 O 0 .__._._...._—— 39 ‘2 3 area of the recess, :12 a brick thick. 32 0 0 152 () 0 m.- 223 ‘2. 3 area of the whole vacuity, % abrick thick. PROBLEM II.—-To measure any angle chimney, standing equally distant each way from the angle thhe room. Figure 20.—Multiply the breadth, AB, by the height of the story, and the product by the num- ber of half bricks contained in the half breadth, AB, and it will give the solidity at half a brick thick, after deducting the vacuity, or opening of the chimney, PROBLEM [IL—To measure an angle chimney, when the plane of its breast intersects the two sides oft/2e room unequally distantfrom the angle. Figure Ql.-—From the points A and B, where the plane of the breast intersects the sides of the room, draw two lines, A E, E B, parallel to the two sides of the room; then multiply either of the lines, A E or E B, suppose E B, by the height of the room, and multiply that product by the num- ber of half bricks contained in the otherline, A E, and deduct the vacuity as before, and the re- _— mainder will be the content, at half a brick thick. PROBLEM IV.—-To measure an angle chimney, when the plane of the breast projects out from each wall, and unequally distant from the angle of the room. Figure 622.—Draw the two lines, G Fand F H, parallel to the two sides of the room, as before; then multiply the breadth, F H, by the height of the story, and the product contained in the half of the other side, F G; from this product deduct F D, multiplied by the height of the story, and by the number of half bricks contained in the half of F C, and also the vacuity Of the chimney. PROBLEM V.——To find the area of an arched aperture. To twice the height at the middle add the height of the jambs; and one-third of the sum multiplied by the breadth of the aperture will give the super- ficial content, sufficiently near for practice. Example—Let the height of the arch be 12 feet, each jamb 10 feet, and the breadth of the aper- ture 5 feet; what is the superficial content? Feet. 12 2 .—._ 24 10 3)34 11% 5 56% feet, the answer. But if greater accuracy be required, add the quotient arising from the division of the cube of the altitude by twice the breadth of the aperture, and the sum will be exceedingly near the truth. Example—In the foregoing example, the height of the arch is 2 feet and the chord of the arch, or twice the breadth of the aperture, is 5 feet; then the cube of Q. is 8; and 8 divided by 10, or twice five, gives .8 of a foot for the quantity to be added to the above. Now the above 56%. = 56.666, Ste. ' .8 57.466, the area, exceedingly near the truth. PROBLEM VL—Tojlnd the area qfa wall, or ofthe foundation of a building, placed upon a curved sur- face, supposing it to be built upon uneven ground. MEN 349 MEN 4 M Divide the length into any number of even parts (the more the truer) by parallel vertical sections; call the first of these sections odd, the next even, the next odd, and so on alternately; and thus the first and last sections will always be odd. Then add together four times the sum of the odd sec- 'tions, twice the sum of the even sections, and the two ends: divide the sum by three times the number of parts that the length is divided into; then multiply the quotient by the length of the wall, and the product will be the superficial con- tent. Example.——Suppose a brick wall, 32 feet long, to be divided into eight equal parts by seven sec— tions of the following heights, taken in successive order, 5 feet, 6 feet, 6 feet 2 inches, 6 feet 3 inches, 5 feet 5 inches, 4 feet, 3 feet, the one end 3 feet, and the other 2 feet 6 inches; re- quired the area of the wall. Now 5 feet, 6 feet 2 inches, 5 feet 5 inches, and 8 feet are the odd ordinates; and 6 feet, 6feet 3 inches, 4 feet, are the even ordinates; there— fore, Feet. In. Feet. In. 5 O 6 0 6 2 6 3 5 5 4- 0 3 O "'——'- 16 3 19 7 2 4 -—————— -_._.__ 32 6 [tions 78 4- : four times the sum of the odd sec- 32 6 = twice the sum of the even sections. 3 0 = the one end. - 2 6 = the other end. 3)]16 4 8) 38 9—4 4 10—3 32 T573 1 4 The following erroneous method is usually prac- tised by ineasurers and workmen: Add all the heights together, and divide the sum by their number; then the quotient multiplied by the length is supposed to give the area. Let us therefore resume the same example by this method : Feet. In. 3 0 5 0 6 0 6 2 6 3 5 5 4 O 3 0 2 6 9)4l 4 the sum of all the heights. 4- 7 lg- 32 146 11 633. the answer, considerably below the truth. Where the foundation would consist of several straight lines, forming trapezoids, the best method is to find the content of each trapezoid separately; and then adding all the trapezoids together, their sum will be the area of the whole: but if the figure of the ground on which the building is raised be a curve, the measurer will be grossly de- ceived, as to the true contents of the work, unless he divide the length into equal parts, as already recommended. The contents in brickwork may be found by mul- tiplying the area by 3, and dividing by the num- ber of half bricks. The following example is added, in order to shew the use of the method of equidistant ordinates. . Example—Figure 23. Let E F G H be a wall of brickwork, or the back of a house, to be built over a public road, or valley, H L G ; the under part of the wall is built from the foundation, H L G, up to the level at l K, three bricks thick, and from l K, to the top, E F, parallel to it, two bricks and a half thick, to the height of 15 feet, -having five windows in it; the vacuities on the outside of each window are 8 feet by 4 feet, and halfa brick thick; the vacuities on the inside are 8 feet by 4 feet 9 inches, two bricks thick; the recess on the inside for the finishing of the backs in each window, one and a half brick thick; the the height 2 feet 6 inches, from the top of the floor to the sill of the window; the width is that of the vacuity on the inside of the window, viz. 4 feet 9 inches. There is an arched way under- neath for carriages, 8m. to pass through, whose opening is 12 feet, and its height from the level of the pavement to the crown or top of the arch 11 feet, and the height, from the pavement to the MEN 35o MEN W, WWW springing of the arch9 feet; the under wall is divided into an even number of equidistant spaces, whose ordinates are respectively as follow: 6feet, 10 feet, 18 feet, 14 feet, 10 feet, 4 feet 6 inches, and 1 foot; the whole length of the building is 50 feet; required the number of bricks, and the quantity of sand and lime to build the said wall. Erplanation.——The under part of the building being an irregular figure,‘it is measured accord- ing to the method of equidistant ordinates, Pro- blem VL; the upper part is found, as in the fore- going examples. The arched way is measured by Problem V. The contents of the windows are obtained by Problem I. Then deduct all the vacuities at halfa brick thick from the area of the whole, found as if it were solid, at half a brick thick, as before: the remainder being divided by 3, will reduce it to the standard thickness of one brick and a half. Feet. In. Feet. 10 0 13 l 4 0 10 4 6 —- .._....... 23 28 6 2 4 46 114 0 four times the sum of the even ordinates. add 46 twice the sum of the odd ordinates. 3)]60 53 4 5O 2666 8 6?...“ [3 bricks thick. 444 5 area of the under part of the wall, 6 number of half bricks. 2666 8 area of the under part of the wall, % a. brick thick. 15 0 height of the upper part of the wall. 50 0 MW“ [bricks thick. 750 0 area of the upper part of the wall, 2% 5 0 number of half bricks. 3750 0 area of ditto, é a brick thick. ———-— Feet. In. 8 0 if.) [brick thick. 32 0 area of the vacuity on the outside, é a .. o 0 number of windows. 160 0 area of the vacuities on the outside of fire wina dows, é a brick thick. sum not: I .- cart-‘- 3 6 [window, 2 bricks thick. . 39 7 area of the vacuity of the inside for one 5 number of windows. . . _ [the insule. 197 11 area of the vacuities for five windows on 4 half bricks thick. l 791 8 area of the vacuities on the inside, % a brick thick. -—-——- 49 2 6 96 2 4 6 .________ [(ler each window 1%. brick thick. 11 10 6 area of the vacuity of the recess un- 5 __ [dow backs, 1% brick thick. 59 4 6 area of the vacuities of the live win- 0 a number of half bricks. —_ 178 l 6 area ofthe vacuities of the five window backs. — é a brick thick. 11 0 height of the archway, from the pave- ment to the crown. og . add 9 0 height from the pavement to the springing of the arch. O 31 10 0 width of the archway. O 3)310 0 [3 bricks thick. 103 4 area of the vacuity of the archway, 6 number of 1‘s bricks thick. 620 0 area of the vacuity of the archway, i: a brick thick. 160 O 791 8 178 l 6220 0 1749 9 areas of all the vacuities, é a brick thick. MEN 851' MEN Feet. In. 2666 8 3750 O 6416 8 area of the whole, % a brick thick, deduct 1749 9 as if solid. ._ [thick 3)4666 ll true area of the whole, s a brick 272)1555 7 (5 rods 195 feet, reduced to the 1360 standard thickness. -_.... 195 ._... Then 5 195 x 4.500= 25726 number of bricks, nearly. 5 195 x 1% = 7%‘7% cwt. oflime, nearly. .5 195 x 2% = 14;,‘12—loadsofsand, nearly. MASONS’ WORK. Masons’ work is measured in the same manner as bricklayers’, so far as the superficial content is concerned. The joints of the plane surface of an ashlar wall are measured in breadth, according to the thick- ness of the ashlar work, which is generally about six inches; and the two surfaces which are sup- posed to come in contact, or to be cemented, both of the vertical and horizontaljoints, are account- ed as only one surface, as in cornices; and are supposed to be equivalent to that of the vertical facing of the wall after being rubbed smooth. 1n brick walls, stone strings must correspond to the thickness of the bricks. Strings are generally bevelled, or weathered, upon the upper side, and grooved on the under side: the weathering is de- nominated sunk work, and the grooving, t/Iroat- ing. Stone sills in common use are about 4% inches thick, and 8 inches broad; they are wea- thered at the top, which reduces the front, or ver— tical face, to about4 inches, and the horizontal , surface at top to about 1% inch on the inside; so that the part taken away is 6% inches broad, and three quarters of an inch deep. Sills of windows, when inserted in the wall, most commonly project about 25 inches The horizontal plane part, left on the inside of the top, the vertical part, or face, and the horizontal part on the lower side without the wall, are denominated plain work; the sloping part is the sun/c work. Plain and sunk work are measured by the foot superficial; throating by the foot fun; and are thus entered in the measurer’s book: ‘ 1% adding 4- 2% the sum is 8 inches for the breadth of the plain work in the sill, according to the dimensions stated. Feet. In. 3 3 Plain work. 3 2% Sunk work. 2 33 2% Plain to end. 4- 0 Run of throating. The sawing is not taken into account. Cornices are measured by girting round the mould- ings; that is, round all the vertical and under sides: this is denominated moulded work. Thus, suppose a cornice to project one foot, and to girt two feet, and to be 40 feet in length; then the dimensions are entered as below: Feet. .— 4: Moulded work. 40 1 Sunk work at top. To this must be added all the vertical joints. All cylindrical work is measured in the girt, and the surface is accounted equivalent to plane work taken twice. Thus, suppose a cylinder girts 4feet 9 inches, and is in height 12 feet, then the dimensions are written as follow: Feet. In 12 0 Superficial plain work. 4 9 Double measure. Rough stone, or marble, is measured by the foot cube; but for workmanship, the superficies are measured before it is sunk, for plain work; one bed, and one upright joint, are also accounted plain work, as before stated; then to take the plain sunk work, or circular, if any, and the straight moulded work, or circular moulded work, if there be any such. In taking the dimensions, particular care is required to distinguish these dilferent species of work in the progressive state of pre- paring the stone. Throatings, and all narrow .m MEN‘- 352 MEN sinkings, are measured by the foot running mea- sure. [11 taking the dimensions of moulded work, the mouldings must be girt with a string. The contents of pavements, slabs, and chimney- pieces, are found by superficial measure; as also stones under two inches thick are valued accord- ing to the same measure; but those that are solid by the foot cube. The construction of rubble-walls Is not known In London, from the want of stone; but in many countries such erections are very general. In Scotland, where stone abounds, the standard thickness of a rubble—wall is ’2. feet; the content is first found in feet and inches, then divided by 9, which reduces it to superficial yards; and the yards are again divided by 36, which reduces it to roods, should the superficial content in yards ad- mit of such division: when the wall is above 2 feet, it is reduced to that standard by adding one-eighth, one-fourth, one-half, according as the additional thickness may be 3 or 6 inches, or a foot. The customs, in taking the dimensions of a house, vary according to the place, and the nature of the agreement. In Glasgow, if the builder engages for workman- ship only, the dimensions are taken round the house, on the outside, for the length, and multi- plied by the height at the same thickness, 01' by as many heights separately as there are thick- nesses. The outside measure gives something more than the truth, by the addition of the four quoins, which are pillars of two feet square; but this is not more than sufficient to compensate for the trouble of plumbing the returns. If the building have a plinth, a string, a cornice, or a blocking-course, the height is then girt from the bottom of the plinth to the top of the blocking-course, including the thickness of the same; that is, suppose the measurer to begin at the plinth with a line or tape, then stretching the line to the top, bend it into the offset, orweather- ing, and keeping the corner tight at the internal angle, stretch the line vertically upon the face of the wall, from the internal angle to the internal angle of the string , then girt round the string to the inte1nal angle at the top of the string; and keeping the string tight at the upper internal angle, stretch it to meet the cornice; then bend it round all the mouldings to the internal angle of the blocking-course; keeping the string tight at meg-w this internal angle, stretch the string up the“ blocking-course to the farther extremity of the: breadth of the top of the same, and the whole» extent of the line will be the same as the vertical. section stretched out; which is accounted the ,height of the building. In regard to the length, if there are pilasters, or recesses, the girt of the whole is taken as the length. This practice is perhaps the most absurd of any admitted 1n the art of measuring, since this addi- tional extension in height and length does not 111 l 1 make asufficient compensation for the value of ' workmanship on the ornamental parts; for the price per rood varies, even where the whole front is rubbed ashlar, from £90 to £30; and it is evi- dent that it gives an excess of materials not used in the building. The value of the mod of w ork- manship must be first obtained by estimation, by finding the cost of each individual species of work, as plinths, strings, cornices to building, architraves, cornices. to windows, Sic. with the quantity of plain ashlar work, and the value of the materials; all which particulars added together, will give the amount of the whole; and this be- ing divided by the number of mods, will exhibit the mean price per rood. No deductions are made, either for materials or workmanship, where the aperture is of an ordinary size, as from?) to 5 feet wide, and hom 6 to 12 feet high. As this \Vork is intended to be of general utility, the following data, which the Author collected during his residence in Glasgow, will not only be if necessary in that city, but in many other parts of . the country. They will be useful to the builder, by enabling him to make a proper estimate of the expense of his undeitaking , and, if he is a stranger, they will enable him to make the proper reseaich for “hat he may it ant. How many ashlars are there in a rood, the face of each ashlar being 2 feet 6 inches long, and 1 foot broad ; the mod being 6 yards square? . Feet. 36 9 394 feet superficial in a mod. Now since each ashlar is 1 foot broad, there will be‘? -13, 01 2.5 feet superficial in each stone. MEN W Therelbre2.5)324(129.6, the number of ashlars 25 required, which may 7:“ be called 130; but to 50 allow for waste, it - -‘ ._.. will require 140, at an 240 average. 225 150 150 —_ Given the wages of a mason, or stone-cutter, at three shillings per day, and the price of a foot, Superficial at Sixpence; to find the time a man will require to hew a mod. Now it will be, as the wages per day are to the price ofa foot, so are the number of hours in a day to the time required to work a foot superficial: that is, d. d. H 36:6::10 6 36) 60( 1% hour = —§—. 36 -—- 24 Now the quantity done by the workman will be as the time he employs; therefore, H. H. Ft. § : 10 : : l l 10 x % : 6 feet, the quantity done in a day, which is very near the quantity in hard stone, as the Possil. But it is found, upon an average, that a workman will cut and hew 7 feet of stone, of a moderate degree of hardness, including beds and vertical joints; as in Scotland the joints are never mea- sured, only the superficial contents of the face. Ft. Ft. Day. Again, as6 : 324 :: l 1 6)324 54 the number of days re-, quired by one man to hew a mod: but if he cut 7 feet in a day, he will only require 46 days to a rood. Now if one man in 54 days hew arood, how many men will hew a rood in 6 days. Here the time employed will be less, as the num- ber of workmen is greater -; and the time will be VOL. n. 353 ’Ashlars, per piece, from 8d. to 1 moves at the rate of 2% MEN ~ reciprocally as the number of workmen: there~ fore as 6 days are to 54 days, so is the number of men employed in 54 days to the number of men employed in 6 days. Days. Days. Man. Thatis, 6 : 54 :: 1: l (3)54 ~ 9 men required in a week to hew a mod of ashlar, including the joints. I But it is found that seven men will hew arood in a week, and this allows a sufficient price for the master. / ’ Or, since 46 days would require one man, 6 days would require 7%- men; say 8 men. To build a mod of plain rubbed .ashlar would re- quire 7 stone-cutters, 4 builders, and 2 labourers, in a week, or 6 days. Some allow only ‘2 labourers to 6 builders. Four labourers would slake, riddle, and properly prepare the mortar in one day. The following prices were allowed for materials, workmanship, and workmen, in the year 1808. s. d. . 1‘2 0 8 at thequarry. 0 at the quarry. A cart, per mile . . . . l O A mason, per day . . . . 3 O A labourer, per day . . . 2 O The materials required in a mod will be 30 carts of rubble; 140 ashlars, requiring ‘23 cart-loads; l chaldron of lime, requiring 2 cart-loads; and 5 or 6 carts of sand. N. B.—The cart is drawn by one horse only, miles an hour, and re;- quires two men to load it in a quarter of an hour. Back filletings are plain fillets of hewn stone, mn- structed at the quoins of a building, and round the apertures of doors and windows, when the i1;- termediate parts of the building are constructed of rubble, in order to make a finish at the mar- gins, and defend the corners, when the interme- diate rubble work is covered with rough-cast. A window, 3 feet wide and 6 feet high in the clear, will cost £1. Is. in back filleting, with the sill. The workmanship upon quoins is 6d. per foot, running measure. The number of carts required to build a mod con- sisting entirely of rubble, without apertures, is 40. Lime, per chaldron . Rubble, per cart . . . . 0 Qz MEN m In smoothed, or rubbed ashlar, all the joints should be rubbed, as well as the face, in order to make-close work. ' The following examples will shew the use of the data given. Tofind the value of the workmanship of a road of rubble. of s. d. 4 builders, 6 days, at 33. per day . . 3 12 O 2 labourers, 6 days, at 25. per day . l 4 0 Value of the workmanship ofa rood . 4 l6 0 The number of labourers here stated is supposed to be the average for building three stories; but if the building goes higher, it will require three «labourers to four masons. T 0 find the value (f a road of ashlar work, for workmanship only. of s. d. To 7 stone-cutters, 6 days, at 3s. per day 6 6 O 4- builders, 6 days, at 35. per day . . 3 12 0 2 labourers, 6 days, at 2s. per day . 1 4- O The price of a mod of ashlar . 11 2 O A two-feet gable, with fire-places on both sides, is valued at work and half; but it the wall be thicker than 2 feet, the value is not in proportion to the solid contents, but less as the thickness is greater. Droved work, which retains all the marks of the chisel, is the most common kind of hewn sur- face. The time required to prepare a foot of droved ashlar to that of preparing a foot of rubbed ashlar, will be nearly in the ratio of 2 to 3, or sometimes double. If the work be droved and broached, or tooled, the price is the same as if it had been rubbed smooth. Possel broached . . . . . Ditto droved . . . . . . Ditto rubbed smooth . . . . Rutherglen stone, broached . . Ditto droved . . . . . . Ditto rubbed smooth . . . . 42 The following, taken from Elsam’s Gentleman’s and Builder’s Assistant, printed in 1808, will shew the customs allowed in Ireland: “ It is the custom in Londonderry, and some other parts of the province of Ulster, for masons to in- clude in their measurements all manner of open- ings, such as windows, chimneys, fines, 8tc. in the solidity of the walls, as if they were built up; then to measure the reveals, arches, flues, 8m. in addition thereto; though the quantity of perches easements?" IHNV 354: 4-__. J MEN # w — * _ n—m contained in the openings often equal one-third, or one-fourth, of the whole building; injustifica- tion of this system, it is observed, that the price is somewhat lower than in other places, but by no means equivalent to the current price of the country. “ The fairest and most proper way to measure masons’ work of the above description, is to take the work as it is actually built, then to deduct all manner of openings, and to allow a just and rea- sonable price for it, and the square and splayed quoins, reveals, arches, 8Lc. Sic. “ Tofind the number of perches contained in a piece of rough stonework. “ If the wall be at the standard thickness, that is, 1‘2 inches high, 18 inches thick, and 21 feet long, divide the area by 2), and the quotient, if. any, will be the answer in perches; and the remainder, if any, is feet. If the wall be more or less than 18 inches thick, multiply the area of the wall by the number of inches in thickness, which product divided by 18, and that quotient by 21, will give the perches contained. Example—A piece of stonework is 40 feet long, 20 feet high, and 24 inches thick; how many perches are contained thereini> 40 length. 20 height. 800 24- 3200 1600 21 ) Per. Ft. In. 18) 199.00 (1066 (50 16 18 18 105 120 16 108 "“' 120 108 {-3, equal to 8 inches. —.-— “ The method last described, of finding the value of masons’ work, is usually adopted, the perch being the standard of the country ; but the most expeditious way of ascertaining the value is to cube the contents of the wall, and to charge the work at per foot. “ To ascertain the value of common stonework, a calculation should be made of the prime cost of all the component parts, consisting of the stone in 'MEN 3 MEN M 4., the quarry, the expense of quarrying, land-carriage to the place where it is to be used, with the extra trouble and consequent expense in carrying the stone one, two, three, or more stories high: also the price of the lime when delivered, together with the cost of the sand, the expense of scaffolding, and extra expense of wages to workmen, ifin the country: all these circumstances must be taken into consideration, in finding the value of a perch of common stonework, the expense of which will be found to vary according to local circumstances, in degrees scarcely credible; wherefore a definite price cannot with propriety be fixed, but may at any place be ascertained by making the above in- quiries. “ Method qffinding the price of a perch of stone- work, in the city of Derry, in building a common dwelling-house. “ Four car-loads of the common building 3. (1. stone will perform a perch of stonework, which, together with quarrying, loading, and land-carriage one mile, will cost on theaverage..........46 “ Abarrel of lime, containing 42 gallons, will perform a perch of stonework, and will cost, including carriage, on the ave- rage............110 “Two barrels of sand to each barrel of lime, will perform a perch of stonework, and will cost, including carriage, on the average...........l4 “ A mason’s time in performing a perch of stonework, reckoning on the average, foundations, basements, principal one and two pair stories, gables, scaffolding, and such other unavoidable expenses, will cost ............24 “ Labourers’ time in making the mortar and attending the masons with it, together with a supply of stones from the founda- tions to the top of the building, will cost, on theaverage . . . . . . . . . l 6 “Profit............10 “ It must be remembered, that in the above calcu- lation all manner of openings are supposed to be deducted,viz. doors, windows, chimneys, and their flues; but if the latter be included, no charge to be made for pargeting.” CARPENTERS’ WORK. Definition—By carpenters’ work is meant the measuring of common centres, groined centres, floors, partitions, centering, bond-timbers, lintels, wall-plates, and roofs. For the generalcustoms see the article. PROBLEM I. —— To measure the centering of a cylindrical vault. RULE—Multiply the length of the vault in feet, by the circumference of the arch, for the breadth ; and divide the product by 100, if greater than the same, and the quotient will give the number of squares and feet. Example 1.——-How many squares of centering are there in a vault, whose length is 18 feet 6 incheb; and the circumference 31 feet 6 inches? By duodecimals. By vulgar fractions. Feet. In. 31% 31 6 18% 18 6 —— 15é+t 248 0 9 310 O 248 9 0 31 15 6 —--— 0 3 5,82% 582 9 or 5 squares, 82 feet, 9 inches. By decimals. 31.5 18.5 1575 2520 315 5,232.75 PROBLEM IL—To measure naked floors, whether for materials, or workmanship. RULE 1.—If there be any number of pieces of timber of the same scantlings and length, findthe solidity ofone of them; and that solidity multi- plied by the number of pieces will give the solidity of the whole. RULE 2.—lf the pieces be of the same scantling, but of different lengths, add all the different lengths together, multiply the sum by the area of the end of one of the pieces, and the product will give the solidity of the whole. RULE 3.—[f the pieces be of different scantlings, but of the same length, find the areas of the ends of all the pieces, and the sum of these areas 2 Z 2 MEN 3 being multiplied by the common length, will give the solidity of the whole number. RULE 4-.—-lfsome of the pieces be of one scant- ling, equal among themselves, and others of the pieces of another scantling, equal among them- selves, but all of the same length; multiply the area of the ends of each, by the number of such as are of the same scantling, add the products to- gether, and their sum, multiplied by the common length, will give the solidity. RULE 5.—-lf the lengths vary, as well as the scant- lings, find the solidity of each piece separately, and the sum will give the solidity of the whole. Nate—VVherever a tenon is made, the length of the piece must be taken from the ends of the tenons, and not from the shoulders. If the floors be fixed in the building, the distance the timber goes into the wall, which is about one- third of the thickness of the wall, must be added to the length of the respective pieces that are clear of the walls. Explanation of the timber in aflaor. Let Figure 24 be the plan of a naked floor; Figures 25 and '46 are sections each way; the girder is marked A, and the section ofits end a, in Fig ureQG; the binding—joists are marked B, B, B, B, See. the sides are marked 6, b, in Figure 26; the ends are marked 1), 6, 12,1), in Figure 25; the bridging-joists are marked C, C, C, Sec. in the plan, Figure 24; the ends are marked c, c'. c, Ste. at Figure 26; and the side is marked 0, at Figure 25; the ceiling-joists do not appear on the plan at Figure 24, because of the bridging-joists appearing before them; the ends are marked e, e, e, Figure 26, and the sides are marked e, e, e, &c. Figure 25. The best method of finding the solidity ofajoist, where the length is given in feet, inches, Ste. and the dimension of the section in inches, is to mul- tiply the inches together, and throw the twelves out of the product; also throw the twelves out of the length, and multiply these together. Example—Suppose ajoist 15 feet long, 3 inches by 9; the product is 27, which divided by 12 gives 2 feet 3 inches; also .15. divided by 12 gives 1 foot 8 inches; then, t5 Dblwt— © (:50) 0009 ‘9 Q9 'MEN I ._.___. Let Figure 25 be the plan of a floor, as before; suppose the girder, marked A, to be 1 foot broad, 1 foot 2 inches deep, and 20 feet long; there are eight bridging-joists, marked C, C, C, 8L0. whose scantlings are 3 inches by 6% inches, and ’30 feet long; that is of the same length with the girder; there are also eight binding-joists, whose lengths are 9 feet, and their scantlings 8s inches by 4 inches; the ceiling-joists are 24 in number, each 6' feet long, 4 inches by 2% inches; required the the solidity of the whole, either for materials or workmanship. l 2 l 1 2 area of the end of the girder. 6 6 3 __...__. [joist I 7 Garea of the end of a bridging— 8 number of bridging-joists 1 l 0 0 add] 2 —_ the area of the end of the girder. [mg-joists. 2 3' sum of the areas of the ends of the girder and bridg- 20 common length. Hoists. 45 feet the solidity of the girder and bridging— 8 6 depth. 4 thick. 2 I0 0 9 Q 1 6 solidity ofa binding-joist. 8 —l-7_feet, solidity of all the binding-joists. 2 6 4 10 0 area of the end of a ceiling—joist. 6 5 inches, solidity ofa ceiling-joist. ‘24 number of ceiling-joists. 10 feet, solidity of the ceiling-joists. 1? 45 72 feet, sum of all the solidities in the whole floor. PROBLEM IlI.—-—To measure roofing, or partitions, either jbr materials or workmanship. All timbers in a roof, or partition, are measured in MEN 357 the same manner as floors, excepting king-posts and queen-posts, 8m. when there is a necessity for cutting out parallel pieces of wood from their sides, in order that the ends of such braces as come against them may have, what is called by workmen, a square butment. To measure the work- manship of such pieces,or posts, take their breadth and depth, at the widest part, multiply them by the length, and the product will give the solidity for workmanship. To find the quantity of materials, if the pieces sawn out are 2% inches thick, or more, they are esteemed pieces of timber fit for use; when more than two feet long, their lengths should not be esteemed so long by 5 0r 6 inches, because the saw cannot enter the wood with much less waste, and consequently the pieces must be deducted from the whole solidity, and the remain- der will give the quantity ofmaterials; but if the pieces cut out be less than 2% inches, the whole post must be measured as solid for the materials, because the pieces cut out are of little use. Eramp/e.—-—I4‘igure'-.7. Let the tie-beam, I), be 36 feet long, 9 inches wide, by 1 foot 2 inches deep; the king-post, A, is [1 feet 6 inches high, 1 foot broad at the bottom, by 5 inches thick: out of this are sawn two pieces from the sides, 3 inches thick and 7 feet long; the braces, B, B, are 7 feet 6 inches long, 5 inches by 5 inches; the rafters, D, D, are 19 feet long, 10 inches by 5 inches each; the struts, C, C, are 3 feet 6 inches long, and 4 inches by 5 inches; required the measure- ment for workmanship, and also for materials. 12 9 106 3 31 6 solidity of the tie-beam. 5 5 2 l 15 lengths of the two braces added together. -._—_—_—- 2 7 3 __..._. 5 10 4 ‘2 3 2 8 4 12 6. —— 13 2 4 solidity of both rafters. MEN 1 5 5 I] 6 4 9 6 solidity of the king-post, as if solid. 3 5 l 3 7 8 9 solidity of the two pieces cut from the sides. 4 5 l 8 7 _ 11 8 solidity of the struts. Consequently, Feet. In. ” 31 6 0 tie beam. 2 7 3 braces. 13 2 4 rafters. 4 9 6 king-post. 11 8 solidity of the struts. 53 O 9 solidity of the roof for work- 8 9 manship. 52 4 0 solidity for materials. JOINERS' WORK. In boarded flooring, the dimensions must be taken to the very extreme parts, and from thence the squares are to be computed; out of which de- ductions are to be made for staircases, chimneys, Sic. VVeather-boarding is done by the yard square, and sometimes by the square, containing 100 super- ficial feet. Boarded partitions are measured by the square; out of which must be deducted the doors and windows, except they are agreed to be included. “’indows are generally made and valued by the foot superficial, and sometimes by the window. When they are measured. the dimensions must be taken in feet and inches, from the under side of the sill to the upper side of the top. rail, for the height; and for the breadth, from outside to out- side of the jambs; the product of these is the su- perficial content. For farther particulars, see the article JOINERY. MEN 358 22%.... 5 Example—How many feet does a piece of dwarf wainscoting contain, that is 18 feet 6 inches long, and 5 feet 3 inches high? By cross multiplication. By decimals. 18 6 185 5. 3 £125 __1_E 925 54 370 30 925 12 ) 85 97.125 7 l 90 97 l 6 PAINTERS’ WORK. This work is measured by the yard square, and the dimensions are taken in feet, inches, and tenths. In painters’ work, every part that is coloured is measured; consequently the dimensions must be taken with a line girt over the mouldings. Orna- mental work must be paid double measure; and if carved, at per value, according to the time. PLA STERERS’ WORK. This is done by the yard square, and the dimen- sions are taken in feet and inches. When a room consists of more than four quoins, the additional corners must be allowed at per foot run. In measuring ceilings with ribs, the superficies must first be taken for the plain work; then an allowance must be made for each mitre, and the ribs must be valued at so much per foot run, ac- cording to the girt, or by the foot superficial, al- lowing moulded work. In measuring ofcommon work,the principal things to be observed are as follow : 1. To make deductions for chimneys, windows, and doors. 2. To make deductions for rendering upon brick- work, for doors and windows. 3. If the workman find materials for rendering be- tween quarters, one-fifth must be deducted for quarters; but if workmanship only is found, the whole must be measured as whole work, because the workman could have performed the whole much sooner, if there had been no quarters. 4. All mouldings in plaster work are done by the . foot superficial, asjoiners do, by girting over the mouldings with a line. MEN GLAZIERS' WORK. Glaziers’ work is measured by the foot superficial, and the dimensions are taken in feet, tenths, hun-x dredths, 8tc. For this purpose their rules are ge-I nerally divided into decimal parts, and their dimen- sions squared according to decimals. Circular, or oval windows, are measured as if they were rectangular; because in cutting the squares of glass there is a very great waste, and more time is expended than if the windows had been of a : rectangular form. Example.—H ow many feet superficial of glazing 1 does a window contain, that is 7.25 high and 3.75 3 wide? 7.25 fi75 3625 5075 2175 27.1875 feet, the answer. “—— PLUMBERS' WORK. This is generally done by the pound, or hundred weight. Sheet lead, used in roofing, for guttering and val— leys, is in weightfrom 71b. to lle. per foot; and for ridges from 6 lb. to 8lb. The following table will shew the weight ofa foot, according to several thicknesses. The thickness is set in tenths and hundredths of an inch, in the first vertical column; and the weight opposite, in the same horizontal line, in the second vertical column on the right hand: - the integers shew the number of pounds avoirdu- poise, and the decimals the number of thousandth parts above the integer: so that the weight of a. square foot of 7'5, or % of an inch thick is 511). and 899 thousandth parts. Thickness. lb. to 11 sq. ft. .10 5.899 .11 6.489 1 == .11 &c. 6.554 .12 7.078 g. = .125 7.373 .13 7.663 .14 8.258 ;= .14 &c. 8.427 .15 8.848 .16 9.433 3‘. == .16 &c. 9.831 .17 10.028 .18 10.618 l' .19 11.207 1 % = .20 11.797 .21 19.387 MEN 359 MEN Example—What is the weight of a sheet of lead, 2.5 feet 6 inches long, and 3 feet 3 inches broad; at Silb. to the square foot? 3.25 25.5 i625 1625 650 82.875 86 ——-———- 4 143 75 663000 ___.-—— 704 4375 1b. as required. PAVIOURS' WORK. Paviours’ work is done by the square yard. Erample.-Suppose a pathway to be 45 feet 6 inches long, and the breadth 12 feet 3 inches; how many square yards does it contain ? 45.5 length. 162.25 breadth. 2575 9K) 910 455 9)557375 61.930 the number of yards required. The decimals will be reduced to feet by multiply- ing them by 9; thus, .930 9 8370 feet. It is not necessary to go any farther, as the value of the next denomination is not worth the trouble. SLATERS’ WORK. If the roof be equally hipped on all sides with a flat at top, and the plan of the building be rectan- gular, add the length and breadth of two adjoin- ing sides at the eves, and the length and breadth of two adjoining sides of the flat together; mul- tiply the sum by the breadth of the slope, and the product will give the area of the space that is covered. Add the number'of square feet produced by mul- tipl3’lng the girt of, the roofby the length of'a slate at theeavea, to, the area, for. the trouble of putting on the double row of slates; also add the number of square feet produced by multiplying the length of the hips by one foot in breadth, for the trouble of cutting the slates where they meet, to the said area; and the sum will be the whole contents, so as to make a compensation for the trouble and waste of materials. Example—Suppose a house 40 feet 6 inches in width, and 60 feetS inches in length; the breadth of the slope 15 feet 9 inches, the breadth of the flat 12 feet, and the length 31 feet 9‘inches. Feet. In. 40 6 60 3 12 O 31 9 144 6 15 9 u——.—_— 4 6 1 296 90 ——— 12)]390 115 10 720 144 2275 10 6 the area. To this area add the allowances for workmanship and waste. if there be no flat, add the two adjoining sides and twice the length of the ridge, for the length; multiply the sum by the breadth of the slope, for the area of the space covered ; then add theallow— ances as before. MENSURATION or TIMBER. In order, ifpossible, to set aside the present practice of measuring, which has no foundation in principle, and is con- sequently productive of erroneous answers, the following is extracted from Dr. Hutton's Mensa- ration; which completely exposes the fallacy of the method, and shews the rules by which the true contents may be found in a practical way, well calculated to expedite business. “ PROBLEM l.—Tojind the area or superficialfeet in a board or plan/c. “ RULE.—Multlply the length by the mean breadth. “ Notch—When the board is tapering, add the breadth at the two ends together, and take half the sum for the mean breadth. MEN 360 MEN - “ By the sliding rule—Set 12 on B to the breadth - in inches on B; then against the length in feet on B, is the content on A, in feet and fractional parts. “ Example 1.——What is the value of aplank, whose length is 12 feet 6 inches, and mean breadth 11 inches; at 1%d. per square foot? By decimals. By duodecimals. 12.5 12 6 i 1 l 11 12 137.5 1%d. is%- 11 5 6 lid is % 11.46 —— ls. 4%d. | Is. 5d. ans. 5 in. is O I- 2 1s. 5d. ans. “ By the sliding rule. “As 12B : 11A : : 1Q$B lléA. " That is, as 19 on B is to 11 on A, so is 12—:- on B to 11% on A. “ Example 2.——Required the content of a board, whose length is 11 feet 2 inches, and breadth 1 foot 10inches.—Answer, 20 feet, 5 inches, and 8 se- conds. “ Example 3.—VVhat is the value ofa plank, which is 12 feet 9 inches long, and 1 foot 3 inches broad, at 2éd. a foot.—-—Answer, 33. Bid. “ Example 4_—Required the value of five oaken planks, at 3d. per foot, each of them being 17% feet long; and their several breadths as follow, namely, two of 13% inches in the middle; one of 14,1, inches in the middle, and the two remain— ing ones, each 18 inches at the broader end, and 11% at the narrower.—-Answer, ll. 53. Sid. ‘,‘ PROBLEM IL—To find the solid content of squared, or four-sided timber. “ RULE.——-Multl|)ly the mean breadth by the mean thickness, and the product again by the length, and the last product will give the content. “ By the sliding rule. C D D C “As length : 12 or 10 : : quarter girt : solidity. “ That is, as the length in feet on C, is to 12 on D when the quarter girt is in inches, or to 10 on D when it is in tenths of feet; so is the quarter girt on D, to the content on C. “ Note 1.-——lf the tree taper regularly from the one end to the other, either take the mean breadth and thickness in the middle, or take the dimensions at the two ends, and then half their sum for the mean dimensions. ‘1: “ 2. If the piece do not taper regularly, but is unequally thick in some parts, and small in others, take several different dimensions, add them all together, and divide their sum by the number of them, for the mean dimensions. “ 3. The quarter-girt is a geometrical mean pro- portional between the mean breadth and thickness; that is, the square root of their product. Some- times unskill'ul measurers use the arithmetical mean instead of it, that is, half their sum; but this is always attended with error, and the more so as the breadth and depth differ the more from each other. “ Example 1.——The length of a piece of timber is . 18 feet 6 inches, the breadth at the greater and less end 1 foot 6 inches and 1 foot 3 inches, and the thickness at the greater and less end 1 foot 3 inches and 1 foot: required the solid content. g . Decimals. .’ Duodecimals. 1.5 I 6 1.25 l 3 t2)2.75 2)2 9 1.375 mean breadth 1 4- 6 1.25 l 3 1.0 l O (2)225 2)2 a 1.125 mean depth 1 1 6 1.375 mean breadth 1 4 6 56Q5 I 1 6 7875 6 3375 , 4 1125 6 1.546875 1 6 6 9 18.5 length 18 6 7734375 0 10 19.37.5000 7 1 6 1546875 9 3 4 286171875 content 28 7 410 ~— “ By the sliding rule. B A B A “ As 1 : 13% : : 16%.: : 29.3, the mean square. C D C D “ As 1 : 1 : : 99.3 : 14.9, quarter-girt. C D D C “As 18%: : 12 ' : 14.9 : 9.8.6, the content. “ Example 2.——VVhat is the content of the piece of timber, whose length is 24% feet, and the mean 0 MEN a breadth and thickness each 1.04 feetF—Answer, 26% feet. “ Example 3.-—-Required the content of a piece of timber, whose length is 20.38 feet, and its ends unequal squares, the side of the greater being 19;. inches, and the side of the less 9;. inches.— Answer, 29.7562 feet. “ Example 4.-——-Required the content of a piece of timber, whose length is 27.36 feet; at the greater end the breadth is 1.78, and thickness 1.23; and at the less end the breadth is 1.04, and thickness 0.91 i—Answer, 41.278 feet. “ PROBLEM Ill.—T0find the solidity qfround, or unsquared timber. “ RULE 1, or COMMON Rota—Multiply the square of the quarter—girt, or of one-fourth of the mean circumference, by the length, for the con- tent. “ By the sliding rule—As the length upon C : 12 or 10 upon I) : : quarter girt, in 12ths or 10ths, on D : content on C. “ Note l.——-\Vhen the tree is tapering, take the mean dimensions, as in the former Problems, either bygirting it in the middle for the mean girt, or at ’ the two ends, and take half the sum of the two. But when the tree is very irregular, divide it into several lengths, and find the content of each part separately. “ 2. This rule, which is commonly used, gives the answer about one-fourth less than the true quan- tity in the tree, or nearly what the quantity would be after the tree is hewed square in the usual way: so that it seems intended to make an allowance for the squaring of the tree. When the true quantity is desired, use the second rule given below. “Example 1.——A piece of round timber being 9 feet 6 inches long, and its mean quarter-girt 42 inches; what is the content? 61 Decimals. Duodecimals. 3.5 quarter girt 3 6 3.5 3 6 175 10 6 105 1 9 12.25 12 3 9.5 length 9 6 6125 1 10 3 11025 6 1 6 116.375 content 116 4 6 VOL. 11. MEN “ By the sliding rule. C- C D D As 9.5 10 35 116.} Or 9.5 12 42 116-1- “ Example 2.—The length of a tree is 24 feet, its girt at the thicker end 14 feet, and at the smaller end 2 feet; required the content.——Answer, 96 feet. » “ Example 3.-—-VVhat is the content of a tree, whose mean girt is 3.15 feet, and length 14 feet 6 inches E—Answer, 8.9922 feet. - “ Example 4.—Required the content of a tree, whose length is 17% feet, and which girts in five different places as follows, namely, in the first place 9.43 feet, in the second 7.92, in the third 6.15, in the fourth 4.74, and in the fifth 3.16.—Answer, 42.5195. . “ RULE 2.—Multiply the square of one-fifth of the mean girt by double the length, and the pro- duct will be the content, very near the truth. “ By the sliding Rule—As the double lengthvon C : 12 or 10 on D : : —§- of the girt, in 12ths or 10ths, on D : content on C. “ Example 1.——-VVhat is the content of a tree, its length being 9 feet 6 inches, and its mean girt 14 feet? Decimals. Duodecimals. 2.8 % of girt 2 9 7 2.8 2 9 7 224 _- 56 5 7 2 ____. 2 .1 3 7.84 l 8 . 19 7056 7 10 1 784 19 . 148.96 content 148 11 7 “ By the sliding rule. C D D C AS 19 10 28 149. Or 19 12 3376,. 149. “ Example 2.—Required the content of a tree, which is 24 feet long, and mean girt 8 feet.—-An. swer, 122.88 feet. ‘ ' “ Example 3.—The length of a tree is 14% feet, and mean girt 3.15 feet; what is the content P— Answer, 11.51 feet. “ Example 4.—-The length of a tree is 17%, feet, and its mean girt 6.28; what is the content?— Answer, 54.4065 feet. 3 A MEN 362 MEN‘ M s “ Example 5.—-Sold an oak tree, whose girt at the lower end was 9% feet, and its length, to the part where it becomes, of 2 feet girt, is 27% feet; it hath also two boughs, the girt at the thicker end of the one is 4.3, and at the thicker end of the other 3.94; the length of the timber of the former, that is, to the part where it becomes of only 2 feet girt, is 9 feet; and the length of the latter 7% feet; required the price at 21. 33. 9d. a load of 50 feet, allowing-Egof the mean girt for the bark of the trunk, and 715 of the same in the boughs, by both the rules.-——Answer, true value, 21. 188. 6d.; false value 21. 5s. 93d. " Note l.—-—That part of a tree, or of the branches, which is less than 2 feet in circumference, or 6 inches quarter-girt, is cut off; not being account- ed timber. “ 2. A custom has of late been creeping into use, where the buyers of timber can introduce it, of allowing an inch on every foot of quarter-gilt, for bark. This practice, however, is unreasonable, and ought to be discouraged. Elm timber is the chief kind in which an allowance ought to be made, and it will be found, on examination, that the common allowance of one inch on the tree, is abundantly sufficient for an average allowance. “ 3. Fifty cubic feet of timber make a load; and therefore, to reduce feet to loads, divide them by 50.” Example—How many loads‘of timber are there in 248 feet? 5,0 ) 24,8 448 ——-—_ So that this quantity contains four loads and 48 feet. It is customary, however, to make a difference between square and round timber, in many places. The load of round timber containing 50 cubic feet, while that of square timber contains only 40. This allowance is reasonable, on account of the waste. “ A TABLE, “ For readilyfinding the Content of Trees, according to the common ZlIet/tod of measuring Timber. “RULE.~——Seek the quarter-girt in the first column towards the left-hand, and take out the number opposite. Multiply that number by the length of the tree in feet, 8m. and the product will be the content in solid feet, Ste. In. Ft.1n.” ""1” In. Ft.In. " WW In. Ft.In.” "III” In. FLIn. ""1"” In. FtIu. "I" 'I" In- Ft.In. "'"II" 6 03000 10%09230 15 16900 19% 27830 24 40000 28%57830 a03309 %09769 fi17469g28609 7$41009 §581069 §03630 11 010100 §18030 20 29400 442030 29 510100 3.03969 4010 669 %18809 s210209 g43069 §511S69 7 04100 —;—011oso 16 19400 sen 030 25 44100 §60630 %04469 %011609 4110 009 %2111069 §45169 §61909 $048.30 12 10000 s 110830 2130900 §46230 30 63000 4105009 210609 %111469 {-31769 g47309 %64309 8 05400 41103017 20100 {—326.30 26 48400 §65630 £05809 %11669 420969 $33509 449509 7166969 %06030,13 12100 §21630 22 34400 g410 630 31 68100 %06469 412769 s22309%35309 g411769 §69469 9 06900 a 13230 18 23000 %36230 27150900 %610 830 %07169 $13909 2§23909 %37169 4511069 470009 %07630 14 14400 %24630 23 38100 s53030 32 71400 s071109 % 141109 $25369 %39069 s54209 3:72809 10 08400 a 15630 19 26100 4310 030 23,554.00 s74030 ~08909 %16169 {-261069; g311009 §56609 $75469 1m...“ -.. “ Sc HO L1UM.——In measuring squared timber, un- skilful measurers usually take one-fourth of the circumference, or girt, for the side of a mean square; which quarter-girt, therefore, multiplied by itself, and the product multiplied by the length, they account the solidity, or content: when the breadth and thickness are nearly equal, this me- thod will give the solidity pretty near the truth; but if the breadth and thickness differ consider- ably, the error will be so great, that it ought by no means to be neglected. “ Thus, suppose we take a balk, 24 feet long, and a foot square throughout; and consequently its solidity 24 cubic feet. Ifthis balk be slit exactly in two, from end to end, making each piece 6 inches broad, and 19. inches thick, the true soli- dity of each will be 12 feet; but, by the quarter- girt method, they would amount to much more; MEN 363 MEN M III—— for the false quarter—girt, being equal to half the sum of the breadth and thickness, in this case will be 9 inches, the square of which is 81, which being divided by 144, and the quotient multiplied by 24-, the length, we obtain 13% feet for the soli— dity of each part; and consequently the two soli- dities together make 27 feet, instead of 24. “ Again, suppose the balk to be so cut, that the breadth of one piece may be 4 inches, and that of the other 8 inches. Here the true content of the less piece will be 8 feet, and that of the greater 16 feet. But, proceeding by the other method, the quarter-girt of the less piece will be 8, whose square, 64, multiplied by 24, and the product di- vided by 144, gives 10%. feet, instead of 8. And by the same method, the content of the greater piece will be 16"3 feet, instead of [6. And the sum of both is 27.} feet, instead of 24 feet. “ Farther, if the less piece be out only 2 inches broad, and the greater 10 inches; the true con- tent of the less piece would be 4 feet, and that of the greater 20. But, by the other method, the quarter-girt of the less piece would be 7 inches, whose square, 49, being divided by six, gives 8% feet, instead of 4, for the content. And, by the same method, the content of the greater piece would be 20%, instead of 20 feet. So that their sum would be 28.}, instead of 24 feet. “ Hence it is evident, that the greater the propor- tion between the breadth and depth, the greater will the error be, by using the false method; that the sum of the two parts, by the same method is greater, as the difference of the same two parts is greater, and consequently the sum is least when the two parts are equal to each other, or when the balk is cut equally in two; and lastly, that when the sides of a balk differ not above an inch or two from each other, the quarter-girt method may then be used, without inducing an error that Will be of any material consequence. “ PROBLEM lV.——To find zehere a piece ofround tapering timber must be cut, so that the two parts, measured separately, according to the common me- thod of measuring, shall prod-ace a- greater solidity than when cut in any other part, and greater than the whole. “ Rena—Cut it through exactly in the middle, or at half of the length, and the two parts will measure to the most possible, by the common method. “’ Erample.-Supposing a tree to girt 14 feet at the greater end, 2 feet at the less, and conse- quently 8 feet in the middle; and that the length is 32 feet. “ Then, by the common method, the whole tree measures to only 128 feet; but, when cut through at the middle, the greater part measures to 121, and the less part to 25 feet; whose sum is 146 feet; which exceeds the whole by 18 feet, and is the most that it can be made to measure to by cutting it into two parts. . “ DEMoNSTRATION.—Put G = the greatest girt, g = the least, and x =.- the girt at the section; also L = the whole length, and z =-—- the length to be cut off the less end. “ Then, by similar figures, L : z: : G—g : x—g. GzL gz+g. But (g + x)‘. z + (G + a)? (L —— z) = a maximum ; whose fluxion being put equal to nothing, and the value of a: substituted instead of it, there results z= %L. Q.E.D. ' “ COROLLARY.—By thus bisecting the length of a tree, and then each of the parts, and so on, con- tinually bisecting the lengths of the several parts, the measure of the whole (will be continually in~ creased. “ PROBLEM V.—-To find where a tree should be cut, so that the part next the greater end may mea~ sure to the most possible. “ RULE.—-—-From the greater girt take 3 times the less; then, as the difference of the girts is to the remainder, so is one-third of the whole length,‘to to the length from the less end to be cut off. “ Or, cut it where the girt is one-third of the greatest girt. “ Note—If the greatest girt do not exceed three Hence I = ' times the least, the tree cannot be cut as is re- quired by this problem. For, when the least girt is exactly equal to one—third of the greater, the tree already measures to the greatest possible; that is, none can be cut ofl’, nor indeed added to it, continuing the same taper, that the remainder or sum may measure to so much as the whole: and when the least girt exceeds one-third of the greater, the result by the rule shews how much in length must be added, that the result may measure to the most possible. “Example—Taking here the same example as be- fore, we shall have, as 12 z 8 : : 3’3-2- : 7% = the length to be cut off; and consequently the length of the remaining part is 24%; also 1; = 4% is the 3 A 2 MEN 364 am - L - -' girt at the section. Hence the content of the re- maining part is 135% feet; whereas the whole tree, by the same method, measures only to 198 feet. “ DEMONSTRATION.—Using the same notation as in the last Zdemonstration; we have here also Gz— . x: L0 ~ maximum; which, treated as before, gives 2 = M+g,and(G+x)2. (L— :c)==a G—3g 1 . __G— g WXTL' Andau— L z+g% G, by substituting the above value of z. Q. E. D. “ PROBLEM VI.—-To cuta tree so as that the part next the greater end may measure, by the common method, to exactly the same quantity as the whole measures to. RULE.—-Call the sum of the girts of the two ends 5, and their difference d, then multiply by the sum of d and 4 8, thus: d x (d + 4 s). From the 1oot of the product take the difl'e1ence between (I and 23, thus: 1/(d2 + 4ds)-—-— 28 + d. Then as two times d, are to the remainder, so is the whole length to the length to be cut off; Thus calling the whole length L, and the part to be cut off I, we have: 2d:¢(d2+4ds)—Qs+d :: L: Z= @151 x(¢(d2+4ds)——2s+d). Example—Using still the same numbers as in the preceding examples, we have, s = 16, d = 1%, and L = 32. 1:513 x (¢(d‘ + 4ds) ——2s + d): 32 2x12 4 x(¢(144+768)—20)§ xm122+4x12 x16)—2x16+12) =5 x < «912) —- 20) =§x<30.1993377 —— 20) = L 4 5 X 10.199337 =13 .5991198 the length to be cut off. M EN Therefore the length of the remaining part is 32 -- 13.5991168 = 184008832. And ifs be taken from the root, viz. M (d’r’+4ds) half the remainder will be the girt of the section. ' Therefore, according to the numbels given the girt 1/( d"+4ds)—s $301993377—lti 2 2 of the section := 7.0996688. Hence the girtin the middle of the greater partis 14 + 7.099669 2 part is 2637458; and consequently the content of the same part is 2.6574582 x 18.40083 :2 128, the very same as the whole tree measures to, not- withstanding above one-third part is cut off the true length. “ Note.—-The principles of these last three Prom blems are also applicable to the new, orsecond rule, in page 361, and indeed to any other ap- proximate rule, or such as is not founded on the rule for the frustum of a cone. “ DEMONSTRATION.—-Using still the same nota- tion, we shall have 52 L==(L — 2) X (G + x)”; hence, instead of .1‘, substituting its value %+g, we obtains: 2%, x (M ((48 + d) d) —— 23 + d). “And hencex: 51—, ~/ ((4s+d).d)— % s. Q. E.D.” Rules have already been given for measuring the areas of circular segments, which may at least be depended upon to three places of figures, and which we have thought sufficiently correct for most practical purposes; but where greater accuracy is required, the following Table will carry the approximation to five or six figures. The construction which comes after the Table depends upon the following series for the segment of a circle. = 10.549834, whose one-fourth The area of the segment isA +—— An —%3V2 3C1) 5Dv 7131) n . 4v _. 9V -— 11V jsvvyctc.yvl1eleA:-§-‘/vV, B the second, C the third, 81.0. See also Rules 3 and 4, Theorem XI. pages 335 and 336, which are the same in principle as this, . 2de W MEN 365 L A TABLE OF THE AREAS OF THE SE'GMENTS OF A CIRCLE, MEN \Vhose Diametel is Unity, and supposed to be divided into 1000 equal Parts. 'fleight. AreaSeg. Height. AreaSeg Height. Area Seg. Height. ArraSeg ![I8ight. Area Seg. Height. Area Seg. He1ght. AfeaSeg. Height. AreaSeg. '.001 .000042 .064 .021168 .127 .057991 .190 .103900 .253 .156149 .315 .212011 .377 .270951 .439 .331850 ‘ .002 .000119 .065 .021659 .128 .058658 .191 .104685 .254 .157019 .316 .212940 .378 .271920 .440 .332843 .003 .000919 .056 .022154 .129 .059327 .192 .105472 .255 .157890 .317 .213871 .379 .272890 .441 .333836 .004 .000337 .067 .022652 .130 .059999 .193 .106261 .256 .158762 .318 .214802 .380 .273816 .442 .334829 .005 .000470 .068 .023154 -131 .060672 .194 .107051 .257 .159636 .319 .215733 .381 .274832 .443 .335822 .006 .000618 ' .069 .023659 .132 .061348 .195 .107842 .258 .160510 .320 .216666 .382 .275803 .444 .336816 .007 .000779 .070 .024168 .13“ .062026 .196 .108636 .259 .161386 .321 .217599 .383 .276775 .445 .337310 .008 .000951 .071 .024680 .134 .062707 .197 .109430 .200 .162263 .322 .218533 .384 .277748 .446 .338804 .009 .001135 .072 .025195 .135 .060389 .198 .110226 .261 .163140 .323 .219468 .385 .278721 .447 .339798 .010 .001329 .073 .025714 .136 .064074 .199 .111024 .262 .164019 .324 .220404 386 .279694 .448 .340793 .011 .001533 .074 .026236 .137 .064760 .200 .111823 .263 .164899 .325 .221340 .387 .280668 .449 .341787 .012 .001746 .075 .026761 .138 .065449 .201 .112624 .264 .165780 .326 .222277 .388 .281642 .450 .342782 .013 .001953 .076 .027289 .139 .066149 .202 .113426 .265 .166663 .327 .223215 .389 .282617 451 .343777 .014 .002199 .077 .027821 .140 .06683‘ -203 .114230 .266 .167546 .328 .224154 390 .283592 .452 .344772 .015 .002430 .073 .028356 .141 -067528 .204 .115035 .267 .168430 .329 .225093 391 .284568 .453 .345768 .016 00263;, .079 .028894 .142 .068225 .205 .115842 .268 .169315 .330 .226033 .392 .285544 .454 .346764 .017 .002940 .030 .029435 .143 .068924 .206 .116650 .269 .170902 .531 .226974 .393 _.286521 .455 .347759 .018 .003202 .081 .029979 .144 .069625 .207 .117460 .270 .171089 .332 - .227915 .394 .287498 456 .348755 .019 .003471 4132 .030526 .145 .070328 .208 .118271 .271 .171978 .333 .228858 .395 .288476 .457 .349752 .020 .003743 .083 .031076 .146 .071033 .209 .119083 .272 .172867 .334 .229801 .396 .289453 .458 .350748 .021 .004031 .034 031629 .147 .071741 .210 .119897 .273 .173758 .335 .230745 .397 .290432 .459 .351745 .022 004322 .035 .032186 .148 .072450 .211 .120712 .274 .174649 .336 .231689 .398 .291411 .460 .352741 .023 .001613 .035 .032745 .149 .073161 .212 .121529 . .275 .175542 .337 .232684 .399 .292390 .461 .353789 .094 .004921 .037 033307 .150 .073874 .213 .122347 .276 .176435 .33 233580 .400 .293396 .462 .354736 .0254005230 .038 .033872 .151 .074589 .214 .123167 .277 .177330 .339 .234526 .401 .294349 .463 .355732 .026 .005546 .039 .034441 .152 .075306 .215 .123988 .278 .178225 .340 .235473 .402 295330 .464 .356730 .027 .005867 .090 .035011 .153 .076026 .216 .124810 .279 .179122 .341 .236421 .403 .296311 .465 .357727 .028 .006194 .091 -035585 .154 .076740 .217 .125634 .230 .180019 .342 .237369 .404 .297292 .466 .358725 .099 .005527 .092 .036162 .155 .077469 .218 .126459 .281 .180918 .343 .238318 .405 .298273 .467 359723 .030 .006865 .093 .036741 .156 .078194 .219 .127285 .282 .181817 .344 .239268 .406 .299255 .468 .360721 .031 .007209 .094 .037323 .157 .078921 .220 .128113 .283 .182718 .345 .240218 .407 .300238 .469 .361719 .032 .007558 .095 .037909 .158 .079649 .221 .128942 .284 .183619 .346 ‘.Q41169 .408 .301220 .470 .362717 .033 .007913 {.096 .038496 .159 .080380 .222 .129773 .285 .184521 .347 .242121 .409 .302203 .471 .363715 .034 008273 5.097 .039087 .160 .081112 .223 .130605 .286 .185425 .348 .243074 .410 .303187 .472 .364713 .035 .008633 :_098 .039680 .161 .081846 .224 .131438 .287 .186329 .349 .244026 411 .304171 -473 .365712 .036 .009008 .099 .040276 .162 .082582 .225 .132272 .288 .187234 .350 .244980 -412 .305155 .474 .366710 .037 .009383 .100 .040875 .163 .083320 .226 .133108 .289 .188140 .351 .245934 .413 .306140 .475 .367709 .038 .009763 .101 .041476 .164 .084059 .227 .133945 .290 .189047 .352 .246889 .414 .307125 .476 .368708 .039 .010148 .102 042080 .165 .084801 .228 .134784 .291 .189955 .353 .247845 .415 .308110 .477 .369707 .040 .010537 .103 .042687 .166 .085544 .929 .135624 .292 .190864 .354 .248801 416 .309095 .478 .370706 .041 .010931 .104 .043296 .167 .086289 .230 1136465 .293 .191775 .355 .249757 417 .310081 .479 .371705 - .042 .011330 .105 .043908 .168 .087036 .231 .137307 .294 .192684 .356 252.715 .418 .311068 .480 .372704 .043 .011734 .106 .044522 .169 .087785 .232 .138150 .295 .193596 .357 .251673 419 312054 .481 .373705 .044 012142 .107 .045139 .170 .088535 .233 -138995 .296 .194509 .358 .252631 .420 .313041 .482 .374709 .045 .012554 .103 .045789 .171 .089287 .234 .139841 .297 .-19542.- .359 .258590 .421 .311029 .483 .375702 .046 .012971 .109 -046381 .172 .090041 .235 .140688 .298 .196337 .360 .254550 .422 .315016 .484 .376702 .047 .013392 .110 .047005 .173 .090797 .236 .141537 .299 .197252 .361 .255510 .423 .316004 .485 .377701 .048 013313 .111 .047632 .174 .091554 .237 .142387 .300 .198168 .362 .256471 .424 .316992 .486 .378701 .049 .014247 .112 .048262 .175 .092313 .238 .143238 .301 .199085 .363 .257433 .425 .317981 .487 .379700 .050 .014681 .113 -048894 .176 .093074 .239 .144091 .302 .200003 .364.- .258395 .426 .318970 .488 .380700 .051 .015119 .114 .049528 .177 .093836 .240 .144944 .303 .200922 .365 .259357 .427 .319959 .489 .381699 .052 .015561 .115 -050165 .178 .094601 .241 .145799 .304 .201841 .366 .260320 .428 .320948 .490 .382699 .053 .016007 .116 .050804 .179 .095366 .242 .146655 .305 .202761 .367 .261284 .429 .321938 .491 .383699 .054 .016457 .117 .051046 .180 .096134 .243 .147512 .306 .203863 .368 .262248 .430 .322928 .492 .384699 .055 .016911 .118 .052090 .181 .096903 .244 148371 .307 .204605 .369 .263213 .431 .323918 .493 .38569 .056 .017369 .119 .052736 .182 .096674 .245 .149230 .308 .205.527 .370 .264178 .432 .324909 .494 .386699 .057 .017831 .120 .053380 .183 .098447 .246 .150091 .309 .206451 .371 .265144 .433 .325900 .495 .387699 .058 .018296 .121 .054036 .184 .099221 .247 .150953 .310 .207376 .372 .266111 .434 .326892 .496 .388699 .059 .018766 .122 .054689 .185 .099997 .248 .151816 .311 .208301 .373 .267078 .435 .327882 .497 .389699 .060 .019239 .123 .055345 .186 .100774 .249 .152680 .312 .209227 .374 .268048 .436 .328874 .498 .390699 .061 .019716 .124 .056003 .187 .101553 .250 .153546 .313 .210154 .375 .269013 .437 .329866 .499 .391699 .062 .020196 .125 .056663 .188 .102334 .251 .154412 .314 211082 .376 .269982 .438 .330858 .500 .392699 .063 .020680 .126 .057326 .189 ..103116 .252 .155280 MEN r 366 MER Tofind the area of the segment of a circle by the preceding Table. Divide the height of the segment by the diameter of the circle, so that the quotient may contain three places of decimals; look for the correspond- ing number to the quotient in the column height, then take out the number in the same horizontal row in the vertical column intitled Area Seg. at the top, multiply the square of the diameter by the number thus taken out, and the product will be the area of the segment. Example—Required the area of the segment of a circle, the height of which is two, and the diameter of the circle .52. 52 ) 2.000( .038 156 440 416 —_ 24 There remains 24, which is as = 755. The area of the segment corresponding to .038, is .009763, but since there is a fraction over and above .038 of {-5, find the next greater area .010148; take the difference between these two areas, which is .000385, multiply this difference by the fraction 76?, and it gives .000177, which being added to .009763, gives .009940 for the area of the segment, answering to .038 {7. TheTable is founded upon the following principle: Let the diameter of a circle be 1, which suppose divided into 1000 equal parts, through every one of which imagine perpendiculars drawn and con- tinued both ways to the circumference. Then, since the versed sine is .00], we have r) .001 l v = .001 and - = —— = +-' therefore A = V 999 999’ 4” V—— 4' t/ 000 ——00004214 dB 3 V” "3000 ' 999" ’a“ A 1) .00004215 =~—-—=~—-——-——-=.O 00 01 ’h ill fi‘t, 5V 999 x5 00 O ,u ence 1e rs number of the table is .00004215. The second versed sine is .002 = 72, therefore V ‘2. l 8 = .998 and %= = ——, whence A = 998 199 3000 ——-——- A ,/ .001996 = .00011914, and B = 3'7” = 900119.13 ;_- ,00000005; therefore the second 499 x 5 number is .00011919. fl The third versed sine is .003 = *0, therefore V 3 = 1 —-- .003 = .997, whence {if = 9—973 and A = ~11¢000291- r -l B L” 3000 9 — .0002l876. aso =5V= .000218 6 “ M5 X799; 0 = .00000013; thence the third number of the Table is .00021889. And by this method the whole might be com- puted ; but after a sufficient number of terms are found at the beginning of the table, the rest may be had (to seven or eight places of decimals) by this rule: let a, B, 7, 3, denote any four terms suc- ceeding in the order of the letters, then 3‘ = a + 3 X 7 -— B. And if any term of this Table be divided by 78539816, or multiplied by its reciprocal, it will produce the common table of segments, when the area IS unlty. MERIDIAN, in astronomy, 3 great circle of the sphere, passing through the zenith, nadir, and poles of the world, crossing the equinoctial at right angles, and dividing the sphere into two hemispheres, the one eastern, and the other western. It is called meridian, from the Latin mer‘idies, noon, or mid-day, because when the sun is in this circle, it is noon in all places situated under it. MERIDIAN, in geography, a great circle, as PAQD, Figure l, passing through the poles of the earth P and Q, and any given place at Z. So that the plane of the terrestrial meridian is in the plane of . the celestial one. Hence, 1. As the meridian invests the whole earth, there are several places situated under the same meridian. And, 2. As it is noon-tide whenever the centre of the sun is in the meridian of the heavens; and as the meridian of the earth is in the plane of the former, it follows, that it is noon at the same time, in all places situate under the same meridian. 3. There are as many meridians on the earth as there are points conceived in the equator. In effect, the meridians always change, as the longitude of the place is varied; and may be said to be infinite; each respective place, from east to west, having its respective meridian. MERIDIAN, First, is that from which the rest are accounted, reckoning from west to east. The first meridian is the beginning of longitude. The fixing of the first meridian is a merely MER 367 MET W..- arbitrary; and hence different persons, nations, and ages, have fixed it differently; whence some confusion has arisen in geography. The rule among the ancients was, to make it pass through the place farthest to the west that was known. But the moderns, knowing that there is no such place in the earth as can be esteemed the most westerly, the way of computing the longitudes of places from one fixed point is much laid aside. But, without much regard to any of these rules, our geographers and map—makers frequently as- sume the meridian of the place where they live, or the capital of their country, for a first meri- dian; and thence reckon the longitudes of their places. The astronomers, in their calculations, usually choose the meridian of the place where their ob- servations are made, for their first meridian; as Ptolemy, at Alexandria; Tycho Brahe, at Urani- bourg; Riccioli, at Bologna; Mr. Flamsteed, at the Royal Observatory at Greenwich; and the French, at the Observatory at Paris. MERIDIAN LINE, an are, or part of the meridian of the place, terminated each way by the horizon. Or, a meridian line is the intersection of the plane of the meridian of the place with the plane of the horizon, vulgarly called a north and south line, because its direction is from one pole towards the other. The use of a meridian line in astronomy, geogra- phy, dialling, Ste. is very great, and on its ex- actness all depends; whence infinite pains have been taken by divers astronomers to fix it with the utmost precision. M. Cassini has distinguished himself by a meridian line drawn on the pavement of the church of S. Petronio, at Bologna, the largest and most accurate in the world; being 120 feet in length. In the roof of this church, a thou- sand inches above the pavement, is a little hole, through which the sun’s rays, when in the meri- dian, falling upon the line, mark his progress all the year. When finished, M. Cassini, by a pub- lic writing, informed the mathematicians of Eu- rope of a new oracle of Apollo, or the sun, esta- blished in a temple, which might be consulted, with entire confidence, as to all difliculties in as- tronomy. To draw a meridian line. On the horizontal plane, from the same centre, C, Figure 2, draw several arcs of circles, B A, b a, Ste. and on the same centre, C, erect a style, or gnomon, perpendicular to the plane A C B, a foot, or halfa foot long. About the gist ofJune, between the hours of nine and eleven in the morn- ing, and between one and three in the afternoon, observe the points B, b, &c. A, or, wherein the shadow of the style terminates. Bisect the arcs A B, a b, Ste. in D, d, &c. If then the same right line, D E, bisect all the arcs, AB, a b, Sac. it will be the meridian line sought. As it is difficult to determine the extremity of the shadow exactly, it is best to have the style flat at top, and to drill a little hole, noting the lucid spot projected by it on the ares A B and a b, in- stead of the extremity of the shadow. Otherwise the circles may be made with yellow, instead of black, See. If the meridian line be bisected by a right line, 0 V, drawn perpendicularly through the point C, O V will be the intersection of the meridian, and first vertical; and, consequently, 0 will shew the east point, and V the west. Lastly, Ifa style be erectedperpendicularly in any other horizontal plane, and a signal be given when the shadow of the style covers the meridian line drawn in another plane, noting the apex, or ex- tremity, of the shadow projected by the style, a line drawn from that point through that wherein the style is raised, will be a meridian line. MERIDIAN LINE, on a dial, is a right line arising from the intersection of the meridian of the place with the plane of the dial. This is the line of twelve o’clock, and from hence the division of the hour-line begins. MEROS (Greek) the middle part of the triglyph. The breadth of the triglyph is divided into six parts; of which five are placed in the middle, two and a half being on either side. The middle one makes the regula or femur, which the Greeks call meros. On either side this are the channels, sunk as if imprinted with the elbow of a square. To the right and left of these another femur is formed, and at the extremities semi-channels are slanted. MESAULZE, in Grecian architecture, passages be- tween the peristylium and hospitalium; the same as the audionas of the Romans. See HOUSE, p. 95. METAGENAS, a Grecian architect, who wrote a description of the temple of Diana at Ephesus; he also jointly conducted this edifice with his father Ctesiphontes, the Gnossian. MET 3’68 MET —-' ti METALS, see MATERIALS. METEZAU, CLEMENT, a celebrated French ar- chitect, who flourished in the former part of the seventeenth century, was a native of Dreux, but settled at Paris, became architect to Louis XIII. and acquired much fame by carrying into execu- tion, with Tiriot, a Parisian mason, the plan suggested by Cardinal Richelieu, for reducing Rochelle, by means of an immense dyke, in imi— tation of what Caesar had done at Durazzo, and Alexander the Great at Tyre. This scheme was to run a solid wall across a gulf upwards of 740 fathoms, or more than three-quarters of a mile broad, into which the sea rolled with great force, and, when the wind was high, with an impetuosity which seemed to set at defiance the art of man. Those who had undertaken the business were not to be turned aside by any obstacles: they began by throwing in huge rocks, to lay a kind of foun- dation; upon these were placed vast stones, ce- mented by the mud thrown up by the sea. These were supported by immense beams, driven into the bottom with incredible labour. It was raised so high, that the soldiers were not incommoded by the water, even at spring tides. The platform was nearly 30 feet wide, and 90 feet at the foun- dation. At each extremity there was a strong fort, in the middle there was an open passage of 150 paces, several vessels being sunk immediately before it, together with high stakes in a double row, and before these thirty-five vessels linked to- gether, so as to form a kind of floating palisade. This amazing dyke was completed in somewhat less than six months, and proved the principal means of occasioning the surrender.of the city. So honourable were the exertions of M. Metezau in this business, that his portrait was circulated widely through France, to which were attached the following lines: "Dicitur Archimedes Terrain potuisse movere: ZEquora qui potuit sistere, non minor est.” METOCHE (from the Greek ,ue'roxs) in ancient ar- chitecture, a term used by Vitruvius, to signify the space or interval between the dentils of the Ionic, or triglyphs of the Doric orders. Baldus observes, that, in an ancient MS. copy of that author, the word metatome is found for me— toche. Hence Daviler takes occasion to suspect, that the common text of Vitruvius is corrupted, and concludes that it should not be metoclze, but metatome, q. d. section. ~3- ~ 4 ‘METOPE, or METo PA, (from p.306, inter, between, and am), an aperture) in architecture, the square piece or interval between the triglyphs, in the Doric frieze. In the original Greek,the word sig- nifies the distance between one aperture, or hole, and another, or between one triglyph and another; the triglyphs being supposed to be solives, or joists, that fill the apertures. Vitruvius having shewn that the Doric order took its rise from the disposition of the timberwork in the construction of the original hut, proceeds as follows: “ From this imitation, therefore, arose the use of triglyphs and mutules in Doric work: for it can- not be, as some erroneously assert, that the tri- glyphs represent windows; because triglyphs are disposed in the angles, and over the quarters of the columns, in which places windows are not permitted; for if windows were there left, the union of the angles of buildings would be dis- solved; also, if the triglyphs are supposed to be situated in the place ofthe windows, by the same reason, the dentils in Ionic work may be thought to occupy the places of the windows; for the in- tervals between the dentils, as well as between the triglyphs, are called metopes; the Greeks call- ing the bed of the joists and assers opus, (as we call it cava, columbaria); so because the inter- joist is between two opae, it is by them called met—019w.” As some difficulty arises in disposing the triglyphs and metopes in that just symmetry which the Doric order requires, many architects use this order only in temples. In the Doric order, it is not the space between the mutules, but the space between the triglyphs, that forms the metope. From the authority of Stewart, in his Ruins of Athens, the following proportions are taken; where observe, that feet are distinguished by the mark (') being placed over them, and inches thus (”); the numbers following the latter are de- cimals. In the Doric portico at Athens, the breadth of the metope, or space between the trighphs, is 3' 3” and 3 ‘3”.,6 (see Chap. 1. Plate IV. ); the height is 3 0" .7, including the band, or capital over it (see Plate V.); or without the band, 2’ 9”.O5 (see Plate VI.) In the temple of Minerva, at Athens, (Vol. II. Chap. I.) the height of the metope, without its MIL 369 MIL W - capital, or band, is 3 11".15 (see Plate VI. ); and the breadth of the metope is 4 3". 3.5 - In the Propylma, (Vol II. Chap. V. PlateVI.) the breadth of the metope is 3’ 8’25, and the height 3’ 9”.85, including the band and the bead over . it; and in the entablature of the ante (Plate IX.) the breadth of the metope is 2' 8".734, and the - height 2' 5", without the band. In the temple of Theseus, (Vol. III. Chap. I. Plate VI.) the breadth of the metope is 2' 6".475, and its height 2' 8".55, including a very broad hand. So that the height of the tytnpan, or panel, is universally less than the breadth. MEZAININE, or MEZZAMNE, a word borrowed from the Italians, who call mezzanini those little windows, less in height than breadth, which serve to illuminate an attic, or entresole. It is used by some architects, to signify an intermediate apart— mcnt, frequently introduced into the principal story when all the rooms are not required to be of the same height ; so that where mezanines are in. trodnced, the principal story is divided into two heights, in order to make store-rooms, or lodging- I'OUIIIS for servants. See APARTMENT- MEZZU-ItELIEVU, a piece of sculpture in half relief MICKLEHAM CHURCH, a very ancient build- ing, and rather remarkable in its architecture. It is built of stone, and consists of a have, with a chancel at the east end, a small chapel on the - north side, and a south aisle, separated from the nave by round pillars supporting semicircular arches. The cast window is adorned with hand- some tracery works, and on each side of the chan- cel are two windows, with lancet-shaped tops, within a round-headed arch, which rests upon round pillars, and is ornamented with a single row of square billet-work. At the, west end rises a low square tower, strengthened by double an- gular buttresses, and surtnounted by a pyramidal spire. The font is of solid stone, the bason hav- . ing been hollowed out from it. MIDDLE-QUARIERS OF COLUMNS. When the plan or horizontal section of a column 15 di- vided into four quadrants, bylines not at right angles to the front, but at an angle of 45 degrees therewith, the four quarters are called the middle quarters. MIDDLE~POST, in a roof, the same as KING- I’osr; which see. . MILEtt’rotn the Latin mille, a thousand) a long VOL. 11. measure, whereby the English, Italians, and some other nations, express the distance between places. See MEASURE. ' ‘In this sense mile is used to the same purpose with league, by the French and othet nations. The mile 1s of various extent in different coun- ‘tries. The geographical, 01 Italian mile, contains a thousand geometrical paCes, mille passus, whence the term mile 15 delivcd. The English mile consists of eight furlongs, each futlong of 40 poles, and each pole of 16 fifeet: ‘so that it is equal to 1760 yatds,’ or 5980 feet. The mile employ ed by the Romans 1: 1 Great Bri- tain, and 1est01€d by llemv VII is our present English mile. A degree of the meridian in Eng- land, north latitude 52, according to the measure- ment of Colonel Mudge, is 121,640 yards, or 69.114 miles. A geographical, or sea-mile, is the 60th part of such a degree, 2'. e. ‘2 )‘27% yards; and three sea-miles make a league. A degree of the meridian, in north latitude 45, as measured in France in 1796, is 57,008 tuises= 121,512 yards = 69.099. English miles. Casimir has madeacurious reduction of the miles, or leagues, of the several countries in Europe into Roman feet, which ate equal to the Rhinland feet, generally used throughout the Notth. Feet. The mile of Italy . . . . . . . 50,000 of England . . . . . . . 5,454 of Scotland . . . . . . . 6,000 of Sweden . . . . . . . 30,000 of Muscovy . . . . . . . 3,750 of Lithuania . . . . . . 18,500 of Poland . . . . . . . 19,850 .of Germany, the small . . . 20,000 the middle . . 29,500 the largest . . 25,000 of France . . . . . . . 15,750 of Spain . . . . . . . . 21,970 of Burgundy . . . . . . 18,000 of Flanders . . . . . . 20,000 of Holland . . . . . 24,000 of Persia, called also parasanga 18,750 of Egypt, called also schwnos . 25 000 A Table of the length if lees, Leagues, :30. ancient and modem, 2n Englzsh yards. .Ancient Roman mile . . . . . . 1610.348 Olympic stadium = §~th of an ancient ‘ Roman mile . . . . . . .- . 201.9935 Stadium = {3th of an ancient Roman mile . . . . . . . . . . . 161.0343 SB MIT 3'70 MOD I . Eng. Yards. Stadium .== 1100111 part ofa degree . 111.2 from 15 inches square to 2 feet, squared and hewed ready for building. Jewish risin, ofwhich 715—.an ancient MITRE, or M‘TRA (from. Mnea, a head-dress) a Roman mile . . . . . . . . 214.713 Gallic leuca=== 1% ancient Roman mile 2415.522 German rast, or common league in France = 2 Gallic leuca . . . . 4831.044 Persian parasanga = 2 Gallic leagues 4831.044 Egyptian schoenos == 4ancient Roman V miles . . . . . . . . . . 6.441.392 German league, or that of Scandina- via—— - 2,1 1asts 2 . . . . . . . 9662.088 The mile, 01 league of Germany 2 200 Rhenish yards . . . . . . . 8239.846 Great Arabian mile, used in Palestine in the time of the Crusades, rated at 15 ancient Roman mile =' . . . . 2415.713 Vlodein Roman mile . . . . . . 1628.466 Modem Greek mile of7 Olympic stadia 1.409.0545 pontifical ornament, worn on the head by bishops, and certain abbots, on solemn occasions. The mitre isaround cap, pointed, and cleft at top, with pendants hanging down on the shoulders, and fringed at both ends. The bishOp’s is only surrounded with a fillet of gold, set with precious stones; the archbishop’s issues out of a ducal co- ronet. These are never used otherwise than on their coats .of arms. Abbots wear the mitre turned in profile, and bear the crosier inwards, to shew that they have no spiritual jurisdiction without their own Cloisters. The pope has also granted to some canons of cathedrals the privilege of wearing the mitre. The Counts of Lyons are also said to have assisted at church in mitres. Modern French league = 2500 toises 5328'75 MITRE, in joinery: when two pieces of wood con- 'Mile of Turkey, and the common werst of Russia, supposing it seven Olympic stadia . . . . . . . 1409.0545 League of Spain = 4 ancient Roman miles . . . . . . . . . . 6441.392 Large league of Spain = 5 ditto . . 8051.74 MILITARY ARCHITECTURE, denotes the art of fortification. , See ARCHITECTURE. MILK HOUSE, or BOOM, an apartment for keeping milk sweet and good; this apartment ought to be as cool as possible, and on no ac- count exposed -to- the rays of the sun; conse- quently a. northern situation, when it can be obtained, will be the most eligible for this pur- pose. See DAIRY. MINARATE, or MINNERET, a Turkish steeple with a balcony, from which a peison calls the people to prayers; no bells being permitted in Turkey. MINION, an iron ore, useful in the composition of mortar when mixed with a proper quantity of lime, it makes an excellent water cement. See. CEMENT and MORTAR. MINOTAUR, m MINOTAURUS, a fabulous mon— ster much talked of by thepoets; feigned to be half a man and half a bull. MINUTE (from the Latin minutus, small) in archi- tecture, usually denotes the sixtieth, but some- times only the thirtieth, part or-division of a module. Ml'l‘CliELS, among builders, are Purbeck stones, tain equal angles, and one side of the one piece is joined to one side of the other, so that their vertexes may coincide, the common seam, or joint, is called a mitre, and the pieces themselves are said to be mitred. The whole angle thus joined is generally a right angle, and when this is the case, each of the pieces joined will be forty-five degrees. Mitering is also employed in dovetail joints, in order to conceal the dovetailing. MITRE-BOX, a trough for cutting mitres, having three sides, open at the ends. MIXED ANGLE, an angle of which one side is a curve, and the other a straight line. MIXED FIGURE, one that is composed of straight lines and curves, being neither entirely the sector nor the segment of a circle; nor the sector or segment of an ellipsis; nor a parabola, nor an hyperbola. MOAT (from the Latin mota, a ditch) in fortificao tion, a deep trench dug round a town, or fortress, to be defended on the outside of the wall or rampart. The depth and breadth of a moat oft-en depend on the nature of the soil; according as it is marshy, rocky, or the like. The brink of the moat next the rampart, in any fortification, is called the scarp, and the opposite one the counter- scarp. MODEL (from the Latin modulus, a copy) an origi- nal, or pattern, proposed for any one to copy or MOD 371 M01) W imitate. St. Paul’s cathedral is said to be built after the model of St. Peter’s at Rome. M0981. is particularly used, in building, for an arti- ficial pattern, made of wood, stone, plaster, or other matter, with all its parts and proportions; for the better guidance of the artificers in exe- cuting some great work, and to give an idea of .. the elfect it will have when complete. In allgreat buildings, it is much the surest way to makea model in relievo; and not to trust to a bare design, or draught. There are also models for the building of ships, 8m. and for extraordi- nary staircases, Ste. MODEL, in painting and sculpture, any thing pro- posed to be imitated. Hence, in the academies, theygive the term model to a naked man, disposed in several postures, to afford an opportunity to the scholars of designing him in various views and attitudes. The sculptors have little models of clay, or wax, to assist them in their designs of others that are larger, in marble, Ste. and to judge of the atti- tude and correctness of a figure. Statuaries likewise give the name model to certain figures of clay, or wax, which are but just fashion— ed, to serve by way of guide ,in the making of larger, whether of marble, or other matter. MODERN (French) a term in architecture, impro- perly applied to the present, or Italian manner of building; as being according to the rules of the antique. Nor is the term less abused when attri- buted to architecture purely Gothic. Modern architecture, in propriety, is only appli- cable to that which partakes partly of the antique, retaining somewhat of its delicacy and solidity; and partly of the Gothic, whence it borrows members and ornaments, without proportion or judgment. MUIHLLIONS (French) in architecture, mutules carved into consoles, placed under the solfit or bottom of the drip of the corona in the Corin- thian and Roman otdeis, for supporting the lai- inier and sima, 01 appearing to peifoun the office of support. In Grecian architecture, the lonic order is with- out modillions in the cornice, as are also the Roman examples of the same order, except the temple of Concord, at Home, which has both dentils and modillions. A singular and curious example of a modillion cornice, but contrary to the principles of archi- tecture, is to be found in the interior cornice of the Tower of the Winds, at Athens, in which the projecting part is much thicker than the interior, where the stress seems to lie, and, consequently, gives the idea of weakness. A singular example of modillions is to be found in the frontispiece of Nero, at Rome, where they consist of two plain faces, separated by a small sima-reversa, and crowned with an ovolo and bead. Another very extraordinary form of modillions is that placed in'the frieze of the fourth order of the Coliseum, cut on the outside, or projecting part, of a sima~reversa form. In most examples of the Corinthian and Roman orders, the cornices have both dentils and modil- lions; but, if the two are used together, in good proportion to the other parts, so as to appear dis- tinctly at a' reasonable distance, the cornice will be overcharged, both in proportion and weight, to the other principal members of the entablature, or the entablature to the whole order; the one or the other Ought, therefore, to be omitted in the same cornice. In the general disposition of modillions, if each one is conceived to be divided into two equal parts by a vertical plane at right angles to the surface of the frieze, one of the modillions is so disposed, that its dividing vertical surface will be entirely in a plane passing through the axis of the column, and in the colunm next the angle of the building thereis generally only one modillion be- tween that through which the plane along the axis passes, and the angle of the cornice. The vertical sides of modillions at right angles to the face, are generally finished with volutes of different sizes, and turned on different sides of the same line; the greater being that next to the ver- tical surface, to which they are attached, and the lesser at the extremity. The sofiits of the modillions, so constructed, fol- low the under line- of the volutes, and the con- necting undulated line which joins them. The upper part of each volute is on the same level, and is attached to a moulding of the sima-inversa form, which returns round it; and this moulding is again attached to the corona, which hangs over the modillion. ' In some of the Roman buildings, the u odillions are not placed ovei the axes ol the columns, neither upon those at the extremes, nor over the axes of the intermediate shafts. In the Pantheon, ,the 8 B 2 M OD ., , ....... 372 MOI modillion next each angle of the building has its vertical side, which is opposed to the next modil- lion, nearer to the central plane of the portico, over the axis of the column, and consequently the whole breadth of the modillion on one side of the axis entirely, and on that side next to the angle of the building. In the whole portion are forty- seven modillions, including those at each ex- treme; the intervals are, therefore, forty-six in number, and forty-four between the columns that are between their axes. The portico is octostyle, and, consequently, the intercolumns are seven in number: from this it will be found, that if the columns were placed equidistantly, the number of intermodillions would be 6%- in number. In this temple the corresponding intervals are very irregular. The two extreme ones are, ac- cording to Desgodetz, 9' 4%”, and 9' 2%”; the next two, nearer the centre, are 9’ 5%.”, and 9’ 137—”; the next two, still nearer to the centre, are exactly equal, being 9' 5” each; and the central interco- lumniation is 10’ 4%”: so that the modillions ap- pear to be equally divided, without any regard to the axrs oi the columns. The same irregularity in the disposition of the modillions may be ob- served in the temple of Concord, and in that of Jupiter the Thunderer. In the three remaining columns of the temple of Jupiter Stator, each co- lumn has a modillion placed over its axis, and each interColumn has three modillions regularly disposed : the distance between the lower ends of the shafts are :5 modules,4—§— parts, and the columns are in height 20 modules, 6% parts. In the Pantheon, the modillions are placed in the pediment, contrary to the authority of Vitruvius. MODULAR PROPORTION, that which is regu- lated by a module. See MODULE. MODULATION (from the Latin modular, to re- gulate) the proportion of the parts of an order. MODULE (from the Latin modulus, a pattern) in architecture, a certain measure taken at plea- sure, for regulating the proportions of columns, and the symmetry or distribution of the whole building. Architects usually choose the diameter, or semi- diameter, of the bottom of the column for their module; and this they subdivide into parts or minutes. Vignola divides his module, which is a semidia- meter, into twelve parts, for the Tuscan and Doric; and into eighteen, for the other orders. v.1 » The module of Palladio, Scammozzi, M. Cambray, Desgodetz, Le Clerc, &c. which is also the semi- diameter, is divided into thirty parts, or minutes, in all the orders. Some divide the whole height of the column into twenty parts for the Doric, twenty-two and a half for the Ionic, twenty-five for the Roman, 8m. and one of these parts they make a module, by which to regulate the rest of the building. There are two ways of determining the measures, or proportions, of buildings: the first by a fixed standard measure, which is usually the diameter of the lower part of the column, called amodule, sub- divided into sixty parts, called minutes. In the second there are no minutes, nor any certain and stated division of the module; but it is divided occasionally into as many parts as are judged necessary. Thus the height of the Attic base, which is half the module, is divided either into three, to have the height of the plinth; or into four, for that of the greater torus; or into six, for that of the lesser. Both these manners have been practised by the ancient as well as the modern architects; but the second, which was that chiefly used among the ancients, is, in the opinion of Perrault, pre~ ferable. ’ As Vitruvius, in the Doric order, has lessened his module, which, in the other orders, is the diame- ter of the lower part of the column, and has re- duced that great module to a mean one, which is a semidiameter; M. Perrault reduces the module to a third part, for the same reason, viz. to deter- mine the several measures without a fraction. For in the Doric order, beside that the height of the base, as in the other orders, is determined by one of these mean modules; the same module gives likewise the heights of the capital, architrave, tri- glyphs, and metopes. But our little module, taken from the third of the diameter of the lower part of the column, has uses much more extensive; for, by this, the heights of pedestals, of columns, and entablatures, in all orders, are determined without a fraction. As then the great module, or diameter of the co- lumn, has sixty minutes; and the mean module, or half the diameter, thirty minutes; our little module has twenty. See COLUMN. MOILON, a name given by the French to a kind of stone, that forms the upper crust, and lies round the free-stone, in most quarries. lt isan MOM 37 3 MON excellent substance for forming the body of fluxes, or soft enamel. MOINEAU (French) in fortification, a flat bastion, raised before a curtain when it is too long, and the bastions of the angles too remote to be able menta of the parts of that body ; and, therefore, where the magnitudes and number of particles are the same, and where, they are moved with the same celerity, there will be the same momenta of the whole. See FORCE. to defend each other. MONASTERY, a convent, or house, built for the Sometimes the moineau is joined to the curtain, and sometimes it is divided from it by a moat. Here musqueteers are placed, to fire each way. MOLDING, see MOULDING. MOLE (from the Latin, moles) a. massive work of large stones laid in the sea by means of coffer- dams, extending eitherin a right line, or in the arc of a circle, before a port, which it serVes to close, to defend the veSSels in it from the impe- tuosity of the waves, and to prevent the passage of ships without leave. MOLE is sometimes also used to signify the harbour itself. IVIOLE, among the Romans, was also used for a kind of mausoleum, built in the manner of a. round tower on a square base, insulated, encom- passed with columns, and covered with a dome. The mole of the Emperor Adrian, now the castle of St. Angelo, was the greatest and most stately of all the moles. It was crowned with a brazen pineapple, in which was a golden urn, containing the ashes of the emperor. MOMENT, or MOMENTUM (from the Latin) the impetus, force, or quantity of motion in a moving body; or the word is sometimes used simply for the motion itself. Moment is frequently defined by the vis insita, or power by which moving bodies continually change place. In comparing the motion of bodies, the ratio of their momenta is always compounded of the quantity of matter, and thc celerity of the moving body; so that the moment of any such body may be considered as a rectangle under the quantity of matter, and the celerity. And since it is certain, that all equal rectangles have their sides reciprocally proportionable; there- fore, if the momenta of any moving bodies be equal, the quantity of matter in one to that of the other, will be reciprocally as the celerity of the latter to that of the former; and, on the con- trary, if the quantities of matter be reciprocally proportionable to the celerities, the momenta or quantities in each will be equal. The moment, also, of any moving body may be considered as the aggregate or sum of all the mo- reception of religious devotees; » whether it be abbey, priory, nunnery, or the like. The term is only properly applied to the houses of monks, friars, and nuns. The rest are more properly called religious houses. See ABBEY. The houses belonging to the several religious or- _ ders, which obtained in England and Wales, were cathedrals, colleges, abbeys, priories,preceptories, commanderies, hospitals, friaries, hermitages, chantries, and free chapels. These were under the direction and management of several officers. The dissolution of houses of this kind began so early as the year 1312, when the Templars were suppressed; and in 1323, their lands, churches, advowsons, and .liberties, here-in England, were given by 17 Edw. ll. stat. 3, to the priory and bre- thren of the hospital of St. John ofJerusalem In the years 1390, 1437, 1441, 14-59, 1497, 1505, 1508, and 1515, several other houses were dis- solved, and their revenues settled on different col- leges in Oxford and Cambridge. Soon after the last period, Cardinal Wolsey, by licence of the king and pope, obtained a dissolution of above thirty religious houses, for the founding and en- dowing his colleges at Oxford and Ipswich. About the same time a hull was granted by the same pope to Cardinal Wolsey, to suppress mo- nasteries, where there were not above six monks, to the value of eight thousand ducats a year, for endowing Windsor, and King’s College, in Cam- bridge; and two other bulls were granted to Car- dinals Wolsey and Campeius, where there were less than twelve monks, and to annex them to the greater monasteries; and another bull to the same cardinals to inquire about abbeys to be suppressed, in order to be made cathedrals. Although nothing appears to have been done in consequence of these bulls, the motive which induced Wolsey, and many others, to suppress these houses, was the desire of promoting learning; and Archbishop Cranmer engaged in it with a view of carrying on the Reformation. There were other causes that concurred to bring on their ruin: many of the devotees were loose and vicious; the monks were generally thought to be, in their hearts, attached MON 374 MON W to the pope’s Supremacy; their revenues were not employed according to the'intent of the donors; many cheats in images, feigned miracles, and counterfeit relics, had been discovered, which brought the monks into disgrace; the Observant friars had- opposed the king’s divorce from Queen Catharine; and these circumstances operated, in concurrence with the king’s want ofa large supply, and the people’s desire to save their money, to for- ward a motion in parliament, that, in order to sup- port the king's state, and supply his wants, all the re— ligious houses might be conferred upon the crown, which were not able to spend above 2001. a year; and an act was passed for that purpose, 27 Hen. VIII. c. 28. By this about 380 houses were dissolv- ed, and a revenue of 30,000[. or 32,000]. a—year came to the crown; besides about 100,000]. in plate and jewels. The suppression of these houses occa- sioned great discontent, and at length an open re- bellion: when this was appeased, the king re- solved to suppress the rest of the monasteries, and appointed a new visitation ; which caused the greater abbeys to be surrendered apace; and it was enacted by 31 Hen. VIII. 0. 13, that all mo- nasteries, which have been surrendered since the 4th of February, in the twenty-seventh year of his majesty’s reign, and which hereafter shall be sur— rendered, shall be vested in the king. The knights of St. John of Jerusalem were also suppressed by the 32 Hen. VIII. c. 24. The suppression of? these greater houses by these two acts, produced a revenue to the king of above 100,000]. a.year, besides a large sum in plate and jewels. The last. act of dissolution, in this king’s reign, was the act of 37 Hen. VIII. 0. 4, for dissolving colleges, free chapels, chantries, Ste. which act was farther en- forced by l Edw. VI. c.14. By this act were suppressed 90 colleges, 110 hospitals, and 2374 chantries and free chapels. The number of houses and places suppressed, from first to last, so far as any calculations appear to have been made, seems to be as follows: Ot'lesser monasteries, of which we have the valuation . . . . . . . . . . . 374 'Ot‘ greater monasteries . . . . . . . 186 Belonging to the hospitallers . . . . . 48 Colleges............90 Hospitals. . . . . . . . . . . 110 Chantries and free chapels . . . . . 2374 Total 3182 Besides the friars’ houses, and those suppressed by Wolsey, and many small houses, of which we have no particular account. The sum total of the clear yearly revenue of the several houses, at the time of their dissolution, of which we have any account, seems to be as fol- lows: ' £. 3. (1. Of the greater monasteries . . 104,919 13 3% Of all those of the lesser monas- teries, of which we have the valuation . . . . . . . 29,702 1 10% Knights hospitallers’ head house in London . . . ' . . 2,385 19. 8 We have the valuation of only twenty-eight of their houses in the country . . . . . 3,026 9 5 Friars’ houses, of which we have the valuation . . . . . . 751 2 0 Total 140,78419 3% If proper allowances are made for the lesser mo- nasteries, and houses not included in this esti- mate, and for the plate, 8Lc. which came into the hands of the king by the dissolution, and for the value of money at that time, which was at least six times as much as at present; and we also con- sider that the estimate of the lands was generally supposed to be much under the real worth, we must conclude their whole revenues to have been immense. It doth not appear that any computation hath been made of the number of persons contained in the religious houses. Those of the lesser monasteries dissolved by Q7 Hen.V [l l. were reckoned at about 10,000 If we suppose the colleges and hospitals to have contained a pmportionable num- ber, these will make about . . . . 5,347 If we reckon the number in the greater monasteries, according to the propor- tion of their revenues, they will be about 35,000; but as probably they had larger allowances in proportion to their number than those of the lesser monas- teries, if we abate upon that account 5000, they will then be . . . . . 30,000 One for each chantry and free chapel . 2,1374- -_...—— Total 47,721 But as there were probably more than one person to ofliciate in several of the free chapels, and there MON 375 {MON M were other houses which are not included within , this calculation, perhaps they may be computed in one general estimate at about 50,000. As there were pensions paid to almost all those of the greater monasteries, the king did not immediately come into the full enjoyment of their whole reve- noes: however, by means of what he did receive, he founded six new bishoprics,viz. those of VVest- minstei, (which was changed by Queen Elizabeth intoadeanery, with twelve prebends and ascho: l,) Peterborough, Chester, Gloucester, Bristol, and Oxford. And in eight other sees he founded deaneries and chapters, by converting the friars and monks into deans and prebendaries, viz. Can- terbury, Winchester, Durham, Worcester, R0- chester, Norwich, Ely, and Carlisle. He founded also the colleges of Christ-Church in Oxford, and Trinity in Cambridge, and finished King’s Col- lege Chapel there. He likewise founded profes— sorships of divinity, law, physic, and of the He- brew and Greek tongues, in both the said univer- sities. He gave the house of Grey Friars, and St. Bartholomew's hospital, to the city of London; and a perpetual pension to the poor knights of Windsor; and laid out great sums in building and fortityiug many ports in the Channel. It is observable, upon the whole, that the dissolution of their houses was an act, not of the church, but of the state, in the period preceding the Refor mation, by a king and parliament of the Roman Catholic communion in all points except the king’s supremacy ; to which the pope himself, by his bulls and licences, had led the way. Although none, in this enlightened period, can approve either the original establishment or con- tinued subsistence of monasteries, yet the destruc- tion of them was felt and lamented, fora consi- derable time, as a great evil. One inconvenience that attended their dissolution was the loss of many valuable books, which their several libraries contained: for, during the dark ages, religious houses were the repositories of literature and science. Besides, they were schOols of education and learning; for every convent had one person or more appointed for this purpose; and all the neighbours that desired it might have their chil- dren taught grammar and church music there, without any expense. In the nunneries also young females were taught to work and read; and not only people iof the lower rank, but most of the noblemen’s and gentlemen’s daughters were in- structed in .zthose places... All the monasteries were also in effect great hospitals, and were most of them obliged to relieve many poor people every day. They were likewise houses of entertainment for all travellers. And the nobility and gentry provided not only fortheir old servants in these houses, by corrodies, but for their younger chil- dren, and impoverished friends, by making them first monks and nuns, and in time priors and prioresses, abbots and abbesses. On the other hand, they were very injurious to the secuiar and parochial clergy, by taking on» themselves many prebends and benefices, by getting many churches appropriated to them, and pensions out of many others; and by the exemptionsthey got from the episcopal jurisdiction, and from the payment of tithes. Nor were they less injurious to the nation in general, by depriving the public of so many hands, which might have been very serviceable to it in trade and other employments; by greatly diminishing the number of people. in consequence of the institution of celibacy; and by their houses or churches being sanctuaries for almost all sorts of offenders. And, if the superstition had conti- nued, and the zeal of establishing religious insti- tutions had exerted itself with equal vigour to the present age, we should, ere this, have been a na- tion of monks and friars, or probably have be- come a prey to some foreign invader. We say nothing now of the acts of moral turpitude, which were committed in these abodes of celibacy and indolence; which, however they might have been exaggerated, were without doubt flagrant and atrocrous. MONOP’I‘ERON, or MONOPTRAL TEMPLE (from pores, single, and arrepov, a wing) in architecture, an edifice, consisting of a circular colonnade sup- porting a dome, without any enclosing wall, and consequently without a cell, as in other temples. MONOTRIGLYH (from aoyog, single, and TFWKU¢UQ a triglyph) having only one triglyph between two adjoining columns. The monotriglyph inter- columniation was the general practice in the Grecian Doric; as in the temple of Theseus, and in that of Minerva, at Athens. Mr. Rively, in his preface to the third volume of Stewart’s Athens, says, “ There is a certain ap- pearance of eternal duration in this species of edi- fice (meaning a Grecian Doric temple) that gives a solemn and majestic feeling, while every part is perceived to contribute its share to this charac- MONUMENT 0F LYSICRATES. M00 4376 W _. ter of durability. From this rapid sketch, it will readily be seen that no other intercolumniation than that of the mo-notriglyph can succeed in this dignified order. The Propylaea, indeed, as well as the temple of Augustus, or Agora, 'has one in- terval of the space of two triglyphs; but it is easy to perceive, that this deviation from the general _ principle was merely an accommodation to cir- cumstances; both these buildings requiring a wide opening in. the middle of- the front. Accordingly these are the only instances of this deviation to be found at Athens.” In the island of Delos, the portico of Philip, king of Macedon, is another instance. MONUMENT (from the Latin monumentum, a me- morial) a structure raised to preserve the memory of some eminent person, or to perpetuate some remarkable event. Monuments at first consisted of stones erected over the tombs of the deceased, on which were engraved the name, and frequently the actions, of the person to whose memory they were reared. Monuments received different names among the ancients, according to their figure. When the base was square, and the solid erected thereon a prism, the monument was called steles; whence square pilasters, or attic columns, are supposed to be derived. When the base was circular, and the solid erected thereon a cone, the monument was called styles. Those monuments that were square at the foot, and tapering therefrom in planes to a point in which the planes ended, were called pyramids. Others, which had triangular bases, and their sides ending in a point, were called obe- Iz'sks; being constructed in imitation of the in- struments or spits used in roasting the sacrifices. The choragic monument of Lysicrates, commonly called the Lantern of Demosthenes, is the most beautiful edifice of antiquity of its size. This monument, which is exquisitely wrought, stands near the eastern‘end of the Acropolis. It is composed of three distinct parts. First,a quad- rangular basement; secondly, a circular colonnade, the intercolumniations of which are entirely closed up; and, thirdly, a t/zolus, or cupola, with a beautiful ornament upon it. The quadrangular basement is entirely closed on every side, so as to exclude entrance. On break~ ing through one of the sides, it was found not to be quite solid, but the void is so small, and ir- MOR regular, that a man can hardly stand upright in it. This basement supports the circular colonnade, which was constructed in the following manner: six equal panels of white marble, placed con- tiguous to each other, on a circular plan, formed a continued cylindrical wall; which of course was. divided, from top to bottom, into six equal parts, by the junctures of the panels. On the whole -length of each juncture was cut a semicircular groove, in which a Corinthian column was fitted with great exactness, and effectually concealed thejunctures of the panels. These columns pro- jected somewhat more than half their diameters from the surface of the cylindrical wall, and the wall entirely closed up the intercolumniation. Over this was placed the entablature, and the cupola, in neither of which any aperture was made, so that there was no admission to the inside ofthis monument, and it was quite dark. It is, besides, only 5 feet “25 inches in the clear, and, therefore, was never intended for a habitation, or even a re- pository of any kind. An entrance, however, has been since forced into it, by breaking tl’irough one of the panels; pro- bably in expectation of finding treasures here. For in these countries such barbarism reigns at present, every ancient building which is beautiful, or great, beyond the conception of the present inhabitants, is always supposed by them to be the work of magic, and the repository of hidden treasures At present three of the marble panels are destroyed; their places are supplied by a door, and two brick walls, and it is converted into a closet. It should be observed that two tripods with handles to them, are wrought in basso-relievo on each of the three panels which still remain. They are perhaps of the species, which Homer and Hesiod describe by the name of Tfi'lrod‘sg ainimtg, or eared tripods. The architrave and frieze of this circular colon- nade are both formed of only one block of marble. On the architrave is cut the following inscription: AYZIKPATHE ATXIQEIAOY KIK’TNEYZ EXOPHI‘HI AKAMANTIE DAIAQN ENIKA @ESLN HTAEI AYEIAAHE AGHNAIOE EAIAAXKE ETAINEI OE HPXE From this we may conclude, that on some solemn festival which was celebrated with games and plays, Lysicrates of Kikyua, a demos or borough town of the tribe of Akamantis, did on behalf of MON‘ W 377' ' MOO his tribe, but at his own expense, exhibit a musi- cal or theatrical entertainment; in which the boys of the tribe of Akamantis obtained the victory: that in memory of their victory this monument was erected; and the name of the person at whose expense the entertainment was exhibited, of the tribe that gained the prize, of the musician who - accompanied the performers, and of the composer of the piece, are all recorded on it; to these the name of the annual archon is likewise added, in whose year of magistracy all this was trans- acted. From which last circumstance it ap— pears, that this building was erected above 330 years before the Christian aera; in the time of Demosthenes, Apelles, Lysippus, and Alexander the Great. Round the frieze is represented the story of Bac- chus and the Tyrrhenian pirates. The figure of Bacchus himself, the fauns and satyrs who attend him on the manifestation of his divinity, the chastisemcnt of the pirates, their terror, and their transformation into dolphins, are expressed in this basso-relievo with the greatest spirit and elegance. The cornice, which is otherwise very simple, is crowned with a sort of Vitruvian scroll, instead of a cymatium. It is remarkable, that no cornice of an ancient building, actually existing, and de- corated in this manner, has hitherto been’pub- lished; yet temples, crowned with this ornament, are frequently represented on medals; and there is an example much resembling it, among those ancient paintings which adorn a celebrated manu- script of Virgil, preserved in the Vatican library. This cornice is composed of several pieces of marble, bound together by the cupola, which is of one entire piece. The outside of the cupola is wrought with much delicacy; it imitates a thatch, or covering of laurel leaves; edged with a Vitruvian scroll, and enriched with other ornaments. In certain cavi- ties on its upper surface, some ornament, now lost, probably a tripod, was originally placed. It was the form of the upper surface of the flower, and principally, indeed, the disposition of four remarkable cavities in it, which first led to this discovery. Three of them are cut on the three principal projections of the upper surface; their disposition is that of the angles of an equilateral triangle; in these the feet of the tripod were pro- bably fixed. In the fourth cavity, which is much the largest, and is in the centre of this upper VOL. II. surface, a baluster was in all likelihood inserted; its use was to support the tripod. It is well known, that the games and plays which the ancient Grecians exhibited, at the ce- lebration of their greater festivals, were chiefly athletic exercises, and theatric or musical per- formances; and that these made a very consi- derable, essential, and splendid part of the so- lemnity. In order, therefore, to engage a greater number of competitors, and to excite their emu- lation more effectually, prizes were allotted to the victors; and these prizes were generally ex- hibited to public view, during the time in which‘ these games were celebrated. MONUMENT, T/ze, absolutely so called among us, denotes a magnificent pillar, designed by Sir C. Wren, and erected by order of parliament, in memory of the burning of the city of London, anno 1666, near the place where the fire began. This pillar, begun in 1671, and finished in 1677, is of the Doric order, fluted, 209. feet high from the ground, and 15 feet in diameter, of solid Portland stone, with a staircase in the middle, of black marble, containing 365 steps. The lowest part of the pedestal is 28 feet square, and its alti- tude 40 feet; the front being enriched with curious basso—relievos. It has abalcony within 32 feet of the top, and the whole is surmounted with a curious and spacious blazing urn ofgilt brass. MOOR-STONE, a very remarkable stone, found in Cornwall, and some other parts of England, used in the coarser works of modern builders. This is truly a white granite, and is a very valu- able stone. It is very coarse and rude, but has beautiful congeribs of variously constructed and differently figured particles, not diffused among, or running into one another, but each pure and distinct, though firmly cohering with whatever it comes in contact with. Its colours are princi- pally black and white; the white are of a soft marbly texture, and opaque, formed into large congeries, and emulating a sort of tabulated structure; among these are many ofa pure cry- stalline splendour and transparence; and in some are lodged, in different directions, many small flaky masses of pure tales, of several colours; some are wholly pellucid, others of an opaque white, others of the colour of brown crystal, and a vast number perfectly black. It is found in immense strata in some parts of Ireland, but is disregarded there. 3 C MOR 37‘s 5.; I 47 MOR r It is found with us in Devonshire, Cornwall, and some other counties; and brought thence in vast quantities to London. It never forms any whole strata there, but is found on the surface of the earth, in immense and unmanageable masses ; to separate these, and render them portable, a hole is dug in some part of the mass, which being sur- rounded with a ridge of clay, is filled up with water; this by degrees soaks in, and finding its way into the imperceptible cracks, so far loosens the co- hesion of the particles, that the day after, on driv- ing a large wedge into the hole, the stone breaks into two or more pieces. It is used in London for the steps of public buildings, and on other occasions, where great strength and hardness are required. lVIORESK (from the Spanish morisco) a kind of painting, carving, Sic. done after the manner of the Moors, consisting of several grotesque pieces and compartments promiscuously inter- mingled, not containing any perfect figure of a man or other animal, but a wild resemblance of birds, beasts, trees, Sec. They are also called arabesques, and are particu- larly used in embroideries, damask-work, Sec. ,MORTAR (from the Dutch morter, cement) in ar- chitecture, acomposition of lime, sand, 8Lc. mixed up with water; serving as a cement to bind the stones, 8m. ofa building. The ancients had a kind of mortar so very hard and binding, that, even at this time, it is next to impossible to separate the parts of some of their buildings. The lime used in the ancient mortar, is said to have been burnt from the hafdest stones, or often from fragments of marble. De Lorme observes, that the best mortar is made of puzzolana instead of sand; adding, that this penetrates black Hints, and turns them white. Mr. Worledge observes, that fine sand makes weak mortar, and that the larger the sand the stronger the mortar. He therefore advises, that the sand be washed before it is mixed; and adds, that dirty water weakens the mortar considerably. Wolfius recommends that the sand be dry and sharp, so as to prick the hands when rubbed; yet not so earthy as to foul the water in which it is washed. Vitruvius observes, that fossile sands dry sooner than those taken out of rivers. VVhence, he adds, the latter is fitted for the insides, the former for the outsides of a building. But fossile sand, lying long in the air, becomes earthy. Palladio takes notice, that of all sands the white are the worst; from their want of asperity. The proportion of lime and sand in our common mortar is extremely variable : Vitruvius prescribes three parts of pit-sand, and two of river-sand, to one of lime; but the quantity of sand here seems to be too great. The proportion most commonly used in the mix- ing of lime and sand is, to a bushel of lime a bushel and a half of sand, 2'. e. two parts of lime and three of sand; though the common mortar, in and about London, has more sand in it than according to this proportion. Mr. Dossie, in the second volume of the ZlIemoirs offlgriculture, p. 20, Ste. gives the following me- thod of making mortar impenetrable to moisture, acquiring great hardness, and exceedingly du- rable, discovered by a gentleman of Neufchatel : Take of unslaked lime and of fine sand, in the proportion of one part of the lime to three parts of the sand, as much as a labourer can well ma- nage at once; and then adding water gradually, mix the whole well together with a trowel, till it is reduced to the consistence of mortar. Apply it, while hot, to the purpose, either of mortar, as a cement to brick or stone, or of plaster to the sur- face of any building. It will then ferment for some days in dry places, and afterwards gradu- ally concrete or set, and become hard: but in a moist place it will continue soft for three weeks or more; though it will, at length, attain a firm consistence, even if water have such access to it as to keep the surface wet the whole time. The lime for this mortar must be made of lime-stone, shells, or marle; and the stronger it is, the better the mortar will be. It is proper also to exclude the sun and wind from the mortar, for some days after it is applied; that the drying too fast may not prevent the due continuance of the fermenta- tion, which is necessary for the action of the lime on the sand. “7 hen a very great hardness and firmness are required in this mortar, the using of skimmed milk instead of water, either wholly or in part, will produce the desired effect, and render the mortar extremely tenacious and durable. M. Loriot’s mortar, the method of making which was announced, by order of his majesty,at Paris, in 1774, is made in the following manner: Take one part of brickdust finely sifted, two parts of fine em MOR 3‘ W river sand skreened, and as much old slaked lime as may be suflicient to form mortar with water, in the usual method, but so wet as to serve for the slaking of as much powdered quick-lime as amounts to one-fourth of the whole quantity of brickdust and sand. When the materials are well mixed, employ the composition quickly, as the least delay may render the application im- perfect or impossible. Another method of making this composition is to make a mixture of the dry materials, i. e. of the sand, brickdust, and pow- dered quick-lime, in the prescribed proportion; which mixture may be put in sacks, each contain— ing a quantity sufficient for one or two troughs of mortar. The old slaked lime and water being prepared apart, the mixture is to be made in the manner of plaster, at the instant whenit is wanted, and is to be well chafed with the trowel. Dr. Higgins, who has made a variety of experi- ments, for the purpose of improving mortar, says, the perfection oflime, prepared for the purpose of making mortar, consists chiefly in its being de- prived of its fixed air. On examining several specimens of the lime commonly used in build- ing, he found that it is seldom or never sufficiently burned ; for they all effervesced, and yielded more or less fixed air, on the addition of an acid, and slaked slowly, in comparison with well burned lime. He also recommends that, as lime owes its excellence to the expulsion of fixed air from it in the burning, it should be used as soon as possible after it is made, and guarded from exposure to the air, as much as possible, before it is used. From other experiments, made with the view of ascertaining the best relative proportions of lime, sand, and water, in the~ma\king of mortar, it ap- peared that those specimens were the best which contained one part of lime in seven of the sand. Also, that mortar, which is to, be used where it must dry quickly, ought to be made as stiff as the purpose will admit, or, with the smallest practi- cable quantity of water; and that mortar will not crack, although the lime be used in excessive quantity, provided it be made stiffer, or to a thicker consistence than mortar usually is. In order to the greatest induration of mortar, it must be suffered to dry gently and set; the exsic- cation must be effected by temperate air, and not accelerated by the heat of the sun or fire; it must not be wetted soon after it sets; and afterwards it ought to be protected from wet as much as q MOR’ r possible, until it is completely indurated; the entry of acidulous gas must be prevented as much as possible, until the mortar is finally placed and quiescent; and then it must be as freely exposed to the open air as the work will admit, in order to supply acidulous gas, and enable it sooner to sus— tain the trials to which mortar is exposed in ce— mentitious buildings, and incrustations. Dr. Higgins has also inquired into the nature of the best sand or gravel for mortar, and into the effects produced by bone—ashes, plaster powder, charcoal, sulphur, See. and he deduces great ad- vantages from the addition of bone-ashes, in va- rious proportions, according to the nature of the work for which the composition is intended. This author describes a water-cement, or stucco, of his own invention, for incrustations, internal and external, exceeding, as he says, Portland stone in hardness, for which he obtained his majesty’s letters patent in 1779. As to the materials, of which this is made, drift sand, and quarry sand, or, as it is commonly called, pit sand, consisting chiefly of hard quartose flat— faced grains, with sharp angles, the most free from clay, salts, and calcareous, gypseous, or other grains, less durable than quartz, containing the smallest quantity of pyrites, or heavy metallic matter, inseparable by washing, and admitting the least diminution in bulk by washing, is to be preferred to any other. The sand is to be sifted in streaming clear water, through a sieve which shall give passage to all such grains as do not exceed one-sixteenth of an inch in diameter: and the stream of water and sifting are to be so regulated, that all the sand, which is much fifier than the Lynn sand, together with clay and other matter, specifically lighter than sand, may be washed away with the stream; whilst the purer and coarser sand, which passes through the sieve, subsides in a convenient receptacle; the coarse rubbish and shingle re- maining on the sieve to be rejected. The sub- siding sand is then washed in clean streaming water, through a finer sieve, so as to be farther cleansed and sorted into two parcels; a coarser, which will remain in the sieve (which is to give passage to such grains of sand only as are less than one-thirtieth of an inch in diameter).and is to be saved apart under the name of cam-so sand; and a finer, which will pass through the sieve and subside in the water, and which is to be saved apart under the name ofjine sand. 3 c 2 l i M UK '3 80 M OR These are to be dried separately, either in the sun, or on a clean iron plate set on a convenient sur- face, in the manner of a sand heat. The lime to be chosen, is stone-lime, which heats the most in slaking, and slakes the quickest when duly watered; such as is freshest made, and most closely kept; which dissolves in distilled vinegar with the least elfervescence, leaves the smallest residue in— soluble, and in this residue the smallest quantity of clay, gypsum, or martial matter. Let this lime be put in a brass-wired fine sieve, to the quantity of fourteen pounds. Let the lime be slaked by plunging it in a butt, filled with soft water, raising it out quickly and suffering it to heat and fume; and by repeating this plunging and raising alternately, and agitating the lime, until it be made to pass through the sieve into the water: reject the part of the lime that does not easily pass through the sieve; and use fresh por- tions of lime, till as many ounces of lime have passed through the sieve as there are quarts of water in the butt. Let the water, thus impreg- nated, stand in the butt, close covered, until it becomes clear; and, through wooden cocks, placed at different heights in the butt, draw off the clear liquor, as fast and as low as the lime subsides, for use. This clear liquor is called the cementing liquor. Let fifty-six pounds of the foresaid chosen lime be slaked, by gradually sprinkling on it, and especially on the unslaked pieces, the cementing liquor, in a close clean place. Let the slaked part be immediately sifted through the fine brass-wired sieve. Let the lime which passes be used instantly, or kept in air-tight vessels, and let the part of the lime which does not pass through the sieve be rejected: the other part is called purified lime. Let bone-ash be prepared in the usual manner, by grinding the whitest burnt bones; but let it be sifted to be much finer than the bone-ash commonly sold for making cupels. Having thus prepared the materials, take fifty-six pounds of the coarse sand, and forty-two pounds of the fine sand: mix them ‘on a large plank of hard wood placed horizontally: then spread the sand so that it may stand to the height of six inches, with a flat surface, on the plank; wet it with the cementing liquor; to the wetted sand add fourteen pounds of the purified lime, in several successive portions, mixing and beating them up together; then add fourteen pounds of the bone-ash in successive portions, mixing and fl. beating all together. This Dr. Higgins calls ‘the water-cement coarse—grained, which is to be applied in building, pointing, plastering, stuccoing, 8tc. observing to work it expeditiously in all cases, and in stuccoing to lay it on by sliding the trowel up- wards upon it; to well wet the materials used with it, or the ground on which it is laid, with the cementing liquor, at the time of laying it on; and to use the cementing liquor for moistening the cement and facilitating the floating of it. Ifa cement of a finer texture be required, take ninety-eight pounds of the fine sand, wet it with the cementing liquor, and mix it with the purified lime and the bone-ash as above, with this differ- ence, that fifteen pounds of lime be used instead of fourteen pounds, if the greater part of the sand be as fine as Lynn sand. This is called water- cementfine-grained; and is used in giving the last coating or the finish to any work, intended to imitate the finer-grained stones, or stucco. For a cheaper and coarser cement, take of coarse sand, or shingle, fifty-six pounds, of the foregoing coarse sand twenty-eight pounds, and of the finer sand fourteen pounds; after mixing and wetting these with the cementing liquor, add fourteen pounds, or less, of the purified lime, and then as much ofthe bone-ash, mixing them together. When the cement is required to be white, white sand, white lime, and the whitest bone-ash, are to be chosen. - Grey sand, and grey bone-ash, formed of half-burnt bones, are to be chosen to make the cement grey; and any other colour is obtained, ' either by choosing coloured sand, or by the admix- ture of the necessary quantity of coloured talc in powder, or of coloured vitreous or metallic pow- ders, or other durable colouring ingredients, com- monly used in paint. The water-cement above described is applicable to forming artificial stone; by making alternate layers of the cement and of flint, hard stone, or brick, in moulds of the figure of the intended stone, and by exposing the masses so formed to the open air to harden. \Vhen it is required for water fences, two-thirds of the bone-ashes are to be omitted, and in their stead an equal measure of powdered terras is to be used. ‘ \Vhen the cement is required of the finest grain, or in a fluid form, so that it may be applied with a brush, flint powder, or the powder of any quar- tose or hard earthy substance, may be used in the place of sand, so that the powder shall not be ' M on "3 80 M OR These are to be dried separately, either in the sun, or on a clean iron plate set on a convenient sur- face, in the manner of a sand heat. The lime to be chosen, is stone-lime, which heats the most in slaking, and slakes the quickest when duly watered; such as is freshest made, and most closely kept; which dissolves in distilled vinegar with the least effervescence, leaves the smallest residue in- soluble, and in this residue the smallest quantity of clay, gypsum, or martial matter. Let this lime be put in a brass-wired fine sieve, to the quantity of fourteen pounds. Let the lime be slaked by plunging it in a butt, filled with soft water, raising it out quickly and suffering it to heat and fume; and by repeating this plunging and raising alternately, and agitating the lime, until it be made to pass through the sieve into the water: reject the part of the lime that does not easily pass through the sieve; and use fresh por- tions of lime, till as many ounces of lime have passed through the sieve as there are quarts of water in the butt. Let the water, thus impreg- nated, stand in the butt, close covered, until it becomes clear ; and, through wooden cocks, placed at different heights in the butt, draw off the clear liquor, as fast and as low as the lime subsides, for use. This clear liquor is called the cementing liquor. Let fifty-six pounds of the foresaid chosen lime be slaked, by gradually sprinkling on it, and especially on the unslaked pieces, the cementing liquor, in a close clean place. Let the slaked part be immediately sifted through the fine brass-Wired sieve. Let the lime which passes be used instantly, or kept in air—tight vessels, and let the part of the lime which does not pass through the sieve be rejected: the other part is called purified lime. Let bone-ash be prepared in the usual manner, by grinding the whitest burnt bones; but let it be sifted to be much finer than the bone-ash commonly sold for making cupels. Having thus prepared the materials, take fifty-six pounds of the coarse sand, and forty-two pounds of the fine sand: mix them on a large plank of hard wood placed horizontally: then spread the sand so that it may stand to the height of six inches, with a flat surface, on the plank; wet it with the cementing liquor; to the wetted sand add fourteen pounds of the purified lime, in several successive portions, mixing and beating them up together; then add fourteen pounds of the bone—ash in successive portions, mixing and beating all together. This Dr. Higgins calls 'the water-cement coarse—grained, which is to be applied in building, pointing, plastering, stnccoing, 8w. observing to work it expeditiously in all cases, and in stuccoing to lay it on by sliding the trowel up~ wards upon it; to well wet the materials used with it, or the ground on which it is laid, with the cementing liquor, at the time of laying it on; and to use the cementing liquor for moistening the cement and facilitating the floating of it. Ifa cement of a finer texture be required, take ninety-eight pounds of the fine sand, wet it with the cementing liquor, and mix it with the purified lime and the bone-ash as above, with this differ- ence, that fifteen pounds of lime be used instead of fourteen pounds, if the greater part of the sand be as fine as Lynn sand. This is called water- cementfine-grained; and is used in giving the last coating or the finish to any work, intended to imitate the finer-grained stones, or stucco. For a cheaper and coarser cement, take of coarse sand, or shingle, fifty-six pounds, of the foregoing coarse sand twenty-eight pounds, and ofthe finer sand fourteen pounds; after mixing and wetting these with the cementing liquor, add fourteen pounds, or less, of the purified lime, and then as much ofthe bone-ash, mixing them together. When the cement is required to be white, white sand, white lime, and the whitest bone-ash, are to be chosen. . Grey sand,and grey bone-ash, formed of half-burnt bones, are to be chosen to make the cement grey; and any other colour is obtained, either by choosing coloured sand, or by the admixc ture of the necessary quantity of coloured tale in powder, or of coloured vitreous or metallic pow- ders, or other durable colouring ingredients, com- monly used in paint. The water-cement above described is applicable to forming artificial stone; by making alternate layers of the cement and of flint, hard stone, or brick, in moulds of the figure of the intended stone, and by exposing the masses so formed to the open air to harden. \Vhen it is required for water fences, two-thirds of the bone-ashes are to be omitted, and in their stead an equal measure of powdered terras is to be used. \Vhen the cement is required of the finest grain, or in a fluid form, so that it may he. applied with a brush, flint powder, or the powder of any quar- tose or hard earthy substance, may be used in the place of sand, so that the powder shall not be MOR 381 'M OS morethan six, nor less than four times the weight of the lime. For inside work, the admixture of hair with the cement is useful. See CEMENT. B'IonTAR, lllixing and Blending (f: M. Felibien ob- ~ serves, that the ancient masons were so very scru- pulous in this process, that the Greeks kept ten men constantly employed, for a long space of time, to each bason; this rendered the mortar of such prodigious hardness, that, Vitruvius tells us, the pieces of plaster falling off from old walls served to make tables. The same Felibien adds, it was a maxim among old masons to their labourers, that they should dilute it with the sweat of their brow, 2'. e. labour it a long time, instead of drown- ing it with water to have done the sooner. MORTAR .MILL, a machine contrived by Mr. Supple, for the purpose of saving labour in the making up of mortar, as well as doing the busi— ness more effectually, and at a trifling expense. It may also be useful in working clay, Ste. MORTAR, White, used in plastering the walls and ceiling, is made of ox or cow’s hair mixed with lime and water, without any sand. The common method of making this mortar is one bushel of hair to six bushels oflime. MORTAR, used in making water-courses, cisterns, 8tc. is made of lime and hogs’ grease, sometimes mixed with the juice of figs, and sometimes with liquid pitch; after application, is it washed over with linseed oil. For this purpose, mortar made of terras, puzzolana, tile-dust, or cinders, is mixed and prepared in the same manner as common mortar: only that these ingredients are mixed with lime, instead of sand, in a due proportion, which is about half and half. The lime should be made of shells, or marble; and in works which are sometimes dry and sometimes wet, instead of terras, which is very dear, tile- dust or cinder—dust may be used. MORTAR, for sun-dials on walls, may be made of lime and sand, tempered with linseed oil; or, for wantof that, with skimmed milk. This will grow to the hardness of' stone. For buildings, one part of washed soap-ashes, mixed with another oflime and sand, make a very durable mortar. MORTISE, or MonTiCE (from the French mortcise, perhaps derived from mordeo, to bite, or pinch) in carpentry and joinery, an excavation recessed within the surface of a piece of timber, to re— ceive a projection called a tenon, left on the end of another piece, in order to fix the two together at a given angle. The sides of the mor- tise are generally four planes at right angles to each other, and to the surface whence the excava- tion is made. See CARPENTRY and JOINERY. MOSAIC, or MOSAIC-WORK (from mosaicum, a corruption of musaicum, as that 'is of musivum, as it was called among the Romans: but Scaliger derives it from the Greek [480%, and imagines the name was given to this sort ofwork, as being very fine and ingenious; and Nebricensis is of opinion it was so called, because ex illispicturis ornabanter 77211360) an assemblage of little pieces of glass, marble, shells, precious stones, woods, or the like, of various colours, cut square, and cemented on a ground of stucco, Ste. imitating the natural co- lours and gradations of painting. In this sense, mosaic work includes marquetry, or inlaid work, veneering, Ste. But, in its more proper and re— strained sense, mosaic only takesin works of stone, metals, and glass; those of wood being distin- gushed by the name of marquetry, or inlayz'ng. Others distinguish differently between mosaic and marquetry. In that properly called mosaic, they say the several stones are all of the same colour; and the changes and diminutions of colours and shades are made by applying different stones, one on another, but all of the same colour. Marque- try, on the contrary, consists of stones of different colours; and by these the several colours, shades, gradations, Ste. are expressed. . Mosaic seems to have taken its origin from paving: the fine eficect and use of pavements composed of pieces of marble of'difl'erent colours, so well joined together, as that, when dried, they might be po- lished, and the whole make a very beautiful and solid body, which, continually trodden upon, and washed with water, was not at all damaged, gave the painter the hint, who soon carried the art to a much greater perfection, so as to represent fo- liages, masques, and other grotesque pieces, of various colours, on a ground of black or white marble. But nature not producing variety of colours enough for them in marbles, to paint all kinds of objects, they thought of counterfeiting them with glass and metals coloured. The modems have gone yet farther ; and, setting aside glass and metals, as too mean materials, have introduced, along with the finest marbles, the richest of precious stones, as lapis lazuli, agates, cornelians, emeralds, turquoises, Ste. Of these three kinds of mosaic work, that of MOU 382 _—-* ' * ——— _ MOU J coloured glass and metals is now little in use, though of surprising lustre and durability; of the other two, that of marbles alone is in common use; the mosaic in precious stones being so very dear, that the few workmen who apply themselves to it, make little else but petty works, as orna- v ments for altar-pieces, tables for rich cabinets, 83c. MOTION, Local, a continued or successive change of place. MOT10N, Absolute,the change of place in a moving body, independent of any other motion. MOVEMENT (from the French) in architecture, a term used by some writers to express the rise and fall, the advance and recess, with other diversities of form, in the different parts of a building. MOULD, Glaziers’. The glaziers have two kinds of moulds: in one they cast the lead into long rods, or canes, fit to be drawn through the vice, in which the grooves are formed; this they some- times call ingot-mould. In the other, they mould those little pieces of lead, a line thick, and two lines broad, which are fastened to the iron bars of easements, 8L0. MOULD, among masons, a piece of hard wood, or iron, hollowed on the edge, answerable to the con- tours of the mouldings or cornices, 8L0. to be formed. It is otherwise called a caliber,- and is made to a section of the stone intended to be cut. The ends, or heading-joints, being formed as in a cornice by means of the mould, the inter- mediate parts are wrought down by straight edges, or circular templets, according as the work is straight or circular upon the plan. When the intended surface is required to be very exact, a reverse mould is used, in order to prove the work, by applying the mould in a transverse direction to the arrises. MOULDS, among plumbers, the tables on which they cast their sheets of lead; sometimes called simply tables. Besides these, they have others, in which they cast pipes, without soldering. MOULDINGS, in architecture, prismatic or annular solids, formed by plane and curved surfaces, and employed as ornaments. All parallel sections of straight mouldings, all the sections of annular mouldings, made by a plane at the same inclination to the axis, and, in general, allsections ofmouldings made by a plane perpendi- cular to any one of the arrises, are similar figures. Mouldings are divided into two classes, or kinds; Grecian and Roman. ‘- Grecian mouldings are formed of some conic section, as a portion of the ellipsis or hyperbola; and sometimes even of a straight line,in the form of a chamfer. Roman mouldings have their sections composed of the arcs of circles, the same moulding having the same curvature throughout. In both Grecian and Roman mouldings, their species is determined by the position of their extremities, or the circumstance of their being concave or convex : if the section be a semicircle projecting from a vertical diameter, the moulding is called an astragal, bead, or torus. If the moulding be convex, and its section the quarter of a circle, or less, and if one extremity project beyond the other, that is, approach nearer to the eye than the other, it is termed a Roman ovolo; and if this Roman ovolo project equal to its height, and the portion employed be the qua- drant of a circle, it is then called a quarter—round. If the section of a moulding be concave, but in all other respects the same as the last, it is deno- minated a cavetto. If the section of a moulding be partly concave and partly straight, the straight part being ver- tical and a tangent to the concave part, and the concavity equal to, or less than the quadrant ofa circle, the moulding is denominated an apopltygé, scape, spring, or congé: this is used in the Ionic and Corinthian orders for joining the bottom of the shaft to the base, as well as to connect the top of the fillet to the shaft under the astragal. If the section be one part concave and the other convex, and so joined as to have the same tau- gent, the moulding is named a cymatium; but Vitruvius calls all crowning or upper members cymatiums, whether they resemble the one now described or not. If the upper projecting 'part of the cymatium be a concave, it is called a sima-recta ; this is generally the crowning member of cornices, but is seldom found in other situations, except on pedestals or altars. If the upper projecting part of the cymatium be convex, it is called a sima-reversa, and is the smallest in any composition of mouldings, its oflice being to separate the larger members. Though seldom used as a crowning member of cornices, it is frequently employed with a small fillet over it, as the upper member of architrave‘b‘: capitals, and imposts. MOU 383 ' . * If the convex part ofa moulding recede and meet a horizontal surface, the recess formed by the con- vexity and the horizontal surface is termed aquirh. If the section of the moulding be a convex conic section, the intermediate part of the curve pro- jecting only a small distance from the greatest projecting extremity, and the tangent to the curve at the receding extremity meeting a hori- zontal line, produced forward without the curve at the upper extremity, the moulding is called an ovolo. This is generally employed above the eye, as a crowning member in the Grecian Doric. Ovolos may be used in the same composition of different sizes; it is sometimes cut into egg-and- tongue, or egg-and- dart, when it is teimed echinus. It is employ ed instead of a torus in the base of the monument of Lysicrates, at Athens. The contours ofovolos are generally elliptical or hyper- bolical curves. These curves can be regulated to any degree of quickness or flatness; the para- bola can also be drawn under these conditions, but its curvature, being of the intermediate spe- cies, does not afford the variety ofchange admitted by the other two. If the section be a concave semi-ellipsis, having its conjugate diameter such that the one may unite the extremities of its projections, and the other diameter parallel to the horizon, the mould— ing is termed a scotia. This is always em- ployed below the level of the eye, between two tori. One extremity has generally a greater pro- jection than the other, the greater projection being nearest to the level of the eye. If the section of the moulding be the two sides of a right angle, the one vertical, and the other, of course, horizontal, it is termed afillet, band, or corona. A fillet is the smallest rectangular mem- ber in any composition of mouldings. Its alti- tude is generally equal to its projection; its pur- pose is to separate two principal members, and it is used in all situations under such circum- stances. The corona is the principal member of a cornice. The facia is a principal member in an architrave as to height, but its projection is not more than that of a fillet, unless it be the lower facia, where the soffit is the whole breadth of the top, or sometimes even of the bottom of the shaft. Mouldings are either plain, or enriched with eggs, and with foliage displayed in a variety of forms; Some enrichments are peculiar to certain forms, as egg-and-anchors, or egg-and-tongue, to the ovolo. M OU Mouldings in assemblage are used in the forma- tion of cornices, architraves, bases, capitals, Ste. See APOPHYGE, CAVETTO, CYMATIUM, Ecru- NUS, OVOLo, QUARTER - ROUND, SCAPE, SCOTIA, SIMA-RECTA, SIMA-REVERSA. Plate I. Figure 1, a quarter-round. Figure 2, a cavetto, being exactly the reverse of the last figure; both being the quarter ofa circle. Figure 3, the sima-reversa, composed of two qua- drants of a circle. Figure 4, the sima-recta, being the reverse of the snna-reversa. Figure 5, a torus, which is a semicircle described upon a vertical diameter. Figure 6, a scotia, which, projecting equally at each extremity, occasions the contour to be ex- actly the reverse of the torus. The following are the methods of describing Ro- man mouldings, where the projections and heights are unequal; the extremities of the moulding being given. _ Figure 7.——To describe the Roman ovolo. Let A be the upper extremity, and B the lower; take the vertical line or height; from B, with that radius, describe an are; from A, with the same radius, describe another are, cutting the former at c; then from c, with the same radius, describe the are A B, which will be the contour required. Figure 8.—To describe the cavetto. With a radius equal to the height of the moulding, from the points A and B describe arcs, cutting each other in c; then from c, with the same radius, describe the arc AB, which will give the contour of the cavetto required. Figure 9.——T0 describe a sima-reversa, that shall touch a straight line at the points of contrary flexure. Join the projections A and B by the straight line A B; bisect A B in D; draw the tangent E D, parallel to a line given in position; through D draw c c, perpendicular to ED; bi- sect A D by a perpendicular, g c; from the inter- section 6, describe the are A g D; make D c equal to D c’; from the lower point, c’, describe the are D B: then the curve ofcontrary flexure, A D B, will be the sima-reversa required. Figure 10.—-To describe a sima-recta to touch a straight line at the points of contrary flexure, pa- rallel to a line given in position. Join the points of projection A and B; bisect A B in I), and draw the line D Eparallel to theline given in posi— tion; bisect A D by the perpendicular c g; from MOU 384: M U N c, with the radius c D, describe the arc AD; make D 0' equal to D c and from the other point 0' Within, describe D B: then A D B is the sima- recta required. Figure ,11.—-To describe the Grecian ovolo, two tangents being given, as also their points Qf contact. Let A E and E B be the tangents; A and B the points of contact; complete the parallelogram B E A d; produce B d to c, and make d 0 equal to d B; divide EA and d A each into the same number of equal parts; through the points of division in EA, draw lines to B; draw lines to 0 through the corresponding points in dA, to meet the corresponding lines drawn to B; and the intersections will be in the curve of an el- lipsis. The upper part, A Q, is a continuation of the same curve. The same directions extend to Figures 12, 13, 14: but the following difference may be observed : In ”igure 1], the tangent B E is regulated by taking the point B in the middle of AD. In Figure 12, the point E is one-third of A D from the bottom. In Figure 13, in the middle ofA D, as in Figure 11. In Figure 14, the point E is one-third of A D, from A. Then, according as the tangent is lower or higher, the curve will be quicker or flatter at the same projection: so that, among these curves, Figure 19. is the boldest, and Figure 14 the flattest. When E B and A E are nearly equal, the mould- ing is the boldest of any, taking D E at the same height; but when the projection is very great, or very small, the moulding is extremely flat. Figure 15.—-The same data being given, to describe the Grecian ovolo; supposing the point of contact, B, to be the extremity of one of the axes. Draw B K perpendicular to E B; also P c perpendicular to B K, for the other axis, so that the point P may be above A; then E B and P c will be paral- lel. To find the major axis: from A, with the distance B c, describe an are, cutting P c at F; draw A F, and produce it to meet B K in I; make c P equal to AI; then with CF, half the major axis, and c B, half the minor axis, describe the curve B A P Q, which will be the moulding required. This method forms the most beautiful moulding of any; the curvature being continually increased from the point B to P. The same description applies to Figures 16 and 17. With regard to the quirk at the point Q, it will be more or less, as the point A is more or less distant from Q. The quantity of curvature depends upon the angle E B D; so that when the angle E B D is less, the curvature will be greater. MOULDING—PLANE, see PLANE, and TOOLS. MOULDINGS, Raking, see RAKING Moutmncs. MOUTH, in the courts of princes, an apartment consisting of several rooms, as offices, kitchens, 8Lc. where the meat intended for the first tables is dressed by itself. MULLIONS, in pointed architecture, all those parts of windows which divide the light into com- partments, and are either curved or straight. Vertical mullions are called munnions; and those which run horizontally are called transoms. The whole. of the mullions of a window above the Springing of the arch are called the head-work. MULTILATERAL (from the Latin multus, many, and lateralis, sides) in geometry, a term applied to figures which have more than four sides or angles, more usually called poll/gens. MULTIPLICATION (from the Latin multiplicatio) the act of multiplying, or increasing a number. Accurately speaking, in every multiplication, the multiplier must always be considered as a num- ber; and it is easy to conceive a quantity of any kind multiplied by a number. But to talk of a pound multiplied by a pound, a debt by a debt, or aline by a line, Ste. is unintelligible. How- ever, by analogy, in the application of algebra to geometry, we meet with such expressions, and no- thing is more common than to find A B x B C, to denote the rectangle A B C D, the length of which is A B, and the breadth B C. But this is only to be understood by analogy; because, if the number expressing the measure of the side AB were multiplied by the number expressing the measure of B C, the product would express the measure of A B C D. The sign of multiplication mostly used among algebraists, is X. But the Germans, after Leib- nitz, only make use of a point placed between the quantities multiplying each other, thus: a . b is the same as a x b; and A B . BC, the same as A B x B C, or the rectangle of A B into BC. MUNlh‘lEN'lKHOUSE, a little strong apartment in cathedral and collegiate churches, castles, col- leges, or the like, destined for keeping the seal, evidences, charters, &c. of such church, colleges, Ste. called muniments, or miniments. MQUHAEEHNQEfig ‘ PLATE]; A 11:1. L Fly. 2_ 17:37.3. [N ‘ _ ‘ ' 1 \ i l I 1 C , yea 11 112.13.14.15. Ki 1/ lure/we’d N59 I‘ll 14'/ L 01’ ,- . Max:121 Ail/1211771(>1'{LJI'MJ[MI "VWMZJWL. ‘ ”I ” y M US (A C! MYL *— MUNNIONS, see MULLIONS. MURAL (from the Latin murus) something belong- ing to a wall. MURAL ARCH, a wall, or walled arch, placed ex- actly in the plane of the meridian, 2'. e. upon the meridian line, for the fixing ofa large quadrant, sextant, or other instrument, to observe the meri- dian altitudes, Sec. of the heavenly bodies. Tycho Brahe was the first who used a mural arch in his observations; after him Hevelius, Flamsteed, De la Hire, 8Lc. used the same means. DIUSES (from the Greek pout-m) fabulous divinities of the ancient heathens, who were supposed to preside over the arts and sciences. The ancients admitted of nine Muses, and made them the daughters of Jupiter and Mnemosyne, or Memory. At first, indeed, their number was butthree; viz.Melete, Mneme, and Aoede; Greek words, signifying meditation, memory, and singing.- but a certain sculptor of Sicyon, according to Varro, having orders to make three statues of the three Muses for the temple of Apollo, and mis- taking his instructions, made three several statues of each Muse: these, however, were found so beautiful, that they were all set up in the temple; and from that time they began to reckon nine Muses; to whom Hesiod afterward gave names; viz. Calliope, Clio, Erato, Thalia, Melpomene, Terpsichore, Euterpe, Polyhymnia, and Urania. Each of these was to preside over her respective art; Calliope over heroic poetry; Clio over his- tory; Melpomene over tragedy; Thalia over co- medy; Euterpe over wind-music; Urania over astronomy; Terpsichore over the harp; Erato, the lute; Polyhymnia, rhetoric. They are painted as young, handsome, and mo- dest; agreeably dressed, and crowned with flow— ers. Their usual abodes were about mount Heli- con, in Boeotia, and mount Parnassus, in Pliocis. Their business was to celebrate the victories of the gods, and to inspire and assist the poets; and hence the custom of invoking their aid at the beginning of a poem. MUSEUM (from the Greek powuov) originally sig- nified a palace of Alexandria, which occupied at VOL. II. least a fourth part of the city; and was so called from its being set apart to the Muses and the scrences. Here were lodged and entertained a great number of learned men, who were divided into companies or colleges, according to the sciences or sects of which they were professors. And to each house or college was allotted a handsome revenue. This establishment is attributed to Ptolemy Phi- ]adelphus, who fixed his library in it. Hence the word has passed into a general deno- mination, and is now applied to any place set apart as a repository for things that have some immediate relation to the arts, or to the Muses. MUTILATED CORNICE, one that is broken or discontinued. MUTILATED ROOF, see ROOF. MUTI LATION (from the Latin mutilatio, maiming) the retrenching or cutting away any part of a regular body. The word is extended to statues and buildings where any part is wanting, or the projection of any member discontinued. MUTULE, in architecture, a part of the Doric cornice, appearing to support the corona and the superior members, formed by three vertical pa- rallelograms at right angles, and an inclined plane which descends towards the front of the cornice, until it meets the rectangular vertical plane, the inclined plane being the sofiit, and the two verti~ cal parallel planes being at right angles to the surface of the frieze, and the vertical plane on the front parallel thereto. . Mutules had their origin from the ends of rafters in the original wooden structures, and are, there- fore, properly represented with a declination to- wards the front of the corona; though repre- sented by an architect of the last century with a level soflit. See Dome ORDER. MYLASSENSE MARMOR, in the works of the ancients, a species of marble dug near the city of Mylassense, in Caria. It was of a black co- lour, but with an admixture of purple, not dis- posed in veins, but diffused through the whole mass. It was much used in building among the Romans. 3 n ' 386 N. N AI NAILS (from the Saxon nwgl) in building, Ste. small metalline spikes, serving to bind or fasten the parts together, See. The several kinds of nails are very numerous; as back nails, made with flat shanks to hold fast, and not open the wood. Clamp nails, proper 'to fasten the clamps in buildings, 8L0. Clasp nails, or brads, whose heads being flatted, clasp and stick into the wood, rendering the work smooth, so as to admit a plane over it: the most common in building are distinguished by the names ten-penny, twenty-penny, two-shilling, 8L0. Clench nails, used by boat, barge, kite. builders, with boves or nuts, and often without: for fine work, they are made with clasp heads, or with the head beat flat ontwo sides. Clout nails, ordi- narily used for nailing on of clouts to axle-trees, are flat-headed, and iron-work is usually fixed with them. Deck nails are for fastening of decks in ships, doubling of shipping, and floors laid with planks. Dog nails, or jobent nails, pro- 3 per for fastening of hinges to doors, 8L0. Flat points are of two kinds, viz. long, much used in shipping, and proper where there is occasion to draw and hold fast, yet no necessity of clench— ing; and short, which are fortified with points, to drive into oak, or other hard wood. Lead nails, used to nail lead, leather, and canvass, to hard wood, are the same as clout nails, dipped in lead or solder. Port nails, commonly used for nailing hinges to the ports of ships. Ribbing nails, used to fasten the ribbing, to keep the ribs of ships in . their place in building. Rose nails are drawn square in the shank, and commonly in a round tool. Rother nails, chiefly used to fasten rother- irons to ships. Scupper nails, much used to fasten leather and canvass to wood. Sharp nails, much used, especially in the West Indies, with sharp points and flat shanks. Sheathing nails, used to fasten sheathing-boards to ships: the rule for their length is, to have them full three times as long as the board is thick. Square nails, of the same shape as sharp nails; chiefly used for hard wood. Brads, long and slender, without heads, used for thin deal work, to prevent splittinO‘. To NAK these may be added tacks; the smallest serving to fasten paper to wood; middling, for wool-cards and oars ; and larger, for upholsterers and pumps. They are distinguished by the names of white tacks, tam-penny, three—penny, and four-penny tacks. NAKED FLOORING, the whole assemblage, or contignation of timber-work, for supporting the boarding of a floor on which to walk. Naked flooring consists of a row of parallel joists, called floorjoz'sts. “’hen naked flooring consists of two rows of joists, of which, the upper is supported by the under row, all the joists of the upper row cross- ing every one of the under at right angles, the supporting or lower row are called bindingjoists; while thejoists supported, or those of the upper row, are denominated bridgingjoists. “7 hen the ends of binding-joists are framed into each side of a strong beam, such beam is called a girder. There are many curious methods ofjoining timbers in shortlengths; for which the reader, whose curio- sity inclines to investigations of this nature, may consult the subsequent part of this article, from VVallis’s Opera llIathematica, Vol. I. Prop. X. Chap. VI. where he will find the demonstrations relating to the strength of timbers, according to their dispositions and bearings, and where several very ingenious methods of combining timbers in the forms of squares, oblongs, equila- teral triangles, and pentagons, are shewn by that renowned author. Of this species of flooring, Serlio has exhibited a design. Godfrey Richards, in his Paladin, exhibits the diagrams of two floors of this description, executed in Somerset House, which, he says, "‘ was a novelty in England.” Not- withstanding the ingenuity of this method of construction, it has been long out of use, pro- bably, from the general introduction of foreign timber, which furnishes any lengths requisite for the purpose of building. All thejoists in the same floor, to which the board- ing is attached, should be disposed in one direc- tion, as the heading-joints of one set of boards should never meet the edges of another: the strength of the work, however, is by no means 2 rz {4} Nu... z [.1 RATE 1 . v y "6‘. NAKED FLOORING. HATE], fig. 1. NF]. zfljzr—T—HHHQH’QHHHHHHHH iglmz. LJ‘AW'ALJm/meJummLcmM—UULT .Jl 122,. 2. 2m. EM M H H $é H H H H L F137. 2. At" 2 1% jg? |\ z J54? 5a / 1&3]. h’. /)r.\-{}1ne¢/ 111/ lffl’ll'llul-ron. V 6 WI I” men [71/ .l/.xl."\/ll'/m/xvu. LondL'nJ’zl/rlzlrlml 1).” 1’. .1'12‘1201‘wnfi- J. liar/'01:], Wardour J‘trretJfiu . 5’1”"1'“! "’ ' m .x. ¥ HAW w.» NAK 387 NAK to be sacrificed, by a wrong disposition of the joisting, in order to make thejoints of the board- ing parallel to each other; symmetry of appear- I ance being but a trifle compared to the strength of the work. Indeed, the ends of the boards may be made to meet the edges of others under the ‘ bottom edge of the door in each apartment, should such a disposition be necessary. In double naked flooring, when the binding-joists run parallel to the chimney side of the room, the joist nearest to such side ought to be placed at a distance from the breast of the chimney, equal to the breadth of the hearth, with an allowance for the brick trimmer by which the hearth is supported. Floors are constructed by different methods, ac- cording to the bearing of the timber. When the rooms have small dimensions, the floor generally consists of single joists: when large, the framing for the support of the floor consists of two rows of beams, the lower supporting the higher: when the extent is so great, that the lower rows of beams would be too much weakened to support the upper rows and the floor for walking upon, a strong beam, called a girder, is introduced, so as to divide the length of the apartment; or two, three, Ste. are introduced, so as to divide the length into three or four equal parts, as may be required for hearing the timber. The girders thus introduced should always be placed in the breadth or least dimension of the rectangle, or floor. The lower row of parallel beams are called bindingjoists, and the transverse beams, which are supported by them, bridgings, or bridging-joists. The binding-joists are framed into the girder, or girders, and the bridgings are notched upon the binding-joists. Plate I. Figure 1.—A section of naked flooring, without binding—joists, but with a girder, into which the joists that support the flooring are framed, and the ceiling joists into deep joists, which also support the boarding. The end of the girder is shewn in No. l, as also the sections of the ceiling-joists. No. 2, is the transverse section of the floor, showing the sections of the boarding- joists, as also the sections of the strong joists, and the sides or longitudinal directions of the ceiling—joists. Figure 2.—A section of a double floor. No. 1, shows the longitudinal section of the binding- joists, a section of the girder, and the sections of the bridging and ceiling joists. No. Q, shews the sections of the binding-joists, and the longi- tudinal directions of the bridging and ceiling jOISts. When girders are extended beyond a certain length, they acquire a degree of curvature from their weight, which in time reduces them toa concavity on the upper side, called sagging. To prevent this disagreeable consequence, without any intermediate support from the floor below, a strong truss, in the form of a low roof, is intro— duced between two equal beams, so as to make the whole discharge the weight at each extremity. To prevent the bad effects resulting from the shrinking of the timber, the truss-posts are gene‘ rally constructed of iron, screwed and nutted at the ends; and to give a firmer abutment, the braces are let into a groove in each flitch or side. The abutment at each end is also made of iron, and is either screwed, nutted, and bolted through the thickness of both halves, that the braces may abut the whole dimensions of their section; or otherwise the two abutments are made in the form of an inverted wedge, where they are screwed and nutted. These modes may either be con- structed with one truss-bolt in the middle, or with two, dividing the whole length into three equal parts: a straining-piece being placed .in the middle, shortens the braces, and elevates them at a higher angle, so that the truss may give a more powerful resistance to the superincumbent weight. The braces may be constructed of oak,- or of cast iron; the bolts, from their nature, must be of wrought iron. As iron is subject to contraction and expansion, it is less eligible for the braces than wood, which is almost invariable in any degree of temperature, as to heat or cold; oak is therefore generally em- ployed for this purpose. Figure 3.—-—A longitudinal section of a truss- girder, consisting of two braces, meeting the truss-bolt in the middle. Figure 4.—A longitudinal section of a truss- girder, divided into three parts; consisting of two braces, with a straining-piece in the middle. No. 1. A longitudinal vertical section. No. ‘2. The upper side. \Vhen the bearing is very great, the truss would require to be deep, to enable it to resist with greater efi‘icacy: this construction may be as in Figure 5. Figure (Sr—Middle bolt. 3 n 2 NAK 388' W Figure 7.—Abutment, as shewn in Figures 3 and 4. Figure 8.-Washers, to prevent a partial sinking of the nuts. “ T a construct the plain raftering for a floor, by joining together rafters that otherwise would not extend across the given space, so that the whole extent of the area may be perfectly level; and to estimate, by calculation, the pressure upon the whole, and upon the parts separately. “ I. The construction of the tht€ri7rg.—-PLATE II. Let Figure 1 exhibit the square area, any side of which is about quadruple the length of the long- est rafter: the rafters are so fitted into each other as reciprocally to support themselves. The rafters that are dovetailed into the beams laid on the wall, are cut the whole depth of the timber, into the tenon of the dovetail; the mortise for this tenon is therefore in the wall-beam. The other ends of these rafters, each of which is fitted into the wall-beams, is formed into a tenon of about half the depth of the rafter; the mortise for this tenon is therefore, in another rafter, notched to a correspondent depth, so that the upper parts of both may be flush with each other, as will also happen to the lower sides. And because the tenon is but half the depth of the wood, the rafter to which it belongs is supported by half the depth of the rafter in which is the mortise, every rafter carrying the one that is fitted into it; as this is the case throughout the whole extent of the area, they must necessarily support each other over all parts of the area: and the parts towards the middle of the area, where, from the natural flexibility of the timber, the only fear is to be apprehended, lest, by the weight above, the inte- rior of the floor should sink down, have this dis- advantage provided against, by the excavations not extending precisely to the middle of the tim- ber, but being a little deficient towards the middle. For, as by this method the raftering will rise progressively with each joint from the exterior to the centre of the area, any small depression that, from the weight above, might take place, will not be sufficient to reduce it below the fair level throughout; the curvature produced on the whole will compensate the weight, and prevent any hollow taking place. “ Figure 2, exhibits the side face of one of the longer timbers; where the end tenons and mor- tises, at one-third and two-thirds of the whole lengths, are sufficiently well exhibited: and NAK Figure 3, shews one of the shorter timbers in that View which, offers the end tenons and the single mortise. The upper face of all the rafters appears very plainly from Figure 2. “ But since they are disposed in so compact an order in this last-named Figure, the process may be much more easily understood from a close investigation of the diagrams than it can be from any explanation. “ It is very obvious, that the four great beamslaid upon the wall are the first with which we ought to begin; for we would naturally proceed from these principal beams to the secondaries or rafters. Now, if we examine these principal beams, we shall find, that into each there are dovetailed five rafters or secondaries, and these have their other ends supported by other rafters parallel to the wall-beams; and those which carry the rafters dovetailed into the wall-beams, are themselves supported by others in a transverse direction; and so on, till they arrive at the opposite wall. “ For example, the rafter 8y S has one end dove- tailed into the wall-beam, but the other end is supported by the rafter 8;Z; this last rafter, 25‘ Z, has one end dovetailed into another wall-beam, but the other end, Z, is supported by the rafter P Q: and the rafter U Y has one end dovetailed into the wall-beam, but the other end, Y, is carried by P Q in the same manner as 8; Z: PQ is sup. ported at P by IK, and at Q by RS: but IK and RS do also support the rafter ON, which in its turn supports the ends F M, of the rafters FE, M L; H M L supports RX and V W; then we have determined the support of B, one end of the rafter S R; and V W supporting V, the end of the rafter V U, we come to V U supporting H G and I K: but the end, U, of the rafter VU, is supported by Y U; Y is supported by P Q, and PQ supports also &Z, and is itself supported by SR: but S R is supported by RX and SSr: and thus we trace round the exterior framing, and discover the aid which these rafters reciprocally lend each other, to render the whole secure and compact. For if we follow the concatenation, we shall discover, from the slightest inspection of the diagram, the principle upon which, in regular succession, the parts conduce to give strength to the whole. In the same manner, when we begin to trace, frOm the centre of the framing, every rafter, A B and C D are supported by AB and EF; and also from these we trace NAKEB FLOGRING. PLA '1 'I' II. lv‘qul. | “ ’—"' T i '. Q 0 ‘ H K s s — R vii ——‘—‘_ U 3c . 1 L J J 2 E L P ‘ 1 Q x~ w Y 2 U D B F “ Y F * ~ , E N _, 1 o _ 4 K I C E D X 1 . P N G I R L E C V E: G A A B w 529.5. C 1w B A G H \ v c A E L R I G N P ‘ X D m JC‘ I fir K ( \ l 0 N E ’ —“ F Y M F B D ‘ U i 1 2 Y w X 1 ‘ 3: i Q 'lP L ‘ r “’M z fi:——‘,—L___j I, f t 1 1 ‘ i ‘ l \ . KC U ” fv R L ‘5 l s K 11 0 Q * 7 ' J [537 t) 4" ') 115/.-. _._l V i‘ V —1 .. (1 A L M I 1'15]. 3. 14%}1. 7. P M [ I I L x x P [1 _ i L A "" 4 . ‘ 3 "fi ‘. l , P I [ a H e 1 ,, . l , Q R F B F x3 ' Q I P J/ iE C A 5: E E 7__ l fl 1 V g ,3 F B F \R Q r —T T - 7 n: R K B K ,5 7; F p [1. I H (I 4‘1 ‘ 8 [ / T 6 i l \ N 1 D H N 1, ~ [I P x I L x M P —* T r A A M L X {l v 2 - v Jami/1 111/ 11d,.’Vzl-Izo[wrz. Ellf/I'thr’d by ll.’ dowry. lvmlon, Puélzlr/Ird by If J’zl'lwlwn X‘ J. liar/'z'r/J, 11 IInlnur Java, 1191;. l!‘ , x / ‘ ‘ .w—mmw w (I grew «M+uw9_ '1’ msw/ NAK 389 - ‘ - LM, G H, and N O, reciprocally supported and giving their support; and following the others that are connected with those now named, we go on till we arrive at those which terminate, and are supported by the principal beams on the wall; as clearly appears from the plan. “This method enables us to constructa floorscant- ling of this description with many, or even with few rafters; but in any other method, as in the case of an oblong differing but little from a square, we shall have to employ the following conditions : “ For example, in this same case the whole wall can be laid out, so that the rafters R S, U V, and 8:8 brace, and are themselves braced; or, where the rafters 8; Z, M L, and P Q, are braced by others, or themselves are bracers; whence the area is extended less widely, as by the paucity of the rafters it extends from wall to wall by the rafters S 15‘, Q P, U V, L M, R S and Zdyz but so long as there is occasion for only four rafters, the construction may be similar to Figure 4, or even of only three, as in Figure 5, which is the most simple form of any. “ But even if there were occasion (Figure l) the rafters X R, W V,(and the remaining shorter ones that terminate in the wall) might be produced to an equal length with the others, and would sup- port the corresponding rafters parallel to the principal beams, in which are fixed X H, V W, and Y U; and thus the ends of these, continued, would either be supported by the beams lying upon the wall, or even by others, as far as the area is extended, parallel to ML and PQ; and so on, to any distance that the work may require. For in the continued area, the number of the rafters being augmented, the weight may be in- creased to as much as the walls are able to sustain ; for rafters may be found that will not give way, nor break under any weight the walls will carry. “ But although we are able to proceed safely in this regular proportion, it is from calculation that we'must discover the weight which such a piece of framing will bear. For if it appears, from the quantity of weight laid on, that the rafters will every where bear it, then as much of the weight as any situation, or place of the area, has laid upon it, being in like proportion also laid on another, it becomes regularly and fairly distributed over the whole; and hence is the bestjudgment formed of what may safely be done. The calcula- NAK 4' E tion when the number of timbers is few is pretty easy; but more laborious where there are many. “ But i shall shew by what method this may be effected; each rafter of the continued framing, joined to its fellow, is subjected to this calcula- tion; perplexed in a manner, it is true, from their number, but producing the result much more rapidly where there are few rafters. “ Calculation accommodated to the rafierz'ng now explained. _ “ That the calculation delivered in the following synopsis may be more clearly understood, it is to be observed, as is indeed sufficiently indi- cated to the eye, that some of the rafters are longer than others; and that the longer are about one and a half of the shorter ones. On this account we shall designate the weight of each of the longer rafters by T; and that of each of the shorter by % T. “ But the weight upon every one of the joints of the rafters, will be indicated by the letter written on that joint in the diagram. “ Let it be moreover observed, since it may tend to elucidate our subject, that there are always four points which, on account of their similarity of situation in regard to the whole framing, equally determine the weight laid on them: these we shall always designate by the same marks, lest the number of the symbols should increase, and the calculation be thereby perplexed. Hence we shall have four A’s, similarly situated and equally loaded, the same number of B’s, and so on with the others. VVhence it will be, for example (to No. 2 or the following equation) B =% T + 13- C + .1. A; in the same way, also, if the point, B, of the rafter, A B, thus subjected, be said to sustain as much weight as is laid upon it; besides that firmness which is necessary to prevent the wood giving way from the weight it carries, as this equation does not involve it; so much then is a T (one-half of the weight lying on A. B, one of the longer rafters); then 33- C (two-thirds of the weight of the same A B, situated on the point C; seeing that in C, A, it is understood to be cut in three different ways by the points); then éA (one-third of the weight of the same rafter A B is placed in A.) VVhence also there will be (to No. 21.) W =%T + is V: here we discover that in the point W of the rafter L M, the weight placed upon it is as much as is J‘s-T (one-half of the weight of the short rafter, which is also a NAK 390 NAK third ofthe longer one); then is V (one-halfof the weight, which is placed over the middle point, V, of the rafter so lying upon this one); which, by similarity, enables us to obtain twenty-five in the first equations. “ The equation 26, and those which follow, are derived from the preceding, which we have cited by numbers written for those equations; whence the manner of the whole process may be more clearly deduced. These partly serve for abbre- viating fractions, as often as the numerators and denominators may be divided by the same com- mon measure: but their most essential use is, to reduce and explain the preceding equations, by Substituting the value of every individual symbol, and explaining it by other marks, on which ac- count, as often as any symbols are expunged, the number of those which remain is sensibly lessened, till at last some one of the symbols unknown from the beginning, is expressed by the known quan- tity T, the weight of the longer rafters, consi- dered simply by itself; and then, by examining every step of the preceding equations, the values of the remaining symbols are also found first of the unknown weights. “ For example, when there is (No. 1.) A = 5% T + 33’. A + .3. C (on account of A being found on both sides of the equation) it is manifest, that on taking away % A on both sides, there will remain %-A = % T + g C; that is (by multiplying both sides by 3) A =g T + C; and thus we have (No. 26.) this equation, as derived from the first equation (No. 1.) and which we have cited. “ By similarity, since it may be (No. Q.) B = a T +—§- C + g-A; and (by No. 26) it may be A = g'l‘ +C; and so §~A=§T +-§-C; B will be (= T+%C+%A=%T+%C +%T+%C) = T + C. VVhence we have this equation (B: T4- C) No. 927, as derived from No. 2 and 26. And in like manner for the others. “ But, at no time, as we have said, is there more than one abbreviation ofthe fraction, as a reduction to less results by a common divisor. As when (N0. 64) we have H_6912T+672G +5521+e790 ”‘ 9907 = 3 x 969 all the members can be divided by 3; we have No. 65 (as derived from No. 64) the equation 2304149246 +184I+930 H = 696 ; and then ; and so for others. “ But as all these‘reductions and abbreviations of the equations are deduced singly, as we have deduced these few, we shall here briefly express them all in a continued synopsis; indicating those antecedent equations upon which the other depend. “ SYNOPSIS OF THIS CALCULATION .-—Figure 1. No. 1.A=%T+gA+§C. 2 B=%T+§C+§A. 3 C=%T+§.G+§L 4 D=—§~T+§l +§G. 5.E=%T+§B+%D. 6 F =§T+§D+§B. 7.G=%T+§E+§L. 8.H=§T+§L+§E. 9.1 =%T+§N+1§P. 10.K=%T+§P+§N. ILL =§T+§W+§X. 12.M=%T+§X+%W. 13.N=%T+§F +13M. 14.0 =—;—T+§.M+-§F. 15.1) =.;_'r+§Y+§z. 16.Q =§T+§Z +§Y. 17.R=%T+§O+§Q. 18.8 =%T+-§Q+§O. 19.V =%T+§H+§K. 20.U =§T+§K+§H 21.w=;'r+%v. 22.X=13T+éR. 23.Y=§T+%U. 24.2 =3.T+§&:. 25.&=1,'r+%s. 26. A = g'l‘+C,by No.1. 27.13 = T+C,byQ,26. 28.13 =gT+§G+§I,by27,3. 29.13 =10T+59G+41’by5,28,4. 30. F =anaaea 31,W=fli‘_‘:g_Hii15,by 21,19, 32 X = me 22.17. 33. Y = Wwwam 34. 8: = W, by Q5, 13. ,. 35.2 =Lfl—‘l;2_9i9_Q, by ease. ,. " o 36.L=39T+8H+26K+40+2Q,by11,31,32. 37. M = wild- garage—3.9, m12,31,32, n . 33.1) =39 if + 4 H t: K + O + 2 Q,by15, 33,35. 39. Q =20T + 11+ 91: + 0 + 2 Quby 16, 35,35. 40. Q =2l‘ifl171fl, by 39. 41. N = 94.}.‘1‘+ 16 G +9 H + «201 + K + 40 + 2Q, by13,30.37~ M NAK NAK 391 —"'""" 1 , l W 4% 0 =45T+ 46 + 2 H +251 + K + 40 +2 Q, 1,3,14,30,37. 74. G = 215610T +3123: + 30393 I, by 73. 43. 0: 451' + 4 G + 2 [:34- 5 I + K + 2 Q by 4% 75. H =6917568T4962629297567:222:81:23+ 565563 I,by65,71. 44. G = 213 T + 40 G + 3H 1:2 I +4K+40 + 2Q,by7,29,36. 76. H = 69175:: 416 $463116? :1 $523563 I, by 75' ‘45. G =213T+8H+32162— 4.K+40+2Q’by44. 77. H: 1030371‘ +lfgigG+8837I by“ 46. H = 43 T + G + 4 H +2171 + 2 K + 2 o + Q,by 3, 29, 36' 73. I = 15437200 ngfiogjlgfgjfggsfl-f95330 I, by 63,71. 47. H = 43 T + 5 G + 412-;- 2 K + 2 0 + Q, by 46. 79. I = 1543722201; $812055: G4;3.:13216 H, by 73. 43.1 =6581T+GIG+20H+SS4I+28K+190+14Q by9,33,41. 30. I = 161.325 '1‘ + 11:22.26 + 5346 H, by 79' 49. I =653 1 T + 61 G + 201914;}- 23 K + 19 O + 14 Q by 43 31. G ___ 9309571641230) 1‘ :— ffgfztogs-i—Ggigimss‘s I) by 74, 77. 59' K: 291T+IGG +14}! i620 1+ 95K+70+8Q why“) 38’41' 82' G = ::::::;::::16l—2:395109431363423’ by 81' 51.K= 294T+16G+1»1.II;7-|—201+70+3Qby 50. 83.G=658901::890711,by83. 52. G=1724. T + 65 :1 x+6:o:15;: 34 K + 33 0 by 45‘ 4o. 34. I = 724717765382 iii—1 2:354:32: $1122842602 I, by 80’ 77' 53.11 ==++o,., .2. =2222222222222222222223s4 54. H =733 T+ 30 G + 2371 + 34 K + 32 0’ by 53. 86. I _ 4331561'Egéi9306 G, by 35. 56 K: 608T + 3261;232:4373? 2K + 15 O: by 51: 40- 88‘ I = 1562727913:9:::991Tx 340167’ by 87‘ 57.K= 608T+32g§jii€4401+150by56' 89.I =%?fg—:T. by33. 53 0_ =330T+32G;|—31;18{:;1§:+ 10K+ 0 “43,40. 90. G =2:_:__:::z: T.by33,39. 59. 0—_—. 380T +32 G +1153“ + 40 I + 10 K, by 53. 91. C = 243% T. by 3, 39, 90. 60. G = 14400 T + 32:4:x5:9:4—;—5:033 I + 279 0’ by 52’ 57. 92. D =2::_:_—0::; T by 4 39,90. 61. G = 1440” 4:12:21: 33’ 33:01 + 279 0 ,by 60. 93. B— = 2:13:23? T. by 27, 91. 62. G = 1600T+ 611:; 2’2 1+ 31 O by 61. 94 = 512.53%; T.by 26. 91. 63. H= 691” + 67:: :59f2:6552 I + 279 O ,yb 54, 57. 95. =%% T. by 5, 92,93. 54.. H =69” T +233: it :53619"' 279 O ,by 63. 96. F = gfig T. by 6, 92, 93. 65. H = 25°" T + 924 (36'3“ 184 I + 93 O, by 64. 97. H = 3%? T. by 77, 39,90. 66. I = 47520 T + 43123;: 25:91:;12801 + 13770, by 55, 57. 93. 0 = %T. by 71,39, 90,97. 67. I =475‘0T +123226 31:32:; + 1°77 0 ,by 66. 99. K =1%’1—2% T. by 57, 39, 90, 97, 93. 63. I =1760 H” 160 (:6: 57 H + 51 O ,by 67. 100. v = 2—3—2323 T. by 19,97, 99. 69. o =54720 T + 4235:3114: iggé‘m'l‘ 75 O, by 59,57. 101. U = %51:5’1—2: T. by 20, 97,99. 70. o = 54720 T 2:21; G _tfgfil + 5640 I b,y 69. , 102. w .-= 1:32: T. by 21,100. ., =‘824°T222°:2::222 - Y =32-2—22: 1...... 72. G =.1:3799010 T:::6:4837-§1-.:9:::OI:$1977152 I,by 62” 71. 104. Q = 322%? T. by 40’ 97:93, 99. 73. G =137990:g;g:2=9::0;15:315:71” I,by-72. 105. R =%§f% .T,by 17, 98, 104. ’92 NAK NAK 1337898 106. S -—*34h{6‘% T. by 18, 98,104. 976759 107. X —- m T, by 22, 105. 807338 . =—-——— T.b 25 106. 108 8‘ 340167 3' ’ 517058 . , _-_—_ .— T.b 24 108. 109 z * 340167 y ’ , - I. 110. L =MTJ>y 11,102,107. 340167 1201827% =_.___ .b 12 102,107. “LM 340167 T y ’ 112. N =24‘8926 T. by 13, 96,111. 340 1 67 113. P =19fl§§§ T. by 15,103,109. 340167 “ OR THUS, IN ALPHABETICAL ORDER. 27191 194583§,r A = - — ' 340167 340167 ~ V0“891 B .. a 19723§§tr. P __ O a o#_, “ 340167 340167 1 198678 C = 7 197274, T. Q _ 9 34016731" 340167 I)-—- 7 629255 T. 1} __ 5 ZEEEEB T. " 340167 040107 209186 T 5 == _?ZE§9 T. E = 8 3261—677 ' ' 340167 15728 " 340167 340107 161540 T 1; == 5 ?EZZEE 1; G = '7 m ' 340107 3 121253 H = 5 £3,971; T W: 3 EE— T’ 340167 0 167 296405 I 6 33929 T X = 2 7—— T. 340167 $40167 7 170 K __ 4. ”92% '13 Y = 3 :L T. 340167 040167 . 176891 L—3?—3—6-i3—1éT. z=1a—.- T. — 340167 040167 1.. L 1970041 31:39.32—62'1‘, &=2;20—‘—-T. 340167 a 167 77757 N = _"__- 7 340167 “ All this weight lying on the building, or wall, is not necessarily distinguished by a distinct calcu- lation; because those evidently correspond with others which are situated in the ends of their re- spective rafters. For example, when the rafter X R does not rest exactly upon its middle, the fulcrum, whether it sustains one-half the weight of the rafter at X, and the other on the wall, then also the half of the burden is placed at R. “ It is obvious, from this calculation, that thejoin- ings about A, toward the middle of the framing, press most of all. Since the particular weight of these is about nine of the longer rafters (but of the others, less by a ninth part of the wood) to each of which there will be added, half the weight of the rafter for firmness deducted, lest by its own weight it should break, and moreover one-half of the weight of thejoint C lying upon it, being about four of the rafters. And so, by computing the whole, the strength requisite, lest a rafter should give way, will equal more than thirteen times the weight of the rafters, and be . 97191 394549 about fourteen times 9 340167 ~13606fi§_ 0 503313 __ 0167771, h . . 13 W68 — 10453556' t e computation “1 weight of each rafter. “ N o doubt can now remain that the rafters, even the longest, can be made of such firmness as shall enable them to sustain any weight that may be placed upon them individually to fourteen times the weight of the whole; neither can it be doubted, that raftering of this description is the safest that can possibly be applied to purposes where great weights are to be carried. “ Another form of this construction. Figure 6 exhibits another form, differing from the preced‘ ing in this, that where the ends of two of the rafters lie upon a third, they are joined by two distinct dovetails; into these a third rafter is notched, and all are so placed as to be supported by those parts: hence to the middle part of each rafter are fastened two others, but to opposite parts. “ Figure 7 exhibits the lateral face: the upper face is sufficiently obvious from Figure 6. All these rafters are of an equal length, and similar among themselves. But here, as in the preceding construction, the work may be more or less extended, and the con- dition of the timber will be equally determined both as to the aid it gives and the weight it will carry. For, as in the protracted area the number of the beams is augmented, so is also the weight- But this construction is attended with a disadvan- tage from both the beams’ weight lying upon one, which having to endure the burden on an indivi- dual part of the beam, it is more strenuously pressed: that is, it has to sustain the entire Weight of two ends, one entire beam; for, in this con- struction equal to that of the half, which in the preceding was not borne, is here to be supported at one and the same point; on this account, also, the wood at that mortice is very much weakened, 3 NAK 93 NAK by being cut away to enable it to support the two beams, which rest their tenons in one place. This in some measure seems to be compensated by the resting timbers being placed towards Opposite parts, which in the preceding construction lay to- wards the same parts; although, in this also it is not of much consequence, especially if the ends of the beams, resting on the others, are not ex- tended toward the centre, but kept pretty close to the outer part of the framing, which is easily doneby the judicious management of the archi- tect. “ But this inconvenience forms no substantial ob- jection to the plan, since the rafters are sufli- eiently strong and well joined to support any proportionate weight, as will be obvious from the snbjoined investigation of their strength. “ In looking at what is before us, the former of these figures seems the stronger, because the tim- bers are so disposed that the workmanship is more obvious to the eye; while in the latter it is scarcely distinguishable, and the intervals are so varied as to give the work a distorted appear- ance: yet in both they are squares; and in the latter the spaces beyond the half—rafter from the wall-beams are also resolved into the same figure. “ The calculation in this construction, will result from the same principles as in the preceding; but here it will be much more expeditious, be- cause, as all the timbers are of the same length, and they support the weight of the corresponding timbers about the centre, they are almost all pressed by an equality of weight about the same part: all which conduce to render the results more readily to be obtained. “ Calculation adapted to this construction. “ With'respect to the facility of this calculation, it may be observed, that the points (whether five or four) which are similarly posited in respect of the scheme, and on that account support an equality of weight, are designated by the same symbol that was adopted in the preceding pro- blem. But, here, on account of the individual pieces of wood supporting the same weight, and that too about the same part, the two ends of each rafter have to support the same weight; these ends we shall therefore express by the same symbols, the equal weight being denoted by a similar sign. Other methods of proof might be mentioned, but the foregoing will be. sufficient for our purpose. VOL. II. " SYNOPSIS OF THIS CALCULATION. 1-A=u=%T+B. 2- B =B=%T+%K+%Fo 3.C=%T+A. 4-D=3‘=%T+L. ‘5-E=e=s'r+se+s8- 6.F=%T+—§_—C+%G. . 7.G=7=%T+E. &H=%T+8a+8v. 9' I =‘=%T+%s+%N 10-K=x=%T+%H+%L 11. L=A=§T+ém 12. M=M=%T+§P. 13. N=v=%T+%A+7§-l‘i. 14:.P=7r=%T-|-%t. 15.Q=%T.+%‘y. 16-R=e=%T+—%w+%Q. 17. C=T+B,by3,1. 18.D=T+%7‘,by ,11. 19. F =gT+§B+%E,by6,7,17. 20. H =§T+%B +§x,by8,1,18. 21.M=%T+%i,by12,14. 22. N =T+%K+%P.by13,11.12. 23.N =~§T+§u+§t,by22,l4. 24.Q =g-T+%E,by15,7. 25. R=%T+7}E+%i,by16,14,24. 26.B=%T+%B+}T ‘+%K,by‘2,19. 27.B=9T+2:+4K,by~26. 98. E =§§T+§73E+§I+§K,by5,25,27. 29‘ E =W,by QB. 34 30. H =2T+16E+1J§K,by20,27. 31. I =%%T+%E+j%l+%x,by9’23c _ 17T+8£+2K " - —— ,b 31. 02 I 15 y 33 K = fiT + ,7, E + ,4;,K,by 10,30,32. ‘48 '1‘ 42E . 04. K = 2 7-;- ,by 33. - 361T +14oE , 30- I —————-3 X 77 =231.by 32.84. 11389 T+ 952 E , . =———————.b 29 34, 33. 36 E 34x77=2618 3’ ’ 1527 '1‘ + 156 E n =————— b'36. ”7' E 34 x 11-—"-s74’ 5 38. E =14}; (1‘, by 37. 39. G = 1,73% '1‘, by 7, 38. 40. Q = gas 1‘, by 15, 39. 41. K =1,6;g T, by 34,38. 42. L =54, T, by 11,41. 43. D .—= 12534; T, by 4, 42. 44. B =99; T, by 27,38,114. 45. A = 2,323.1 T, by 1,44. 46. C =25? 'r, by 3, 45. 47. F =2;—;,2 ’1‘, by 6, 39, 46. 48- H = 1573132 ’1‘) by 8) 4‘3) 45- 49. I = 151.31; T, by 32,38, 41. 50. P = gggT, by 14, 49. 51. M = 554%1‘, by 12, 50. 52. N _-= 42g”, by 13,42,51. . 53- R =12031§4 T, by 16, 40) 50a l NAK l THAT IS, IN ALPHABETICAL ORDER, A =sgggr. I =5rggr. B _8,2,8,T K=6gggT C _9,2,a,T L =3%3%T 13:4,51‘. M=2ig2§T 13:61,;31’. N =3;_;.gT F=8§€§ P=3§34sT G =7§8§OET Q=454318T H =7g3'r R =4,§,§T. It appears from this calculation that the greatest . . ‘21 0f the separate weights Will be A = 8 “2—3.; . When therefore upon this point (C C in the middle of the wood) therelie two A’s (on both sides) it is 17 {2%ST; and so on, in like manner, lest any rafter give way by its own weight. VVhence one—half the weight of the timber is determined. The strength requisite there, is the same, lest that beam give way, which is equal to the weightof the respective beams 217 217 1 i 77 11 __ *— ~=18—-——-= 18—0 8238 +8231+2 238 34 But indeed this weight is not so great as to oc- casion any apprehension for the strength of the timber; for even if the timbers be pretty long, they are sufficient to bear any weight that may be laid upon them, to eighteen, or even to nineteen times their own weight. “Here the weight is indeed heavier than in the preceding case; for there, the pressure amounted only to fourteen times the weight of the timber. “ In the mean time, the conditions ofthis construc- tion dispense with a multiplicity of rafters, as the length of the area within the walls extends to twelve times the length of the whole, the length and breadth of the rafters remaining. For in this case the rafters being joined are equal to 49, but in the other the longer are 40 and the shorter (2.0.” NAKED or A COLUMN, OR PILASTER, the sur- face of the shaft or trunk, when the mouldings are supposed to project. Thus we say, a pilaster ought to exceed the naked of the wall by so many inches, and that the foliages of capitals ought to answer to the naked of the columns. 394 m NAKED OF A WALL, the remote face whence the NBC projectures take their rise. It is generally a plain surface, and when the plan is circular, the naked is the surface of a cylinder, with its axis perpendi- cular to the horizon. NAOS or NAVE (from the Greek mag, a temple) the chamber or enclosed apartment of a temple. The part of the temple which stood before the naos, comprehended between the wall and the columns of the portico, was called the pronaos: while the corresponding part behind was called the posl‘icum. ' NATURAL BEDS, of a stone, the surface: from which the lamina were separated. It is of the utmost consequence to the duration of stone walls, that the lamina: should be placed perpen- dicular to the face of the work, and parallel to the horizon, as the connecting substance of these thin plates, or laminae, is more friable than the laminae themselves, and consequently liable to scale off in large flakes, and thus reduce the work to a state of rapid decay. NAVE (from the Saxon an) in architecture, the body of a church ; or the place where the people are seated; reaching from the rail or baluster of the choir to the chief door. The ancient Greeks called the nave pronaos; the Latins frequently call it cella. See NAos. The nave of the church belongs to the pa- rishioners, who are bound to keep it in repair, 8Lc. NAUMACHIA or N AUMACHY, (from mug, ship, and [taxmfightfi a spectacle, or show, among the an- cient Romans, representing a sea-fight. NAUMACHIA is also used, by some, for a circus en- compassed with seats and porticos; the pit of which, serving as an arena, was filled with water, by means of pipes, for the exhibiting of sea-fights. There were several of these naumachias at Rome: three built by Augustus, one by Claudius, and another by Domitian. Nero’s naumachia was stamped on the reverse of his medals. NEBULE (from the Latin nebula, a cloud) an ornament of the zigzag form, but without angles. It is chiefly found in the remains of Saxon ar- chitecture, in the archivolts of doors and windows. NECK, of a capital, the space between the channe- lures and the annulets of the Grecian Doric capi- tal. In the Roman Doric, it is the space between the astragal and the annulet. The rich Ionic capitals of Minerva Polias, and Erechtheus, at Athens, have neckings. But NEW — ‘— ' most other antique examples of the Ionic order are without them. NEEFS, PETER, in biography, a painter of ar- chitecture, and a disciple of Henry Steenwick, born at Antwerp, in the year 1570. He was par- ticularly skilful in perspective, and generally chose such subjects as required a considerable display of that science; such as the interior of churches, splendid halls, Sic. These he drew with great neatness and effect, and painted very clear, gay, and agreeable, but he never equalled the truth of his master. His execution of the mouldings and masses of columns, in the various Gothic works which he chose as models, is too neat, and too much made up of lines for real imitation; but that very defect gives them lightness; and the truth with which he drew the forms of the build- ing, and pr0p01t1oned his figmes, which we ve1y freely wrought, though not unfrequently by other artists, renders them very agreeable. Van Fulden, Teniers, and Breughel, were often called upon to assist Neefs, and by their skilful execution made amends for his want of knowledge of the human figure. He died at the age of 81, leaving a son, whose name also was Peter, and who is denomi- nated tile Young, in contradistinction to his father, whose excellence in the art of painting he never rivalled, although he had the advantage of his ex- ample and instruction, and practised in the same branch of the art. NERVES, in architecture, the mouldings of the groined ribs of Gothic vaults. NET, or RETE, (from the Saxon net, derived from the Gothic nati) the covering of a body or geo- metrical solid. See ENVELOPE and SOI‘FIT. NET MEASURE, 1n building, is when no allowance is made fo1 finishing; and 111 artificers’ wo1ks, when no allowance 15 made for waste of materials. NET MASONRY, see MASONRY and STONE WALLS. NEVVEL, in architecture, the upright post which stairs turn about; being that part of the staircase which sustains the steps. The newel is, properly, a cylinder of stone, which bears on the ground, and is formed by the ends of the steps of the winding-stairs. There are also newels of wood, which are pieces of timber placed perpendicularly, receiving the teuons of the steps of wooden stairs into their mortises, and wherein are fitted the shafts and tests of the staircase, and the flights of each story. 395 NIC NICHE(from the Italian niechia, shell) in architec- ture, a cavity, or hollow place, in the thickness of a wall, to place a figure or statue in. Niches are made to partake of all the segments under a semicircle. They are sometimes at an equal distance from the front, and parallel or square on the back with the front line; in which case they are called square recesses, or square niches. The larger niches serve for groups of figures, the smaller for single statues, and sometimes only for busts. Great care mustbe taken to proportion the niches to the figures, and the pedestal of the figures to the niches. Niches are sometimes made with rustic work. Few niches are to be found in Grecian antiquity, but what may be supposed to have been erected under the dominion of the Romans. In the Pantheon at Rome, the niches are all rect- angular recesses, dressed in the same manner as the apertures of doo1s , the columns are insulated, and the entablatures crowned with triangulai and cilcula1 pediments altelnately. The large niches, or exaedrae, on the sides, have cylindrical backs, but finish at top with the 50th of the archi- trave of the general entablature; these niches have each two columns placed in the aperture which supports the architrave. The entablature ~is continued without any break or interruption of recesses, except by the large cylindro—spherical niche opposite the entrance, and the side through which the entrance is made; but neither of these are supposed to have been in the orginal edifice, but to have been introduced at some later period. The large niches on the exterior side within the portico are cylindro-spherical, without any dress- ings. In the remains of the piazza of Nerva (see Desgodetz’s Antiquities (fRome) a niche is exhibited upon a circular plan, with a rectangular front and Cylindrical head in the middle of the attic, over the intercolumns; the axis of the cy- linder, forming the head of the niche, is horizon- tal, and parallel to the naked of the wall. This niche is surrounded with an architrave, standing upon the base of the attic, which projects to receive it, and the head ofthe architrave supports the crowning of the attic. The Ruins of Palmyra, by Wood, exhibit niches of various kinds, some of which are very fan- tastically dressed. The inside of the portico of the temple of the sun has two niches, one on 3 E 2 NIC 3 JJ each side of the doorway, with cylindrical backs, terminated at the head with spheroidal tops, which shew an ellipsis on the face with its greater axis horizontal. These niches are decorated with four attached columns, whose axes are placed in the surface of a cylinder: the entablature over the columns terminates under the spheroidal head; the head is decorated with a shell, and surrounded on the front with an elliptic archivolt upon the face of the wall. See Plates VI. and IX. of the Ruins of Palmyra. The inside of the portico of the court of the same edifice, shewn in Plate XI. exhibits two niches on each side of the doorway, which termi- nate on the front in parallel lines, and with a semi— circle at the head ; they finish with a pilaster on each side: the capital, which is Corinthian, serv- ing as an impost to the archivolt surrounding the head. Besides this dressing, a column is placed on each side, attached to the wall, so that the distance between the insides of the columns is greater than that between the outsides'of the pilasters; the architrave of the entablature rests upon the archivolt of the head of the niche. The inside of the court of the great temple of Balbec exhibits niches dressed in the most whim- sical manner; the sides of the niches terminate with the wall in vertical lines, and the head with the said wall in a semicircle. The sides finish with Corinthian pilasters; the entablature is horizontal over the pilasters; but the architrave and cornice are carried round the semicircular head of the niche, which appears to be spherical within, being. decorated with a shell resting upon an impost, and corresponding in its situation to the height of the capital on each side. The inside of the temple of Jupiter, at Spalatra, is decorated with niches, one between every two columns; the one opposite the entrance, and those on each of the two sides, are rectangular below, but finish with cylindric heads: the axis of the cylinder, which forms the head, is parallel to the horizon, and in the direction of radii which be- long to the cylindric wall, in which these niches are placed. The other four niches are cylindro-spherical ; that is, they have cylindrical backs, and are terminated with spherical heads. All these niches are deco- rated with an impost, continued from side to side, and the heads are furnished with archivolts. In the pointed style of architecture, niches are 96 NIC fr sometimes highly decorated. The back very fre— quently consists of three sides ofa hexagon, and the head is terminated with a rich canopy, form- ing a complete hexagon with the interior; the under part of each of the three projecting sides of the canopy has a Gothic arch, and the soffit represents a groined vault, decorated with tracery and ribs in the most beautiful manner. The bottoms of these niches are formed by a table of the same shape as the head, and terminate below in the form of a pendent. The ceiling of the canopy represents the groined roof of an hexagonal building in miniature, as some of the highly decorated chapter-houses exhibit; the top of the canopy finishes with bat- tlements; and the vertical angles are sometimes finished with pendent buttresses, which are sur- mounted with pinnacles elaborately finished with crockets. NICHE, in carpentry, the wood-work to be lathed over for plastering. The most usual construction of niches in carpen- try, are those with cylindrical backs and spherical heads, called cylindro—sp/zeric niches; the execu- tion of which depends upon the principles of spheric sections. As all the sections of a sphere are circles, and those passing through its centre are equal, and the greatest which can be formed by cutting the sphere; it is evident, that if the head of a niche is intended to form a spherical surface, the ribs may be all formed by one mould, whose curvature must be equal to that of a great 1circle of the sphere, viz. one passing through its centre: but the same spherical surface may be formed by ribs of wood moulded from the sections of lesser circles, in a variety of ways ; though not so eligi- ble for the purpose as those formed of great cir- cles; because their disposition for sustaining the lath is not so good, and the trouble of moulding them to different circles, and offorming the edges according to different bevels, in order to range them in the spherical surface, is very great, com- pared with those made from great circles. The regular dispositions for the head of a niche are the following: The ribs of niches are generally disposed in a vertical plane, parallel to each other, or intesect— ing each other in a vertical line. When the line of intersection passes through the centre of the sphere, all the ribs are great circles; but if the NIC 3 H each side of the doorway, with cylindrical backs, terminated at the head with spheroidal tops, which shew an ellipsis on the face with its greater axis horizontal. These niches are decorated with four attached columns, whose axes are placed in the surface of a cylinder: the entablature over the columns terminates under the spheroidal head; the head is decorated with a shell, and surrounded on the front with an elliptic archivolt upon the face of the wall. See Plates VI. and IX. of the Ruins of Palmyra. The inside of the portico of the court of the same edifice, shewn in Plate XI. exhibits two niches on each side of the doorway, which termi- nate on the front in parallel lines, and with a semi- circle at the head ; they finish with a pilaster on each side: the capital, which is Corinthian, serv- ing as an impost to the archivolt surrounding the head. Besides this dressing, a column is placed on each side, attached to the wall, so that the distance between the insides of the columns is greater than that between the outsides'of the pilasters; the architrave of the entablature rests upon the archivolt of the head of the niche. The inside of the court of the great temple of Balbec exhibits niches dressed in the most whim- sical manner; the sides of the niches terminate with the wall in vertical lines, and the head with the said wall in a semicircle. The sides finish with Corinthian pilasters; the entablature is horizontal over the pilasters; but the architrave and cornice are carried round the semicircular head of the niche, which appears to be spherical within, being. decorated with a shell resting upon an impost, and corresponding in its situation to the height of the capital on each side. The inside of the temple of Jupiter, at Spalatra, is decorated with niches, one between every two columns; the one opposite the entrance, and those on each of the two sides, are rectangular below, but finish with cylindric heads: the axis of the cylinder, which forms the head, is parallel to the horizon, and in the direction of radii which be- long to the cylindric wall, in which these niches are placed. The other fourniches are cylindro-spherical; that is, they have cylindrical backs, and are terminated with spherical heads. All these niches are deco- rated with an impost, continued from side to side, and the heads are furnished with archivolts. In the pointed style of architecture, niches are 96 NIC' fl sometimes highly decorated. The back very fre— quently consists of three sides ofa hexagon, and the head is terminated with a rich canopy, form— ing a complete hexagon with the interior; the under part of each of the three projecting sides of the canopy has a Gothic arch, and the sofiit represents a groined vault, decorated with tracerv and ribs in the most beautiful manner. U The bottoms of these niches are formed by a table of the same shape as the head, and terminate below in the form of a pendent. The ceiling of the canopy represents the groined roof of an hexagonal building in miniature, as some of the highly decorated chapter-houses exhibit; the top of the canopy finishes with bat— tlements; and the vertical angles are sometimes finished with pendent buttresses, which are sur- mounted with pinnacles elaborately finished with crockets. NICHE, in carpentry, the wood-work to be lathed over for plastering. The most usual construction of niches in carpen- try, are those with cylindrical backs and spherical heads, called cylindro-sp/zeric niches; the execu- tion of which depends upon the principles of spheric sections. As all the sections of a sphere are circles, and those passing through its centre are equal, and the greatest which can be formed by cutting the sphere; it is evident, that if the head of a niche is intended to form a spherical surface, the ribs may be all formed by one mould, whose curvature must be equal to that of a great ‘circle of the sphere, viz. one passing through itslcentrc: but the same spherical surface may be formed by ribs of wood moulded from the sections of lesser circles, in a variety of ways ; though not so eligi‘ ble for the purpose as those formed of great cir- cles; because their disposition for sustaining the lath is not so good, and the trouble of moulding them to different circles, and offorming the edges according to different bevels, in order to range them in the spherical surface, is very great, com- pared with those made from great circles. The regular dispositions for the head of a niche are the following: The ribs of niches are generally disposed in a vertical plane, parallel to each other, or inteseet- ing each other in a vertical line. When the line of intersection passes through the centre of the. sphere, all the ribs are great circles; but if the 4~§2. %, IIII‘I'IIIII II IIIIIIIIIIIIIIIIIIIIIIIIIIIII I=IIII IIIII IIIIIIIIIIIIIIiI II ‘I I IIIII lIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII 3” I u;— anz/rt/ 13V BMr/Io/o‘qu. / fi\ ['29. 3 . ’ IIII " III‘ Drawn /3v .Il.,1.A.I'ir/m/.mn . sz/ir/m/ lav lz’t'Ir'IL'lzolu'n/I A“ J. b‘ufflr/d, H EIrz/uur .I'rl'w'l. 1(‘01. ”EM N I C H E S . ELI/.27 . PIA/112»: IIII ‘17"“I3‘I'IIIIIII, iIIIIII": IIIIIIIIIIIIIIIIIIIIIIIIIIII II E IWIIMH IIHI [m'entzd [3v 1’. NirlmlJon. [7:17. 4. \>\\\\\ ”ng—w JIAHMWMMIIIHINIWMJ ling/m ml [2 r J. Tqvlnr \. me (D ‘1 NIC line of intersection do not pass through the cen- tre of the sphere, the circles which form the spherical surface meal] of different radii. When the ribs are fixed in parallel vertical planes, their disposition is either parallel to the face of the wall, or parallel to a vertical plane passing through the centre of the sphere perpendicular to the surface of the wall; and this will be understood whether the surface be a plane, or that of a cylin— der, or that of a cylindroid. Though these dispositions are the most common and most fit for the purpose, there is still another regular position of the ribs of a niche, which is easily constructed in practice, viz. by making all the ribs intersect in a line passing through the centre of the sphere perpendicular to the surface of the wall; but this method is. not so eligible for lathing upon. Another method is by making the planes of the ribs parallel to the horizon: this is not only at— tended with great labour in workmanship, but is incommodious for lathing upon. The number of positions in which the ribs of a niche may be placed are almost infinite; as the ribs may have a common intersection in a line or axis obliquely situated to the horizon, or their position may be in parallel planes obliquely situ~ ated to the horizon: but the regular positions, already enumerated, ought to be those to which the carpenter should direct his attention. Plate I. Figure 1, No. Q, the elevation of a niche, where all the ribs intersect each other in a ver- tical line, coinciding with the inside of the front rib, as shewn by the plan, 1V0. 1. To describe any one of the ribs, as m 72, continue the inside circle of the plan round beyond the wall, as far as may be found necessary: produce fi, the base of the rib, to meet the opposite cir- cumference in g,- bisectg e at it; from It, with the radius 11 e, describe the are e Z; draw df perpen- dicular to the other side of the plan of the rib, cutting ge at f; from h, with the radius hf, describe the arcfk; from the centre draw in perpendicular to ge, the base, cutting the other circles at k and I; from the same centre, It, draw m n at any convenient distance, so as to make the rib sufficiently strong: the two inner arcs,fk, and e Z, shew the part to be taken from the side of the rib in order to range its inner edge. In the same manner every other rib may be described. Figure 2, No. 2, the elevation ofa niche, where the ribs are positedin parallel vertical places per- pendicular to the face of the wall. The method of describing the ribs 13 as follows: Draw a line through the centre of the circle which forms the plane, parallel to the face of the wall. Suppose it were required to describe the rib whose base isf k: produce fit to meet the line parallel to theface of the wall in g; from g, as a centre, with the distance gf, describe the arc fk; draw the short line d e perpendicular to g f, cutting dfin e: from g, with the radius g e, de- scribe the arc e 2', so that e i and fk may termi- nate upon the inside of the front rib, A C, in the points 2' and It: then eiand fk will shew the bevelling of the edge in order to range in the spherical surface. In the same manner may all the other ribs be described. Figure 3, shews the method of forming the spheri- cal head of a niche, when the planes of the ribs are parallel to the front rib, or to the face of the wall. No. 1, the plan; No. 2, the elevation. The figure is so obvious as hardly to require any de- scription, the ribs being all semicircles of dif- ferent diameters, as shewn by the plan: the parts darkly shadowed, are the places where the ribs come in contact with the plate or sill, on which they stand; and shew the degree of bevelling requisite for the edges, in order that they may range with the spherical surface. This disposi- tion of the ribs is very convenient for fixing the laths, which may be all directed towards the cen- tre, though the workmanship in bevelling is very considerable. In order to strengthen the work, a vertical rib is made to pass through the centre of the sphere, perpendicular to the surface of the wall. Figure 4, is a very convenient method of forming the head of a niche, by making the planes of all the ribs to intersect in a common axis, passing through the centre of the sphere, perpendicular to the surface of the wall; but it is not so‘conve- nient for fixing the laths. Plate ll. Figure 1, is the most convenient method of any for fixing the laths, and the ribs are all described from one mould: they need only be cut to different lengths in order to agree with their seats or plans. . No.1, is the elevation; No.2, the plan. The lengths of the ribs are shewn below, at No. 1, Q, and 3, which are erroneously figured; for No. 1 NIC 393 ought to have been No. 3; No. 2, should have been No. 4; and No. 3, should have been No. 5. The bases of the different ribs are taken from their seats on the plan. The, double lines shew the bevel at the top, where they come in contact with the back of the front rib. Figure 2, on the left side at the top (numbered by mistake Figure 1) is a different construction from the foregoing methods, which all spring from a horizontal‘plane passing through the centre of the sphere, and consequently the cylindrical surface will he a tangent to the spherical surface, at their junction. Whereas, in the present instance, the head of the niche is still spherical, but the hori- zontal plane from which it springs is higher than the centre of the sphere: this occasions a little more difficulty in the formation of the ribs, of which the construction is as follows : The plan, or springing rib, which forms the top Qf the cylindric back, and the front rib, which is the segment of a circle, being given; to form the moulds of the back ribs. Through the centre, cl, of the plan, draw LM parallel to GI, the seat of the front rib; from d, with the radius (Z G, or d I, describe the arcs G L and I M; draw de perpendicular to L M; then find the centre, E, of the front rib; and draw DE perpendicular to AC, cutting AC in D; make d e on the plan equal to D E; from 6, as a centre, with the radius e L, or e M, describe the are L m n o M, which will be the curve of all the ribs. Tofind the length required for any rib. Letf, h, and h, be the points where the back ribs join the back of the front rib: from d, as a cen- tre, with the distance d j, describe the arc fg, cutting L M at g; drawg m perpendicular to L M : then the part 772 M is the length which will stand over the seat of the rib, which meets atf. In the same manner, the lengths of the other ribs, which meet at h and It, will be ascertained; and thus having obtained the ribs for one half, the other half is also found ; they being duplicates of each other. The method of bevelling the heads of these ribs is the same as in the preceding examples. The plan (fa niche in a circular wall being given, to find the front rib. Plate Ill. Figure 1, No. 1, is the plan given, which is a semicircle, whose diameter is a b,- and a, i, h, l, m, h, the front of the circular wall; sup- NIC 1 pose the semicircle to be turned round its diame- ter, a b, so that the pointv may stand perpendicular over hin the front of the wall, the seat of the semicircle standing in this position upon the plan will be an ellipsis; therefore divide half the in- terior arc of the plan into any number of equal parts, as five;'draw the perpendiculars l d, 2 e, 3f, 4 g, 5 h,upon the centre, 0, with the radius c h; describe the quadrant of a smaller circle, which divide into the same number of equal parts as the interior of the plan; through the points 1, 2, 3, 4, 5, draw parallel lines to a b, to intersect the others, or the points (I, e, j, g, h; through these points draw a curve, and it will be an ellipsis ; then take the stretch-out of the interior of the plan, round 1, 2, 3, 4, .5, and lay the divisions from the centre both ways at F, stretched out; take the same distances d i, e h,fl,g m, from the plan, and at F make d i, e h, jl, equal to them, which will give a mould to bend under the front rib, so that the edge of the front rib will be perpendicu— to a, i, h, l, 772. Note, The curve of the front rib is a semicircle, the same as the ground-plan;and the back ribs at C, D, and E, are likewise of the same curve. The reason of this is easily conceived, the niclu- being part of a sphere, the curvature must be every where the same, and consequently the ribs must fit upon that curvature. Note, The curve of the mould F will not be exact- ly true, as the distances d i, e h,fl, Ste. are rather too short for the same corresponding distances upon the soflit F; but in practice it will be suffi- ciently near for plaster-work. In applying the mould F, when bent round the under edge of the front rib, the straight side of the mould, F, must be kept close to the back edge of the front rib; and the rib, being drawn by the other edge of the mould, will give its place over the plan. C, D, E, are the back ribs shewn separately. The plan and elevation of an elliptic niche being given, to find the curve of the ribs. PLATE IV. Figure 1,—Describe every rib with a trammel, by taking the extent of each base, from the plan whereon the ribs stand, to its centre, and the height of each rib to the height of the top of the niche; it will give the true sweep of each rib. To range the ribs cf the niche.—'l‘here will be no occasion for making any moulds for these ribs, but make the ribs themselves; then there will be N E f. H E S . PLATE 11. a H" mil J ‘ “W ‘ Hllllllllllllfil W } imwz/m’ fnwm‘t’d lyp/"A'. _ l 3,‘ ,, Mimi i 1171' l \. l 4 mm..- m /"1L//.1‘11,'." 2. I) 753/ H |) EJEH/uQu/l . Landau /'11/I/1:"/11'1/ //‘l//.‘."I;'/Il‘/.‘117I:“.//flI.I/iI‘/l/ I / 'uniul/rn'f/wl 15/11. Eng/rural flap/Hauler. _ $53.}? 5 7*. x, _‘ ‘ ‘ saw n g A r) 19% .9 . NICHES. PLATE m, Fig.1. Ch N914 : 1. —% V g & \ , g, ',, ,, ,. _ . , . ‘ , . I!” '11-'{/)/ {An/2". 7’ 7.’ ’~"'/“’/”’7L [um/1w,I’ll/I/Ia'l/r’d111/13.VI/'/HI/.ww‘\-Iii/17711411,Martini/r AIM/11:91.0. -”" ” -' l‘ ‘ ' NICHES. 21 c 3 LL \ \ a b T?j?tfi0/J'IJIL. £1u1don}P11/)li.r/zrd [{1/ liV/‘v/m [mm x J. jig/field , Mil/dour o7rrrt,u)’4q. PLATE 1V. Eryn-mu] [1'11 flJl’n/ii’. arr?- V ‘ ‘44:” n x M g .95. :n NIC two ribs of each kind: take the small distances 16, 2d, from the plan at B, and put it to the bottom of the ribs D and E, from d to 2, and e to 1; then the ranging may be drawn off by the other corresponding rib, or with the trammel; as for exam ple,at the rib E, by moving the centre of the trammel towards e, upon the line ec, from the centre, c, equal to the distance 1 e, the trammel- rod remaining the same as when the inside of the curve was struck. Given one of the common ribs (f the bracketing of a cove, to find the angle-bracket for a rectangular room. Figure 2.—Let H be the common bracket, 12 0 its base; draw I) a perpendicular to b c, and equal to it draw the hypothenuse a c, which will be the place of the mitre; take any number of ordinates in H, perpendicular to b 0, its base, and continue them to meet the mitre line a c, that is, the base of the bracket, at I; draw the ordinates of l at right angles to its base; then the bracket at I, being pricked from H, as may be seen by the figures, will be the form of the angle-rib required. Note, The angle-rib must be ranged either exter- nally or internally, according to the angle of the room. NICHE, Angular, one formed in the corner of a building. NICHE, Cul de Four of a, see CUL DE FOUR. NICHE, Ground, that which, instead of bearing on a massive base, or dado, has its rise from the ground; as the niches of the portico of the Pan- theon at Rome. Their ordinary proportion is two diameters in height, and one in width. NICHE, Round, one whose plan and circumference are circular. NICHE, Square, a niche whose plan and circum- ference are square. NICHED COLUMN, see COLUMN. NICOME DES, an ancient geometrician,celebrated for having been the inventor of the curve named the conchoid, which has been made to serve equally for the resolution of the two problems relating to the duplication of the cube, and the trisection of an angle. It was much used by the ancients, in the construction of solid problems. Sir Isaac Newton approved of it for trisecting angles, or finding two mean proportionals, and for constructing some other solid problems, as maybe seen in his Arithmetica Universalis. It is not cer- tain at what period Nicomedes flourished, but it 399 NOR was probably at no great distance from the time of Eratosthenes, who holds him up to ridiculeon account of the mechanism of his Mesolabe, and also from the circumstance that Geminus, who lived in the second century before the Christian zera, wrote on conchoids, of which Nicomedes was then allowed to be the inventor. NIDGED ASHLAR, a kind of ashlar used in Aber- deen, which is brought to the square by means of a cavil, orhammerwithasharp point; whereby the asperitus of the stone may be reduced in any de- gree proportioned to the time employed. As the species of stone found in that country is so very hard as to resist the mallet and chisel, this sort of operation becomes necessary. NOGS, the same as VVoon-BRICKS, which see. The term is used in Liverpool, and perhaps in other parts of Lancashire. NOGGING, a species of brickwork carried up in panels between quarters. NOGGING—PIECES, horizontal boards placed in brick-hogging, nailed to the quarters, in order to strengthen the brickwork. They are disposed at equal altitudes in the brick work. NONAGON (Greek) a figure of nine sides, and consequently of as many angles. NORMAL LINE, in geometry, a term used for a perpendicular line. See PERPENDICULAR and SUBNORMAL. NORMAN ARCHITECTURE, that species of building which was practised by the Normans after the conquest of England. rl‘his style of building was merely an adoption of that practised by their Saxon predecessors; and, therefore, the Normans are not the inventors of this style of building, as is generally supposed. Before we can form any idea of the style ofbuild- ing practised by the Normans, it will first be ne- cessary to shew the characteristic features of the Saxon style, which were, thick walls generally without buttresses, which, if introduced, was more for the sake of ornament than strength, as the sub- stance of the walls rendered them unnecessary. The arches employed were all semicircular; or, at least, if the pointed arch is to be found, it is to be attributed rather to an accidental circumstance than to any prevailing taste. The plan of the first Saxon churches consisted only of a simple oblong, extending in its longer dimension from east to west; but in after-times the east end was converted into a semicircle: the NOR 400 NOR north and south sides were each branched out with a wing, so as to give the edifice the form ofa cross, and over the intersection of the cross was erected a tower. The entrance was through the west end. The large Saxon churches had three aisles in a breadth, and the walls of the nave were supported by cylindrical or polygonal columns, with a regular base and capital, which was gene- rally plain; but it was also sometimes enriched with foliage, and even animals. The archivolts of the arches, which rested upon the columns, con- sisted,at first, of faces receding from each other in parallel planes and soffits, which were cylindric surfaces perpendicular to the naked or general face of the building. The shafts of the pillars, in the most ancient examples, were in general plain. Many discordant opinions have been advanced concerning what really constitutes Norman archi- tecture. The only material difference between Saxon and Norman architecture, appears in the magnitude of the structures of the latter people, and the more frequent use of stone. The Normans were not the inventors of the point- ed arch, as several instances of that species are to be met with prior to the Conquest ; and, indeed, the first buildings erected by the Normans had circular arches. The frequent use of the pointed arch did not take place till long after the Con- quest, and even then it was often mixed with the circular, in the same building. The changes of the style of architecture were not immediate, but effected in succession, and though but small at a time, the change was great in the end, so that the edifices were much improved in point of grandeur, proportion, and elegance of decoration. The Norman aera may be stated to be from A.D. 1066 to 1154, that is, from the Conquest to the death of Stephen. The Normans greatly increased the dimensions of the churches. The ornaments formerly used in the Saxon arches were retained, and others were added, of a much more exuberant kind. The fo- liage and other carvings were much more elabo- rate; however, their edifices still wanted the pedi- ments and pinnacles, as in those which afterwards were termed Gothic, or pointed. The prelates in the early Norman reigns were men of consummate skill in architecture; they applied themselves to the rebuilding of cathedral churches, and also the rebuilding of the greater abbeys. No less than fifteen of the twenty-two English cathedrals retain considerable portions, which are undoubtedly Norman workmanship, and of which! the several dates are ascertained. The Normans, who either were architects themselves, or under whose auspices architecture flourished, are Gun- dulph, bishop of Rochester, who flourished from A.D. 1077 to 1107; Mauritius, bishop of London, who flourished from 1086 to 1108; Roger, bishop of Salisbury, from 1107 to 1140; Ernulf, bishop of Rochester, from 11 15 to 1195; Alexander, bishop of Lincoln, from 1123 to 1147; Henry of Blois, bishop of Winchester, from 1129 to 1169; and Roger, archbishop of York. The works of Gundulph may be seen at Rochester, Canterbury, and Peterborough. Mauritius, of London, built old St. Paul’s cathedral; Roger, of Salisbury the cathedral ofOld Sarum ; Ernulfcom- pleted the work begun by Gundulph at Roches- ter; Alexander, of Lincoln,rebuilt his own cathe- dral; and Henry of Blois, bishop of iViuchester, a most' eminent architect, built the conventual churches ofSt. Cross and Ramsey, in Hampshire; but with respect to Roger, archbishop of York, none of his works remain. By these architects, the Norman style of arcl1itec= ture was progressively brought to perfection in England, and it will be easily supposed, that the improvements made by any of them were only adopted in succession. Many of the churches belonging to the greater abbeys were constructed in this aera; but of these, few, indeed, have escaped the general demolition that took place at the Reformation. From A.D. 1155, the style of ecclesiastical edi- fices began to assume other features; and at this period the conquerors became blended with the conquered, and, therefore, the Norman {era pro- perly ceases. From this period also we may date the commencement of the pointed arch style, or what 18 vulgatly called Gotlnc. With respect to the military structures of the Nor- mans, they knew they could not live in security without building strong places of defence , they therefore erected a castle upon every lordship, or assimilated with their own, what they found al- ready erected to their hands. The leading discrimination in a Norman fortress, is a lofty mound of earth thrown up in the centre of the other works, from the excavations necessary in forming the ditch, fosse,0r moat. A square or NOR 401 L - —— I circular tower, consisting of several stories, rose from the upper ballium, or a low circular story of considerable diameter, which was usually ap- proached by a very steep stone staircase on the outside. The gateway, or tower of entrance, and the barbi- can, or watch-tower, had both of them a commu- nication with the keep. Remarkable instances in the square form, are those of the towers of London, Norwich, Rochester, Dover castle, Hedingham (Essex), Bamborough (Northumberland), Por- chester, Colchester, Kenilworth, Knaresborough, Carisbrooke, and Oxford. Of the circular are Arundel, Pontefract, and Conisburgh (Yorkshire), Lincoln, and Tunbridge in Kent. Besides the above stated towers, an irregular form, of which the plan consists of several segments of circles, may be seen in Clifford tower, in York, and Berke- ley castle, Gloucestershire. These keeps, or cita- dels, in subsequent aeras underwent no alteration, whatever additions or improvements took place in architecture. Bishop Gundulph seems to have considered the lofty artificial mound,originally of Danish usage, as unnecessary. His central towers are so lofty as to contain four stories, as was also the case with most other keep towers. The basement was the dungeon, without light: the portal or grand entrance was raised many feet above the ground; but his great merit consisted in various architec- tural contrivances, by which as much security during a siege was given to his keeps by strata- gem, as by real strength. The walls were not un- frequently from 12 to 20 feet thick at the base. In the souterrain of the vaulted stone, the mili- tary engines and stores were deposited. In the thickness of the walls were placed winding stair- cases, the well for water, the vast oven, enclosed galleries and chimneys, with an aperture, open to the sky, and communicating with the dungeon, in which prisoners were confined, and to whom it gave all the light and air they could receive. There was also a kind of flue for conveying sound to every part, not more than eight inches in dia- meter. The state apartment occupied the whole third story, and the staircases leading to it were much more commodious than the others, and even so large as to admit of military engines. Adjoin- ing to the great chamber was the oriel, lighted by a window embowed withinside. In Rochester castle the chief room was 32 feet high, including VOL. II. NOR the whole space within the walls. The walls of the ground story had no light, the second had only loop-holes; but the third had large arched windows, placed so high as not to be looked through, and so defended by an internal arcade, that no missile weapon could enter or fall with effect. Each floor had its communication with the well. The chimneys were very capacious, projected considerably into the rooms, and rested upon small pillars; and the sinks were so con- trived, in an oblique direction, that no weapons could be sent up them. Gundulph is said to have introduced the architec- tural ornaments of the ecclesiastic style into for- tresses, both withinside and without. Most of the Norman castles had a richly carved door- case or portal, as the remains of Arundel and Berkeley amply testify. The windows were de- corated with mouldings, frequently sculptured. Castle-Rising, Norfolk, and Norwich, abound in admirable specimens of Norman arcades and mouldings. The great tower of entrance was built at the foot ofthe artificial mount, from which was a sally-port, with stone stairs leading to the keep. It con- tained the portcullis and drawbridge affixed to the archway, and several spacious chambers. In point both of formation of the mount and keep, and their connection with the entrance-tower, the remains of Tunbridge, and the more perfect state of Arundel castle, exhibit a singular resemblance. The walls were protected by strong buttresses, and the round towers had a central space left open, to admit the light and air. At Arundel, the corbel stones, which supported the beams of timber, are still to be seen. See CASTLE. The well-authenticated buildings of Norman con- struction, erected from before A. D. 1100 to 1150, are the abbeys ofAbingdon, Reading, and Cirencester, destroyed; Malling, Kent; Tewkes- bury, nave, aisles, transept, and west front; Malmsbury, nave and west front; Buildwas, SalOp; St. Botolph, Colchester; Bolton, York- shire; \Vinborn minster, Dorsetshire; Castle-Acre, Norfolk; Dunstable, Bedfordshire; St. Cross, Hams; Romsey, Hams; Furness, Lancashire, the most ancient parts; Llandisfarne, Northum- berland; Byland, Yorkshire; Sanercost, Cumber- land; Sherbourn, Dorset; Southwell, Notting. hamshire; Kirkstall, Yorkshire, nave. Of those now named, Tewkesbury, Malmsbury, VVinborn O 01" ‘NUI minster, St. Cross, Romsey, and Sherbourn, are now used as parochial churches. From A.D. 1155, the style of architecture prac- tised by the Normans began to be mixed with new forms and decorations, and was at length super- seded by that much more elegant and lofty style of building, improperly denominated Gothic. The principal works that may be consulted in Norman architecture, are the Archaeologia, Car- ter’s Ancient Architecture of England, Britton's Architectural Antiquities of Great Britain, and Dalaway’s English Architecture. NOSINGS OF STEPS, the projecting parts of the tread—board or cover, which stand before the riser. The nosings of steps are generally rounded, so as to have a semicircular section, and, in good staircases, a hollow is placed under them. NOTCH-BOARD, a board notched or grooved out, to receive and support the ends of the steps of a staircase. NOTCHING, the cutting ofan excavation through- out the whole breadth of a substance. By this method timbers are fastened together; or their surfaces, when joined at angles, are made to coincide. NUCLEUS (Latin) the internal part of the flooring of the ancients, consisting of a strong cement, over which they laid the pavement, bound with mortar. NUEL, see NEWEL and STAIRCASE. NUISANCE, or NUSAN CE (from the French, nuire, to hurt) in law, is used not only for a thing done to the hurt or annoyance of another, in his free lands or tenements, but also for the assize, or writ lying for the same. Nuisances are either public orprivate: a public or common nuisance is an' offence against the public in general, either by doing what tends to the an- noyance of all the king’s subjects, or by neglect— ing to do what the common good requires. A private nuisance is when only one person or family 402' MJ 1 1 NUI is annoyed, by the doing of any thing; as where a person stops up the light of another’s house, or builds in such a manner, that the rain falls from his house upon his neighbour’s; as likewise the turning or diverting Water from running to a man’s house, mill, meadow, Ste. corrupting or poisoning awater—course, by erecting a dye-house, or a lime—pit, for the use of trade, in the upper part of the stream; stopping up a way that leads from houses to lands; suffering a house to decay, to the damage of the next house; erecting a brewhouse in any place not convenient; or a privy, 8Lc. so near another person’s house as to offend him; or exercising any offensive trade; or setting up a fair or market, to the prejudice of another. The continuation of a nuisance is by the law con- sidered as a new nuisance, and therefore, where a person suffers a nuisance to be set up, and then alienates and lets the land, 3w. without removing it, an action of the case lies against him who erected it; and also against the alienee or lessee, for continuing it. Writs of nuisance are now properly termed tres- passes, and actions upon the case. NUISANCE, Abatement of, denotes the removal of it, which the party aggrieved is allowed to do, so as he commits no riot in the doing of it. “If ahouse or wall is erected so near to mine, that it stops my ancient lights, which is apriwte nuisance, I may enter my neighbour’s land, and peaceably pull it down.” Salh.459. “ Or if a new gate is erected across the public highway, which is a common nuisance, any of the king’s subjects passing that way may cut it down, and destroy it.” Cro. Car. 184. The reason why the law allows this private and summary method of doing one’s selfjustice, is, because injuries of this kind, which obstruct or annoy such things as are of daily convenience and use, require an imme- diate remedy; and cannot wait for the slow pro- gress of the ordinary forms of justice. OBE OBELISK, (from the Latin obeliscas) a quadran- gular pyramid, very slender and high; raised as an ornament in some public place, or to shew some stone of enormous size; and frequently charged with inscriptions and hieroglyphics. Borel derives the word from the Greek oCMag, (I spit, broack, spindle, or even a kind of long javelin. Pliny says, the Egyptians cut their obelisks in form of sun—beams; and that in the Phoenician language, the word obelisk signifies ray. The Egyptian priests called their obelisks the sun’s fingers; because they served as styles, or gno- mons, to mark the hours on the ground. The Arabs call them Pharaoh’s needles; whence the Italians call them aguglia; and the English Cleo- patra’s needles. See CLEOPATRA’S NEEDLES. The difference between obelisks and pyramids, ac- cording to some, consists in this, that the latter have large bases, and the former very small ones, compared with their height. Though Cardan makes the difference to consist in this, that obe- lisks are to be all of a piece, or consist of a single stone; and pyramids of several. The proportions of the height and thickness are nearly the same in all obelisks; that is, their height is nine, or nine and a half, sometimes ten times their thickness; and their thickness, ordia- meter, at top, is never less than half, nor greater than three-fourths, of that at bottom. This kind of monument appears to have been very ancient; and, we are told, was first made use of to transmit to posterity the principal precepts of phiIOSophy, which were engraven on them in hie- roglyphic characters. In after-times they were used to immortalize the actions of heroes, and the memory of persons beloved. The first obelisk we know of was that raised by Rameses, king of Egypt, in the time of the Tro- jan war. It was 40 cubits high, and, according to Herodotus, employed 20,000 men in building. Phius, another king of Egypt, raised one of 45 cubits; and Ptolemy Philadelphus another, of 88 cubits, in memory of Arsino'e. See PORPHYRY. Augustus erected an obelisk at Rome, in the OBL Campus Martius, which served to mark the hours on an horizontal dial, drawn on the pavement. - F. Kircher reckons up fourteen obelisks, cele- brated above the rest, viz. that of Alexandria, that of the Barberins, those of Constantinople, of the Mons Esquilinus, of the Campus Flaminius, of Florence, of Heliopolis, of Ludovisio, of S. lVIahut, of the Medici, of the Vatican, of Mount Caelius, and that of Pamphylia. One of the uses of obelisks among the ancients was, to find the meridian altitudes of the sun at different times of the year. Hence they served instead of very large gnomons. One of the obe- lisks now standing at Rome, thatof St. John’s La— teran, is in height 108 English feet, without the pedestal; and the other obelisk, brought to Rome by Augustus, buried under the Campus Martius, wants but little of the same height. Pliny gives a description of this gnomon, lib. xxxvi. sect. 15. From him it appears, that there was laid down, from the foot of the obelisk northward, a level pavement of stone, equal in breadth to the breadth of the obelisk itself, and equal in length to its shadow at noon, upon the shortest day; that is to say, that its length was to the height of the obelisk, almost as 22 to 10, and that under this pavement, there were properly let in parallel rulers of brass, whose distance from the point, directly under the apex of the obelisk, were re- spectively equal to the length of the shadow thereof at noon, on the several days of the year, as the same lengths decreased from the shortest day to the longest, and again increased from the longest day to the shortest. Vide P/zil. Trans. No. 482, art. 5, vol. Xliv. p. 365; where we also find some remarks by Mr. Folkes on Hardouin’s Amendment ofa Passage in Pliny’s Natural His- tory, lib. ii. sect. 74. about the length of the shadows of gnomons in different latitudes. OBLIQUE LINE. \Vhen one straight line stands upon another, and makes unequal angles there- with, the angles are said to be oblique, the one being greater than a right-angle, and the other less. Hence a line is only oblique, as it relates 3 F 2 OCT - g ' E 5-: - to another line: without this distinction, the word would be destitute of meaning. OBLIQUE ANGLE, one that is greater or less than a right angle. OBLIQUE-ANGLED TRIANGLE, one that has no right angle. . OBLIQUE ARCHES, are those which conduct high roads across a river, canal, open drain, 8:0. in an oblique direction.-—Oblique arches are otherwise called ’slcew bridges. The limits of this Work will not permit us to go into the detail of oblique arches; but those who are desirous of the knowledge of such arches, may consult Rees’s Cyclopedia, article Oblique Arches. The Author, however, intends, at some future period, if life permit, to shew the methods of finding the requisite moulds for so useful a structure. OBLONG (from the Latin oblongus) a rectangle of unequal dimensions. OBSERVATORY (from the French) a building accommodated to the observation of the heavenly bodies. Our limits will not permit us to enter into a detail of this article. The reader who is curious, or may have an observatory to erect, may consult Rees’s Cyclopedia, under the word, where he will find a complete history and description of the most celebrated and best constructed observa- tories in the world. - OBTUNDING (from the Latin obtundo) the blunt- ing or taking away a sharp corner. OBTUSE (from the Latin) any thing that is blunt. OBTUSE-ANGLED TRIANGLE, a triangle which has an obtuse angle. OBTUSE SECTION OF A CONE, a name given to the hyperbola by ancient geometricians, because they considered it only in such a cone, whose section through the axis was an obtuse-angled triangle. ‘ OCTAGON from and, eight, and Maria, sides) afigure of eight sides, and consequently as many angles. When all the sides and all the angles are equal, the figure is called a regular octagon. OCTAHEDRON, or OCTAEDRON (Greek, auralzé‘pog) . in geometry, one of the five regular bodies, con- sisting of eight equal and equilateral triangles. The octahedron may be conceived as consisting of two quadrilateral pyramids put together at their bases. Its solidity, therefore, is bad by multiplying the quadrangular base of either by one-third of the OGI M perpendicular height of one of them, and then doubling the product. The square of the side of an octahedron is in a subduple ratio of the square of the diameter of the circumscribing sphere. See REGULAR BODY. OCTOGON, see OCTAGON. OCTOSTYLE (from Sun), eight, and 54ng, a column) an ordonnance with eight columns. It is generally understood of columns when their axes are all in the same plane, as in the portico of the Pantheon at Rome, and the Parthenon at Athens. ODEUM (Greek, drainer) among the ancients, was a place for the rehearsal of music to be sung in the theatre. ODEUM was sometimes also extended to buildings that had no relation to the theatre. Pericles built an odeum at Athens, where musical prizes were contended for. Pausanius says, that Herod, the Athenian, built a magnificent odeum for the sepulchre of his wife. Ecclesiastical writers also use odeum for the choir of a church. (ECUS (Greek) aword used byVitruvius, to denote some apartment connected with the dining-room. The (eci were very magnificent, as will appear by reading chapters v. and vi. book vi. of Newton’s Vitruvius. OFFICES (French) in architecture, denote all the apartments that serve for the necessary occasions of a great house, or palace, or those where the servants are employed ; as kitchens, pantries, brewhouses, confectioneries, fruiteries, granaries, 8L0. as also wash-houses, wood-houses, stables, Sic. The offices are commonly in the bassecour; some- times they are sunk under ground,and well vaulted. OFFSETTS, those parts of a wall which connect two faces in diflbrent parallel planes, where the upper part recedes from the lower. OGEE, or O—G, in architecture, a moulding, con- sisting of two members, the one concave, the other convex, the same with what is otherwise called cymatium. Vitruvius makes each member of the ogee a qua- drant of a circle; Scammozzi, and some Others, make them somewhat flatter, and strike them from two equilateral triangles. The figure of an ogee bears some resemblance to that of an S. OGIVES, in architecture, arches or branches of a Gothic vault, which, in lieu of being circular, pass diagonally from one angle to another, and form a OPT 405 OPT M cross with the other arches which make the side of the squares, whereof the ogives are diagonals. The middle, where the ogives cut or cross each other, is called the key, which is sometimes carved in form of a rose, or a cul de lampe. The mem- bers or mouldings of the ogives are called nerves, branches, or reins,- and the arches which separate the orgives, double arches. ONE-PAIR-OF-STAIRS, signifies the first story, or floor, by passing up the stairs, or pair of stairs, as they are frequently called, from the entrance- floor to the next floor, which is denominated the one—pair-of-stairs floor, and frequently (though very improperly) the first floor, the entrance floor being naturally the first floor. OPAE the space, signifies the space between joists. See Newton’s Vitruvius, book iv. chap. ii. OPENING, see APEBTURE. OPISTHODOMOS, the enclosed space behind a temple. The treasury at Athens was so called, because it stood behind the temple of Minerva. OPPOSITE ANGLES, those which are formed by two straight lines crossing each other, but not two adjacent angles. OPPOSITE CONES, those to which astraight line can be every where applied on the surfaces of both cones. OPPOSITE SECTIONS, the sections made by a plane cutting two opposite cones. OPTIC PYRAMID, see PERSPECTIVE. OPTIC RAYS, see PERSPECTIVE. OPTICS (from the Latin optica) is properly the science of direct vision. In a larger sense, the word is used for the science of vision, or visibles in general; in which sense, optics includes catop- trics and dioptrics, and even perspective. In its more extensive acceptation, optics is a mixed mathematical science, which explains the manner by which vision is performed in the eye; treats of sight in the general; gives the reasons of the several modifications or alterations which the rays of light undergo in the eye; and shews why objects appear sometimes greater, sometimes smaller, sometimes more distinct, sometimes more confused, sometimes nearer, and sometimes more remote. In this extensive signification, it is con- sidered by Sir Isaac Newton, in his admirable work called Optics. Optics makes a considerable branch of natural phi- losophy; both as it explains the laws of nature, according to which vision is performed; and asit L accounts for abundance of physical phenomena, otherwise inexplicable. From Optics likewise arises perspective, all the rules of which have their foundation in optics. In- deed Tacquet makes perspective a part of optics; though John, Archbishop of Canterbury, in his Perspectiva Commums, calls optics, catoptrics, and dioptrics, by the common name perspective. This art, for so it should be considered rather than as a science, was revived, or re-invented, in the 16th century. It owes its birth to painting, and particularly to that branch of it which was em- ployed in the decoration of the theatre. Vitru- vius informs us, that Agatharchus, instructed by .ZEschylus, was the first who wrote upon this sub- ject; and that afterwards the principles of this art were more distinctly taught by Democritus and Anaxagoras, the disciples of Agatbarchus. How they described the theory of this art we are not informed, as their writings have been lost; how- ever, the revival of painting in Italy was accom- panied with a revival of this art; and the first person who attempted to lay down the rules of perspective, was Pietro del Borgo, an Italian. He supposed objects to be placed beyond a transpa- rent tablet, and endeavoured to trace the images, which rays of light, emitted from them, would make upon it. The book which he wrote upon this subject, is not now extant; and this is the more to be regretted, as it is very much com- mended by the famous Egnazio Dante. Upon the principles of Borgo, Albert Durer constructed a machine, by which he could trace the perspec- tive appearance of objects. Balthazar Parussi, having studied the writings of Borgo, endea- voured to make them more intelligible. To him' we owe the discovery of points of distance, to which all lines that make an angle of 45° with the ground-line are drawn. Soon after, Guido Ubaldi, another Italian, found that all the lines, which are parallel to each other and to the horizon, if they be inclined to the ground-line, converge to some point in the horizontal line; and that through this point, also, a line drawn from the eye, parallel to them, will pass. These principles combined, enabled him to make out a pretty com- plete theory of perspective. Great improvements were made in the rules of perspective by subse- quent geometricians, particularly by Professor Gravesande, and still more by Dr. Brook Taylor, whose principles are, in a great measure, new, a DRE 1 r t and much more general than those of any person before him. Although Dr. Taylor really invented this excellentmethod of perspective, yet it is sug- gested by Mr. Robins, that the same method was published by Guido Ubaldi, in his Perspective, printed at Pesaro, in 1600. In this treatise the method is delivered very clearly, and confirmed by most excellent demonstrations. In the last book, Ubaldi applies his method to the delinea- tion of the scenes ofa theatre; and in this, as far as the practice is concerned, he is followed by Sig- nor Sabatellini, in his Practica di Fabrica, Scene, of which there was a new edition at Ravenna in 1638 ; and to this was added a second book, con- taining a description of the machines used for producing the sudden changes in the decorations of the stage. In the catalogue of the great Sir Isaac Newton’s works, at the end of his lye, is a work on perspective, witten in Latin: Newtoni Elementa Perspective Universalz's, 1746. 8vo. We are indebted to opticians of a much later period for ingenious devices to apply the knowlege they had of optics, and especially of perspective, to the purposes of amusement. For the principles and practice of PERSPECTIVE, see that article, where they will be fully treated of. ORANGERY, a gallery in a garden, or parterre, exposed to the south, but well closed with a glass window, to preserve oranges in during the winter season. The orangery of Versailles is the most magnificent that ever was built; it has wings, and is deco- rated with a Tuscan order. ORATORY (from the Latin, oratorium, a temple) a closet or apartment in a large house, near a bed-chamber, furnished with a small altar, or an image, for private devotion, among the Romanists. The ancient oratories were little chapels adjoining to monasteries, wherein the monks offered up their prayers, before they had churches. In the sixth and seventh centuries, oratories were little churches, built frequently in burial-grounds, without either baptistry, cardinal, priest, or any public office, the bishop sending a priest to offi- ciate occasionally. iORB (from the Latin, orbz's, a sphere) a knot of flowers, or herbs, in a Gothic ceiling, placed upon the intersection of several ribs, in order to cover the mitres of every two adjoining ribs. This is otherwise called boss. ORDER (from the Latin ordo, method) a word equi- 405 ¥_ 1 ‘— ’ORD Mum—fig: valent to arrangement, and in architecture may be considered as a decorated imitation of sucha por- tion of the primitive hut, of a certain construction, as might comprehend the whole design by a con- tinuity and repetition of its parts. The hut ori- ginally consisted of a roof or covering, supported by posts made of the trunks of trees, in four rows, forming a quadrangular enclosure. Beams were laid upon the tops of the posts, in order to con- nect them, in their longitudinal direction, in one body. To support the covering, timbers were laid from beam to beam across the breadth; and to throw off the wet, other beams were laid paral- lel to those resting upon the posts, but jutting farther over on each side of the edifice; and these again supported inclined timbers, which overhung their supports, and formed a ridge in the middle of the roof, for throwing off the wet; and thus the part supported formed three principal distinct portions, which, in process of time, were deco- rated with certain mouldings, or other ornaments, each part still preserving its distinct mass, though perhaps not exactly similar to the original form. The three parts, taken as awhole, were called the entablatuz'e; the lower part, consisting of the lin- telling beams, was called the episty/e, or arc/ti- trave; the middle part, which receded from the epistyle, was called the zoop/wrus, or frieze,- and the upper part, which projected considerably over the frieze, being in imitation of the ends of the roof, was called the cornice. Therefore the entablature consists of a cornice, frieze, and architrave. The posts received the name of columns, which always consist of two principal divisions at least, and frequently of three. The columns were orna- mented at the top in imitation of the stones laid upon the posts in the original wooden hut, for throwing off the rain. These decorations at the top received the name of capital, and each of the wooden posts that of shaft. When ornaments were added to the foot of the shaft, they were termed the base. The order, therefore, consists principally of a co- lumn and entablature. The column is subdiruled into a shaft and capital, or, at most, into three principal parts, a base, shaft, and capital; and the entablature, as has been observed, into archi- trave, frieze, and cornice. These parts are again divided into smaller portions, termed 7IIOItltftllg’"i, or other ornaments. 0RD 407 ' ORI .W There are three orders in architecture, though the modern writers generally enumerate five, but without any authority. These three orders are named Doric, Ionic, and Corinthian, according to the place in which they were invented. Except in the general forms above specified, there is no standard of proportion common to the three orders, each having its own symmetry. 'The ca- pitals are their distinguishing features. The Do- ric entahlature is peculiar to the Doric. The Ionic entablature may be applied to the Corin- thian with equal propriety, as the remainsof Gre- cian antiquity amply testify. The proportions of columns vary in the three orders, from five to ten diameters, the standard being the diameter of a section of the shaft at the bottom. The shafts of the columns are the frustums of cones ; they are sometimes of a conoidal form, which however is not so agreeable to the archetype as the conic frustum, and in the antique they are generally fluted. The fluting of the Doric is peculiar to it- self. The columns of this order are in height fewer diameters than those of the other two; and supposing the diameter at the base in the three orders to be equal, the altitudes of the columns will increase from the Doric to the Corinthian, so that the Ionic column is the medium between the other two. The height of the entablature of each order may be generally stated at two diame- ters of its column. The diminution of the shafts is not equal in all the orders: that of the Doric va- ries from one-fourth to one-fifth; the Ionic and Corinthian from one-fifth to one-sixth. Neither are the cornice, frieze, or architrave, in an equal ratio to each other. The height of the Doric cor- niceis about one-fourth of the height of the en- tablatnre; that of the Ionic one-third, and in most examples considerably more. The height of the architrave and that of the frieze of the Doric en- tablature, are in general equal. In the Ionic and Corinthian,the architrave is higher than the frieze, but of less height than the cornice. Though the modems have classed two other orders with the three Grecian, they have no authority for this atl- dition. Vitruvius mentions Tuscan temples, and various kinds of capitals used for the Corinthian, but no where speaks of them as forminga distinct order. The peculiarities of each are noticed under its respective title; see CoRIN'rHIAN, Dome, and Io x 1c ORDER. Also ROMAN andTUSCANURDER. ORDER, Attic, the pilaster of an attic. See AT'ric. ORDER, Caryatic, that in which the entablature is supported by women instead of columns. See CA RYATIC. ORDER, Got/tic, the pointed style of architecture, usually called Gothic. See ARCHITECTURE, CAS- TLE, and GOTHIC. ORDERS, Greek, are the Doric, Ionic, and Corin- thian. See each of these articles. ORDER, Persian, that Where the entablature is supported by men instead of columns. The history is related in Newton’s Vitrth'us, book i. chap. i. page 3. See PERSIANS. ORDER OF TEMPLES, otherwise called SPECIES, are the amphiprostyle, the antaa, the dipteral, the peripteral, and the prostyle. See those respec- tive articles. ORDINANCE, the same as ORDER, which see. ORDINATES, in geometry and conics, are lines drawn from any point of the circumference of an ellipsis, or other conic section, perpendicularly across the axis, to the other side. The Latins call them ordinatim applicatw. The halves of each of these are properly only semi- ordinates, though popularly called ordinates. The ordinates of a curve may more generally be defined to be right lines parallel to each other, terminated by the curve, and bisected by a right line called the diameter. In curves of the second order, if any two parallel right lines be drawn so as to meet the curve in three points, a right line, which cuts these parallels, so as that the sum of two parts terminating at the curve on one side the secant, is equal to the third part terminated at the curve on the other side, will cut all other right lines parallel to these, which meet the curve in three points, after the same manner, 2'. e. so as that the sum of the two parts on one side will always be equal to the third part on the other side. And these three parts, equal on either side, Sir Isaac Newton calls ordinatim up. p/icatce, or ordinates ofcnrves ofthe second order. ORDINATE, in an ellipsis, hyberbola, and parabola, see the respective articles. ORGANICAL DESCRIPTION OF CURVES, a method of describing curves upon a plane by Continued motion. ORIEL WINDOW, in architecture a projecting angular window, mostly of a triagonal or penta- gonal form, and divided by mullions and tran- soms into different bays and other compartments. These windows are not peculiar to the pointed ORT 408 style, as in the barbarous style which succeeded it. During the reigns of Elizabeth and James I. they became still more common than they had been before in the pointed style. ‘ORLE (French, formed from the Latin orletum or orlum, of ora, a border or list) a fillet under the ovolo or quarter-round of a capital. W’hen at the top or bottom of the shaft, it is called cincturc. Palladio also uses orle for the plinth of the bases of the columns and pedestals. ORNAMENTS (from the Latin ornamentmn, to embellish) in architecture, all the sculpture, or carved work, with which a piece of architecture is enriched. ORNAMENTS IN RELIEvo, those carved on the contours of mouldings. The reader who is de- sirous to practise ornaments, would do well to study and draw those in the first part of vol. iii. of the Principles of Architecture, by the Author of the present Work. Antique ornaments are to be collected from Stewart’s Ruins of Athens, the Ionian Antiqui- ties, and Desgodesby’s Roman Antiquities. See also Tatham’s works, sold by Gardiner, Princes- street, Cavendish-square; and Moses’s works, sold by Taylor, Holborn. ORTHOGONAL FIGURE (from 5,924, true, and mania, an angle) the same as rectangular. ORTHOGRAPHICAL PROJECTION, see PRO- JECTION. ORTHOGRAPHY (5,939, true, and WNW), to de- cribe) in architecture, the elevation of a building, shewing all the parts thereof in their true propor- tion. The orthography is either external or internal. ORTHOGRAPHY, External, a delineation of the outer face or front of a building, exhibiting the principal wall, with its apertures, roof, orna- ments, and every thing visible to an eye placed before the building. ORTHOGRAPHY, Internal, called also SECTION, a delineation or draught of a building, such as it would appear, were the external wall removed. See PERSPECTIVE. ORTHOGRAPHY, in geometry, the art of drawing or delineating the fore-right plan or side of any object, and of expressing the heights or eleva- tions of each part. This art has received its name from its determin- ing things by perpendicular right lines falling on the geometrical plan; or rather, because all the OVA horizontal lines are here straight and parallel, and not oblique, as in perspective representations. ORTHOGRAPHY, in fortification, the profile or representation of a work; or a draught so con— ducted, as that the length, breadth, height, and thickness of the several parts are expressed; such as they would appear, if it were perpendicularly cut from top to bottom. OSCULATING CIRCLE, or KISSING CIRCLE, the circle of curvature. See CURVE. OVA (from the Latin ovum, an egg) an ornament in form of an egg, usually employed in the echinus. OVAL, a figure in geometry, bounded by a curve line returning to itself. Under this general definition of an oval is included the ellipsis, which is a mathematical oval; also all other figures which resemble the ellipsis, though with very different properties; and, in short, all curves which return to themselves, go under the name of ovals. For a description of the mathmeatical oval, the reader will turn to the article ELLIPSIS, where, it is presumed, he will meet with full satisfaction. One of the most remarkable properties of the oval kind is the following: Plate I. Figure ].-—Let C E F G be a circle, 0 its centre; draw any line, E I, through the centre 0; then take any point, F, in the Circumference. Let FI be an inflexible line, and let M be a given point in the line F I; then, if the point F bdcon- ceived to move round the circumference of the circle, while the point, I, the end of this line, F I, ' moves or slides along the line E], the point M will describe an oval, almost similar to the conic ellipsis. As we have not seen any equation of this figure, it is presumed that the following investiga- tion, by the author, will be acceptable: Draw F H perpendicular to the diameter, E G, of the circle, cutting E G at H ; also draw M P per- pendicular to E I, cutting EI always in P, where- ever the point M is situated. Let A be the point in the straight line EI, in which M will coincide when F is brought to E, and B the point where M will coincide when F comes to G. Then let A P: .r .. i381“ Invented [11/ I? Jul/1013011. Ilium” [{1/ JL’I “lyric/101nm . OVAL. ‘ ‘13). 3. [um/(m, I’ub/ILr/zm/ (3:7 IKVI'C/wbon X‘ JJiU‘fiHJ, [Vlu‘ll‘ ‘m‘ J'h‘ect . PLATE I. “ Engraved 1:1; ”flow-13;. OVA 409 OVA WW.__MM' From the property of the circle we have H F: A P = IA— I P = (i (62— div+v2)% + ,0 __ c; by (lo—'09; then, by similar triangles, I FH and ‘ b . I M P, we have which the value of,A P, corresponding to PM or I F’2 : I M2 : : HI” : PMQ; 1/: Z. ((112—122)? may be found in the most sim- That is, If : a2 : : d'o—vg zygzg—:(dv—ve)% ple manner. 1 b Therefore, if A P in the figure were always equal Therefore, y— _ _(dv—v‘2)5 to the versed sine E H of the circle, the curve de— Then to find the value fx— A P e have scribed by the motion of the point M, would really , o = , w IPQ=IMg—-—PM°= a2_: — :(dv— v 0) 22—:(62—dv+v2); be an ellipsis; and because P M or 3/ =g— (dv—v‘zfi it follows, that the axis perpendicular Therefore, IP__—_5l_ (be—dz) +93% ; to the ordinates, is to the axis parallel to the or- b dinates, in the ratio of I) to a; that is, in the ratio But IM : IP : : IMF : PH; ofIFtOIMnearly. Thatis,u : 557(62—(1 a(.u-i—v‘lfi: : c : P H : Z—(bew—dv+v9)i Let a = 20; b = 40; C = 20) and d =10; then 1 will = (-1— (d v —— Q i: l (6 v —- v‘z ; from which IE=1P+PH44:E=4m_da+arxfltahg y b, v) 2 , l , b the followmg values are obtained, according to __ __ = 2____ d 2 3 _ . the different assumptions of the versed sine, v, of IA- IE AE— ab +6X :( 256 ) And, lastly, let — i; a 1 27711 97%;“ . a then when .7: = l, 3/ = 1.427r = 1.07; : 71 x 274 = 4 Hience 4 Z 1‘=2,y=2.31r :1.73; I Q, % 1 = 3, 7/ = 2997‘ = 2.24; (alas—:64)? l((1.1."3--—.r) 1=4,y=3.5lr =2.63; Q74 I :1" = 5, y = 3.86r = 9.89; So that 3/ = -2— (a .1‘3 —- 3‘4)4\vhen the greatest 3” = 67 3/ = 4-7' = 3'; 27 1‘ = 7, y = 3-7781' = 9.833. Another equation, which gives the oviform figure more swell at the quicker end, is the following: 7/:(11‘12—1‘“)? Let .1‘=lthen7/=(100 — 1)%: 998:3.15; 3:2 3/:(100 —— 16):: 38 16:11.12; x:< y=(900 — 817% = 81 197—5131 .1: y=(1600—— 956)%:1311i:6.05; 1:5 ::(2300— 623%:1873i: 1.,58 1:6 :(3000—1290)%:2301%:.092; 3:7 j:(4900—21o1)l:e199%: 7.07; .~:8 y:(6100——109614:2304§:6.92 y : (8100 — 6561) :1539!‘ :6.26. Calling the abscissal axis the height, the con- strucrion may be accommodated to any given dimensions, as follows; for this purpose we have the fluxion of a2 .1“ — 11* = 0; therefore 0 a 4 .1“3 .1? = 2 a2 x,- consequently .1 = ;; and hence 5,; = will give the point tlnough which the 0 ,1—4l greatest double ordinate passes. If therefore this quantity be substituted for x in the equat1on 7 = (a2 1‘2 -- 1.1)}. then will 7 —.= (L— t: )+ _ J * 3 j 2 4 __ PLATE ll. Fiji. 1]. 7 5 ,L gig ~:, 3, L. 537.3. Fly. 14. M]. 2'0. 10. lnwnlaz’ 111/ if ZVLk/wlxon. [)rde 53/ MAJVIMoL‘on. Lolldvn,l$¢é/(Lr/Ln/ by I? [Wk/whorl X‘ JBar/fdd, ”lat-dour fired. Engraved fly ”([nwcu. OVA 4'13 4 4 2% I _ .1. 4 (oh:2 ——.r")4 : (Eta: x2— 14): = .7071 (a2 ac" —- x4); . a a so that, taking so = —I, we shall have y = E’ as 95 it ought to be. Therefore, if the ratio be r, we shall have .7071 r ((11.102 —— x4)%, for any proportion according to the nominal value of 7'. Now let 2 . r —_= 73, then a being 10, as before, we shall have the several values ofy as follow : whenx = 1, theny = 2.23; 30:2 1/=3.13,- x=3 y=3.75; 33:4 y=4.28; x=5 y=4.65; :t‘ 6 y=4.89; x=7 y=5.00; cr=8 y=4.89; x=9 y=4.43. If the equation of the curve be 2/ = (c3 ._ 353%, the following values of y will be found, sup- posing c = 5; when x = O, y = (195 ——- O)% = 5.; a: = 1, y =' (125 —- ifsL = 4.986; x = 2, y = (125 ~— sfi = 4.89; x = 3, 2/ = (125 -— ~27)% = 4.610; .r = 4, 3/ = (195 —— 640% = 3.936; x = 5,_y : (125 -125fi= 0. Figure 11, is drawn by these numbers, according to the diagonal scale, Figure 13. Figure 12, is drawn by the same equation, to a different set of numbers, to the same scale, Figure 13. Another equation, by which figures of this de- scription may be obtained, is the following: 3/ = (ax —- xzfi. Leta =10, x=l,_y=(10— 1)%=1.73; x=Q,y=(QO—— 4)i=2.; x=3,y=(30——- 9)%=2.14; x=4,y=(4o—-16)i=2.21; x=5,y=(5o—25)i=e.es. But perhaps the most beautiful figure of the oval species is the ellipses. The equation of the circle is 9 = (d x -— bi; let d = 20, then will 3/ = (201* — xzfig then when (2”4 "4V ("4)2 — “ “ Z —- — 2%—- ,therefoie— : a: : OUT \ x== l,y=(Q0 —— 1)%=195=4.3588989, x=2,y=(4o — 4)%=36%=6. x = 3, g = (60 — 9% = 51% = 7.1414,..84, x=4,y=(80 ~16)%=64%=8., x = 5,3/ = (100 -— 25% = 75% = 8.660254, x=6,y=(IQO—- 36)‘2“=84.é =9.1651514, =7, y=(140-——- 49%)=91%=9539392, x=8,y==(160— 64%:965 =9.797909, a: = 9,3; = (180—— 80% = 99% = 9.9493744; NIH x=10,y = (200 —— 100)é =100‘ 10. From these numbers, an ellipses may be construct- ed, of any length and breadth, by multiplying them by the ratio of the axis §, 1%, %, %, -§-, suppos— ing the breadth to be i, a, %, %, if} of the length. A kind of oval, as it is called, which may easily be described through points, is the following: Figure 14, No. 1, describe a semicircle, A P C, on the diameter A C, for the length : draw A D perpendicular and equal to A C; take any point, B, in AC; join B D; draw Bp parallel to AD, cutting the circle in p,- drawp m perpendicular to Bp, cutting B D at m; make AC, No. 2, equal to A C, No. 1; and every A P in No. 2, equal to every AB in No.1; also every PM in No. 2, equal to the corresponding]; m in No. 1: through all the points, M, draw a curve. This figure is of the form of a pear, and not What may denominated an oval. OVICULUM, in ancient architecture, alittle ovum, or egg. OVOLO (from the Latin ovum, an egg) a convex moulding, of which the lower extremity recedes from a perpendicular or vertical line drawn from the upper. See MOULDINGS. OUNCE, a small weight, the sixteenth part of a. pound avoirdupois, and the twelfth part of a pound Troy. OUTER DOORS, those which are common to both the exterior and interior-sides of a building, made to prevent entrance at the pleasure of the occupier. OUT-LINE, the contour or boundary of an object. OUT OF WINDING, a term used by artificers to signify, that the surface of a body is that of a plane; or, when two straight edges are in the same plane, they are said to be out of winding. OUT-TO-OUT, an expression used when a dimen- sion is taken to the utmost bounds of a body or figure. OUTWARD ANGLE, the same as salient angle. 414 PAG PAD DLE (from the Welsh pattal) a small sluice, similar to those by which locks are filled or emptied. PADDLE HOLES, the crooked arches through which the water passes from the upper pond of a canal into the lock, to fill it; or through which it is let out into the lower pond, on the entrance and exit of vessels. They are sometimes called CLOUGH ARCHES. PADDLE WEIRS, see LOCK WEIRS. PADDOCK, or PADDOCK COURSE (from the Saxon pada, or Dutch padde) a piece of ground, generally taken out ofa park, ordinarily a mile long, and a quarter of a mile broad, encompassed with pales or a wall, for the exhibiting of races with greyhounds, for wagers, plates, or the like. At one end of the paddock was a little house, where the dogs were to be entered, and whence they were slipped; near which were pens to en- close two or three deer for the sport. The deer, when turned loose, ran along by the pale; and the spectators were placed on the other side. Along the course were several posts; viz. thelaw- post, 160 yards from the dog-house and pens; the quarter-of-a-mile post,- half-mile post; and pinching post; beside the ditch, a place made to receive the deer, and preserve them from farther pursuit. Near the ditch were the judges, or triers. PAGOD, or PAGODA, a name, probably indian, which the Portuguese have given to all the tem- ples of the Indians, and all the idolaters of the East. These pagods, or pagodas, are mostly square; they are stone buildings, which are not very lofty, and are crowned with acupola. \Vithin, they are very dark; for they have no windows, and only receive their light through the entrance. The image of the idol stands in the deepest and darkest recess of the temple; it is of a monstrous shape, and of uncouth dimensions, having many arms and hands. Some of these idols have eight, and others sixteen arms; with a human body, and the head of a. dog, with drawn bows and instru- P. l PAG ments of war in their hands. Some of them are black, others of a yellowish hue. In some pa- godas there are no images, but only a single black polished stone, lying upon a round altar, covered with flowers and sandal-wood, which were strewed upon it. Greater veneration is mani- fested for these stones than for the idols them- selves. Their worship of these divinities con- sists in throwing themselves upon the ground, and making their salam, or salutation, with their hands, and ejaculating their prayers in silence, in that posture. The offerings which they are ac- customed to present to their gods, consist of flowers, rice, pieces of silk and cotton, and some- times gold and silver. Every thing is laid before the idols, and is taken care of by the Brahmins,who profit the most by it. They guard the pagodas both by day and night. The pagodas of China are lofty towers, which sometimes rise to the height of nine stories, of more than 20 feet each. See CHINESE ARCHITECTURE. In order to give such an idea of these buildings as may enable the reader to judge with respect to the early state of arts in India, we shall briefly describe two, of which we have the most accu- rate accounts. The entry to the pagoda of Chil- lambrum, near Porto Novo, on the Coromandel coast, held in high veneration on account of its antiquity, is by a stately gate under a pyramid, 122 feet in height, built with large stones above forty feet long, and more than five feet square, and all covered with plates of copper, adorned with an immense variety of figures, neatly exc- cuted. The whole structure extends 1332 feet in one direction, and 936 in another. Some of the ornamental parts are finished with an elegance en» titled to the admiration of the most ingenious artists. The pagoda of Seringham, superior in sanctity to that of Chillambrum, surpasses it as much in grandeur; and, fortunately, we can con- vey a more perfect idea of it by adopting the words of an elegant and accurate historian. This pagoda is situated about a mile from the western exttemity of the island of Seringhaun, formed by the division of the great river Caveri into two PAIN TE RS, House. PAI 415 J PAI channels. “ It is composed of seven square in- closures, one within the other, the walls of which are 25 feet high, and four thick. These inclosures are 350 feet distant from one another, and each has four large gates with a high tower; which are placed, one in the middle of each side of the in- closure, and opposite to the four cardinal points. The outward wall is near four miles in circumfer- ence, and its gateway to the south is ornamented ~ with pillars, several of which are single stones, 33 feet long, and nearly five in diameter; and those which form the roof are still larger; in the inmost inclosures are the chapels. About halfa mile to the east of Seringham, and nearer to the Caveri than the Coleroon, is another large pa- goda, called Jembikisma; but this has only one inclosure. The extreme veneration in which Se- ringham is held, arises from a belief that it con— tains that identical image of the god VVistchnu, which used to be worshipped by the god Brahma. Pilgrims from all parts of the Peninsula come here to obtain absolution, and none come without an offering of money; and a large part of the re- venue of the island is allotted for the mainte- nance of the Brahmins who inhabit the pagoda; and these, with their families, formerly composed a multitude not less than forty thousand souls, maintained, without labour, by the liberality of superstition. Here, as in all the other great pa- gados of India, the Brahmins live in a subordina- tion which knows no resistance, and slumber in a voluptuousness which knows no wants.” The pagodas of the Chinese and Siamese are ex- ceedingly magnificent. SeelNDrAN ARCHITEC- TURE. The price of painters’ work is limited by statute, and they shall not take above 16d. a day, for laying any fiat colour, min- gled with oil or size, upon timber, stone, 8m. and plasterers are forbid using the trade of a painter in London, or to lay any colours of painting, un- less they are servants to painters, 8L0. on pain of .51. But they may use whiting, blacking, red lead, ochre, Ste. mixed with size only. Stat. ]. Jac. I. cap. Q3. Painting is measured by the square yard in the same manner as wainscoting, the mouldings be- ing measured by a thread. The sashes of windows are paid for by the piece: and it is usual to allow double measure for carved mouldings, 8w. PAINTING, the art of imitating the appearances of natural objects, by means of artificial colours spread over a surface; the colouring substances being used either dry, as in crayon painting; or compounded with some fluid vehicle, as oil, water, or solutions of different gums and resins in oil or spirits, &c. The theory and practice of this ingenious art are divided by its professors into five principal parts ; viz. invention, or the power of conceiving the ma- terials proper to be introduced into a picture; composition, that of arranging those materials; design, that of delineating them; Chiaro-scuro, or the arrangement and management of the lights and shades, and of light and dark colours; and colouring, whose name sufficiently designates its end. PAINTING, Economical, that application of artifi- cial colours, compounded either with oils or water, which is employed in preserving or embellishing houses, ships, furniture, 8L0. 86c. The term eco— nomical, applies more immediately to the power which oil and varnishes possess, of preventing the action of the atmosphere upon wood, iron, and stucco, by interposing an artificial surface; but it is here intended to use the term more generally, in allusion to the decorative part, as applied to buildings; as well as to its more essen- tial ones; and as it is employed by the architect, throughout every part of his work, both externally and internally. In every branch of painting in oil, as applicable either to churches, theatres, houses, or any other public or private buildings, or edifices, the general process will be found very similar; or with such variations, as will easily be suggested by the judi- cious artist, or workman. The first coatings, or layers, if on wood or iron, ought always to be of ceruse or white lead; the very best that can be obtained; which should have been previously ground very fine in nut or linseed oil, either over a stove with a muller, or, as that mode is too tedious for large quantities, it may be passed through a mill. If used on wood, as shutters, doors, or wainscoting made of fir or deal, it is highly requisite to destroy the effects of the knots; which are generally so completely saturated with turpentine, as to render it, perhaps, one of the most difficult processes in the business to conquer. The best mode in common cases, is to pass over the knots with ceruse ground in water; bound by a size made of parchment, or PAI 416 PAl some other animal substance. When that is dry, paint the knots with white lead ground in oil, to which add some powerful siccative, or dryer; as red lead, or litharge of lead, about one fourth part of the latter. These preparations should be done carefully, and laid very smoothly with the grain of the wood. When the last coat is dry, which will be in twelve or twenty—four hours, then smooth it with pumice-stone, or give the work the first coat of paint, prepared, or diluted with nut or linseed oil. \Vhen that is dry, all the nail holes or other irregularities on the surface should be carefully stopped, with a composition of oil and Spanish white, a whiting commonly known by the name of putty; but which is frequently made and sold at the shops of very inferior arti- cles. When that is dene, let the work be painted over again, with the same mixture of white lead and oil, somewhat diluted with the essence ofoil of turpentine, which process should be repeated not less than three or four times, if the work is intended to be left, when finished, of a plain white or stone colour; if of the latter, the last coat should have a small quantity of ivory or lamp black added, to reduce its whiteness a little; and this is also of service in preserving the colour from changing: a circumstance which the oil is apt to produce. But if the work is to be finished of any other colour, either grey, green, &c. it will be requisite to provide for such colour, after the third operation, particularly if it is to be finished flat, or, as the painters style it, dead white, grey, fawn, Ste. in order to finish the work fiatted, or dead, (which is a mode much to be preferred for all superior works; not only for its appearance, but also for preserving the colour, and purity of the tint) after the work, sup- posing it to be wood, has been painted four times in oil colour, as directed in general cases, one coat of the flatted colour, or colour mixed up with a considerable quantity of turpentine, will be found sufficient; although in large surfaces it will frequently be requisite to give two coats of the flatting colour to make it quite complete. Indeed, on stucco it will be almost a general rule; but as that will be hereafter treated on, we shall at present say no more con- cerning it. It must be observed, that in all the foregomg ope- rations, it will be requisite to add some sort of siccative. A very general and useful one is made by grinding in linseed, or, perhaps, prepared oils, boiled, are better, about two parts of the best white copperas, which must be well dried, with one part .of litharge of lead: the quantity to be added will much depend on the dryness or humi- dity of the atmosphere, at the time of painting, as well as the local situation of the building. It is highly proper here to observe, that there is a kind of copperas made in England, and said to be used for some purposes in medicine, that not only does not assist the operation of drying-in the co- lours, but absolutely prevents those colours drying, which would otherwise have done so by them- selves. The best dryer for all fine whites, and other delicate tints, is saccharum saturni, or sugar oflead, ground in nut oil; but which being very active, 21 small quantity, about the size of a wal- nut, will be suflicient for twenty pounds of co- lour, where the basis is ceruse. It will be always worthy to be observed, that the greatest care should be taken to keep all the utensils, brushes, 8L0. particularly clean, or the colours will soon become very foul, so as to destroy the surface of the work. If this should so happen, the colour should be passed through a fine sieve, or canvass; and the surface of the work be carefully rubbed down with sand-paper, or pumice-stone; and the latter should be prepared by being ground in water, if the paint be tender, or recently laid on. The above may suffice as to painting on wood, either on outside or inside works; the former being seldom finished otherwise than in oil, four or five coats are generally quite sufficient. We shall now proceed to note what is requisite for the painting of new walls, or stucco, not paint- ed before, and prepared for oil colours. It does not appear that any painting in oil can be done to any good or serviceable effect in stucco, unless not merely the surface appear dry, but that the walls have been erected a sufficient time to permit the mass of brick-work to have ac- quired a su‘fiieient degree of dryness: when stucco is on battened work, it may be painted over much sooner than when prepared as brick. Indeed, the greatest part of the mystery of painting stuc- co, so as to stand or wear well, certainly consists in attending to these observations; for whoever has observed the expansive power of water, not only in congelation, but also in evaporation, must be well aware that when it meets with any to- reign body obstructing its escape, as oil painting PA! 417' PA! for instance, it immediately resists it; forming a number of vesicles, or particles, containing an acrid lime-water, which forces off the layers of plaster, and frequently causes large defective patches, extremely diflicult to get the better of. Perhaps, in general cases, where persons are build- ing on their own estate, or for themselves, two or three years are not too long to suffer the stucco to remain unpainted; though frequently, in speculative works, as’ many weeks are scarcely allowed. Indeed, there are some nostrums set forth, in favour of which» it is stated, in spite of all the natural properties of bodies, that stucco may, after having been washed over with these liquids, be painted immediately with oil colours. It is true there may be instances, and in many experiments some will be found, that appear to counteract the general laws of nature; but, on following them up to their causes, it will be found otherwise. Supposing the foregoing precautions to have been attended to, there can be no better mode adopted for priming or laying on the first coat on stucco, than by linseed or nut oil, boiled with dryers, as before mentioned, with a proper brush; taking care, in all cases, not to lay on too much, so as to render the surface rough and irregular, and not more than the stucco will absorb. It should then be covered with three or four coats of ceruse, or white lead, prepared as described for painting on wainscotting; letting each coat have sufficient time to dry hard. If time will permit, two or three days between each layer will not be too long. If the stucco be intended to be finished of any given tint, as grey, light green, apricot, Sic. it will then be proper, about the third coat of paint- ing, to prepare the ground for such tint, by a slight advance towards it. Grey is made with ceruse, Prussian blue, ivory black, and lake; sage green, pea, and sea greens, with white, Prussian blue, and fine yellows; apricot and peach, with lake, white, and Chinese vermilion; fine yellow fawn colour, with burnt terra Sienna, or umber, and white; olive greens, with fine Prussian blue and Oxfordshire ochre. Painting in distemper, or water-colours mixed with size, stucco, or plaster, which is intended to be painted in oil when finished; but not being sufficiently dry to receive the oil, may have a coating in water-colours, of any given tint re- VOL. II. ' WW -I_ -___m I, quired, in order to give a more finished appear— ance to that part of the building. Straw colours may be made with French white, a ceruse, and masticot, or Dutch pink. Greys, fine, with some whites, and refiners’ verditer. An inferior grey may be made with blue-black, or bone-black, and indigo. Pea-greens, with French green, Olympian green, Ste. Fawn colour with burnt terra de Sienna, or burnt umber and white: and so of any intermediate tint. The colours all should be ground very fine, and incorporated with white, and a size made of parchment, or some similar substance; isinglass being too expensive for common works. It will not require less than two coats of any of the foregoing colours in order to cover the plas- ter, and bear out with an uniform appearance. It must be recollected, that when the stucco is sufl‘iciently dry, and it is desirable to have it painted in oil, the whole of the water-colour ought to be removed; which may be easily done by washing; and, when quite dry, proceed with it after the directions given in oil painting of stucco. . When old plastering has become discoloured by ,stains, and it be desired to have it painted in dis- temper; it is then adviseable to give the old plas- ter, when properly cleaned off and prepared, one coat at least of white-lead ground in oil, and used with spirits of turpentine, which will generally fix all old stains; and, when quite dry, will take the water-colours very kindly. The above processes will also apply to old wainc scotting, in cases where temporary painting is only required; but cannot be recommended for dura— bility. PAISLEY ABBEY CHURCH, a venerable anti- quity in the county of Renfrew, first founded as a priory by Walter, lord high steward of Scot- land, and filled by him with monks of the order of Clugni; but it afterwards attained the rank of an abbacy. The lands belonging to it were farther erected by Robert H. into a regality under the jurisdiction of the abbot. At the Re- formation, this abbey was secularized, and is now in the Abercorn family. Many additions have been made to the buildings of this abbey at dif- ferentaeras since its original erection. Abbot Shaw, in particular, enlarged and beautified the whole monastery, and indeed he may properly be re. garded as a second founder. He built the res 3 H .PAL 4.1 8 PAL fectory and other offices necessary for the monks, the church, and the precinct of the convent; and enclosed the ga1dens and o1cha1ds by a wall ofhewn stone, which measured about a mile 1n circuit. All the buildings of this abbey are much dilapi- dated, excepting the chancel of the church, which is still entire, and has of late years been fitted up for parochial service. Judging from this member, and some additional ruins, the church appears to have been, when complete, a very grand and magnificent structure. It was in the form of a cross, but the only part of the transept standing is the great north window, the arch of which is uncommonly lofty and elegant. The chancel is separated into amiddle and two side aisles, by two ranges of columns, supporting pointed arches, and having their capitals ornamented with gro- tesque figures. The exterior of this building dis- plays much sculptural embellishment, especially the north and south doo1s. PADDLE VVEIRS, see Loex VVEIRs. PALACE (from the Latin palatium) a name gene- rally given to the dwelling-houses of kings and princes. And as the kings usually heard and determined causes in their houses, in what part of the realm soever they were situate, palatium became a name for a court ofjustiee, which usage is still retain- ed, especially in France. In course of time, the name palace has also been applied to the houses of other persons: taking different epithets, according to the quality of the inhabitants; as imperial palace, royal palace, ontifical, cardinal, episcopal, ducal palace, Ste. PALZESTRA (from the Greek 7ra\atspa) among the ancient Greeks, a public building, where the youth exercised themselves in wrestling, running, playing at quoits, 8L0. Some say the palestrae consisted of a college and an academy; the one for exercises of the mind, the other for those of the body. But most authors rather take the paleestra to be a xystus, or mere academy for bodily exercises, according to the etymology of the word, which comes from man, wrestling, one of the chief exercises among the ancients. The length of the palaestra was marked out by stadia, each equal to 125 geometrical paces; and hence the name stadium was given to the arena whereon they ran. PALATINE BlilDG E, a bridge of ancient Rome, * } now called St. Mary’s bridge, which crosses over from the present church of St. Mary the Egyp- tian, at the lower end of the Forum Boarium to the Via 'l‘ranstiberina. This bridge is supposed to be that which Livy speaks of (Decad. 4». lib. 10.) built by M. Fulvius, washed down by the Tiber, and afterwards rebuilt by the censors Scipio Afri- canus and L. Mummius. Another inundation having damaged it, Pope Gregory Xlll. repaired it, partly upon the old piles, in the year 1575. But another inundation sweeping away some of it in 1598, it has never since been repaired, so as to be serviceable. PALE (from the Latin palus) a little pointed stake, 01 piece of wood, used in making enclosures, se- parations, Ste. PALES, or Puss, in carpentry, rows of stakes d1iveri deep 1n the giound to make wooden bridges over 1ive1s, and to e1ect othe1 edifices on. Du-Cange derives the won] from the Latin name palla, a hanging, or piece of tapestry: the ancients gave the name pales to the hangings or linings of walls: thus a chamber was said to be poled with cloth of gold, with silk, 8L0. when covered with bands or stuffs of two colours. Hence also the original of the word pale, a stake, 8w. Tertullian observes, that the Romans planted pales to serve as boundaries of inheritances; and that they consecrated them to the god Terminus, under the name ofpali Terminales. Ovid tells us, they were crowned and adorned with flowers, festoons, Ste. and that the god was worshipped before these pales. See TERMINALIA. PALES for building, serve to support the beams which are laid across them, from one row to an- other; and are strongly bound together with cross- pieces. See PILES. PALETTE (French) among painters, a little oval table, or piece of wood, or ivory, very thin and smooth; on and round which the painters place the several colours they have occasion for, to be ready for the pencil. The middle serves to mix the colours on, and to make the teints required in the work. It has no handle, but a hole at one end, to put the thumb through to hold it. PALIN G, in agriculture, a kind of fence-work for fruit-trees, Ste. planted in exposed places. It consists of three small posts driven into the ground, at a foot and a half distance, with cross bars nailed to each other, near the top. PAL 419 M In fixing the pales, in form of a triangle, room is to be left for the tree to play and bow by the . high winds, without galling. The trees are to be bound to a stake for a year or two; after which fern or straw may be stuffed in between the tree and uppermost rails, to keep it upright. If the place be open to deer, rabbits, or the like, a post is to be nailed to the bar between every two pales. PALING FENCE, that sort of fence which is con- structed with pales. PALISADE (French) or PALIsADO (Italian) in fortification, an enclosure of stakes or piles driven into the ground, each six or seven inches square, and nine or ten feet long; three feet of which are hid under ground. They are fixed about six inchES asunder, and braced together by pieces nailed across them near the tops, and secured by thick posts at the distance of every four or five yards. Palisades are placed in the covert-way, at three feet from, and parallel to the parapet or ridge of the glacis, to secure it from being surprised. They are also used to fortify the avenues of open forts, gorges, half-moons, the bottoms of ditches, the parapets of covered ways; and, in general, all posts liable to surprise, and to which the access is easy. - Palisades are usually planted perpendicularly; though some make an angle inclining towards the ground next the enemy, that the ropes cast over them, to tear them up, may slip. PALISADES, Turning, are an invention of M. Coehorn, in order to preserve the palisades of' the parapet of the covert-way from the besiegers’ shot. He orders them so, that as many of them as stand in the length of a rod, or in about ten feet, turn up and down like traps; so as not to be in sight of the enemy till they just bring on their attack; and yet are always ready to do the proper service of palisades. PALLADlO, AN DREA,in biography, a celebrated Italian architect, born at Vicenza in 1518. He obtained instructions from the poet Trissino, who discovering in him a genius for sculpture and the arts connected with it, taught him the elements of the mathematics, and explained to him the works of Vitruvius. He soon obtained distinc- - tion as an architect, and having an opportunity of accompanying his patron to Rome, he em- PAL #4 ployed all his faculties in examining the remains of ancient edifices in that capital, and formed his taste upon them. On his return, many works of importance were committed to him, which he managed with great skill, and obtained for him- self a high reputation. He was now sent for to Venice, where he built the palace Foscari in the style of pure antiquity. Several other Italian cities were afterwards decorated with magnificent edifices, public and private, of his construction, , and he was invited to the court of Emanuel Phi- libert, Duke of Savoy, who received him with distinguished honours. To Palladio is chiefly at~ tributed the classic taste which reigns in so many of the buildings of Italy. His master-piece is reckoned the Olympic theatre at Vicenza, in imi- tation of that of Marcellus at Rome. He died in that city in 1580, having greatly improved the art, not only by his edifices, but by his writings, which are standard performances. Of these the following account is given : his Treatise on Archi- tecture, in four books, was first published at Venice in 1570, folio, and has several times been reprinted. A magnificent edition, in three volumes, folio, was published at London in 1715, in Italian, French, and English. Another, equally splendid, has since been published at Venice, in four vo- lumes, folio, with the addition of his inedited buildings. Lord Burlington published in Lon- don, in 1730, a volume, intitled, Idisegni delle Terme Antiche di Andrea Palladio. He composed a small work, intitled Le Antichitd di Roma, not printed till after his death. He illustrated Caesar’s Commentaries, by annexing to Badelli’s transla- tion of that work, a preface on the military 3 's- tem of the Romans, with copper-plates, designed, for the most part, by his two sons, Leonida and Orazio, who both died soon after. Palladio was modest in regard to his own merit, but he was a friend to all men of talents; his memory is highly honoured by'the votaries of the fine arts; and the simplicity and purity of his taste have given him the appellation of the Raphael of architects. PALLADIUM (from the Greek HaMag, the goddess oftt'ar) in antiquity, a statue of the goddess Pal- las, or Minerva, three cubits high, holding a pike in the right hand, and a distaf’f and Spindle in the left, preserved in Troy, in the temple of Minerva, on which the fate of that city is said to have de- pended. The tradition is, that in building a citadel, in 3 H 2 _ PAL' 5* #5“ ‘- 420' g PAH honour of Pallas, and atem‘ple in the most ele- vated part of it, the palladium dropped from heaven, and marked out the place which the god- dess was pleased to possess. After this, Apollo gave an oracle, importing that Troy should never be taken while the palladium was found within its walls : which occasioned Diomedes and Ulys- ses, during the Trojan war, to undertake the stealing of it. For this purpose, having entered the citadel by night, or by means of secret intel- ligence, they stole away this valuable pledge of the security of the Trojans, and conveyed it into their camp ; where they had scarcely arrived, when the goddess gave testimonies of her wrath. It is said, there was, anciently, a statue of Pallas preserved at Rome, in the temple of Vesta; which some pretended to be the true palladium of Troy, brought into Italy by IEneas: it was kept among the sacred things of the temple, and only known to the priests and vestals. This statue was es- teemed the destiny of Rome; and there were several others made perfectly like it, to secure it from being stolen. There was also a palladium in the citadel of Athens, placed there by Nicias. PALLIER, or PAILLIER (French) in building, '1 landing-place in a staircase, which being broader than the rest of the stairs, serves to rest upon. The term, which is pure French, is not much used by English builders. On large staircases, where there are sometimes several pillars in a range or line, the palliers ought each to have, at least, the width of two steps. Vitruvius calls the palliers on landing-places of the theatres diazomata. PALLIFICATION, or PILING, in architecture, the act of piling the groundwork, or strengthen- ing it with piles, or timber driven into the ground; which is practised upon moist or marshy soils, where an edifice is intended to be erected. PALMYRA, Ruins of, or PALMYRENE RUINS, the ruins of a celebrated city of this name, situate in a desert of Syria, in the pachalic of Damascus, about 48 leagues from Aleppo, and as far from Damascus. This city. under the name of Tad- mor, appears to haVe been originally built by So- lomon (1 Kings, ix. 18. 9 Chron. viii. 4.) Jose- phus assures us, that this was the same city which the Greeks and Romans afterwards called Pal- myra; and it is still called Tadmor by the Arabs Ana‘s of the country. But many circumstances, be- sides the style of the buildings, render it probable that the present ruins are not those of the city» built by Solomon, though neither history nor tra- dition mention the building of any other. With respect to the ruins, they appear to be of two distinct periods; the oldest are so far decayed as not to admit of mensuration, and seem to have been reduced to that state by the hand of time; the others appear to have been broken into fragments by violence. Of the inscrip- tions, none are earlier than the birth of Christ, nor are. any later than the destruction of the city by Aurelian, except one, which mentions Dioclesian. It is scarcely less difficult to account for the situation of this city than for its magni- ficence; the most. probable conjecture is, that as soon as the springs of Palmyra were discovered by those who first traversed the desert in which it is situated, a settlement was made there for the purpose of carrying on the trade to India, and preserving an intercourse between the Mediter- ranean and Red Sea. This trade, which flourished long before the Christian aera, accounts not only for its situation, but also for its wealth. As it lay between Egypt, Persia, and Greece, it was natural to expect, that traces of the manners and sciences of those nations should be discovered among the Palmyrenes; who accordingly appear to have imitated the Egyptians in their funeral rites, the Persians in their luxury, and the Greeks in their buildings; and therefore the buildings, which now lie in ruins, were probably neither the works of Solomon, nor of the Seleucidee, nor, few ex- cepted, of the Roman emperors, but of the Pal- myreues themselves. Palmyra was formerly encompassed by palms and fig-trees, and covered an extent of ground, ac- cording to the Arabs, near ten miles in circumfer- ence; and might probably have been reduced to its present confined and ruined state by quantities of sand, driven over it by whirl winds. The walls of the city are flanked with square towers; and it is probable, from their general direction, that they included the great temple, and are three miles in circumference. But, of all the monuments ofart and magnificence in this city, the most consider— able is the temple of the sun. The whole space containing its ruins, is a square of 220 yards, en- compassed with a stately wall, and adorned with pilasters within and without, to the number of PAN 421 PAN W sixty~two on a side. Within the court are the remains of two rows of very noble marble pillars, 37 feet high; the temple was encompassed with another row of pillars 50 feet high; but the tem- ple itself was only 33 yards in length, and 13 or 14 in breadth. This is now converted into a a mosque, and ornamented after the Turkish man- ner. North of this place is an obelisk, consisting of seven large stones, besides its capital and the wreathed work about it, about 50 feet high, and, just above the pedestal, twelve in circumference. Upon this there was probably a statue, which the Turks have destroyed. At a small distance, there are two others, and a fragment of a third, which gives reason for concluding that they were once a continued row. There is also a piazza 40 feet broad, and more than half a mile in length, en- closed with two rows of marble pillars, 26 feet high, and eight or nine feet in compass; and the number of these, it is computed, could not have been less than 560. Near this piazza appear the ruins of a stately building, supposed to have been a banqueting house, elegantly finished with the best sort of marble. In the west side of the piazza there are several apertures for gates into the court of the palace, each adorned with four porphyry pillars, 30 feet long, and nine in cir- cumference. There are several other marble pil- lars differently arranged, on the pedestals of which there appear to have been inscriptions, both in the Greek and Palmyrene languages, which are now altogether illegible. Among these ruins there are also many sepulchres, which are square towers, four or five stories high, and vary- ing in size and splendour. We are indebted for an account of these very magnificent remains of antiquity, partly to some English merchants who visited them in 1678 and 1691, (Phil. Trans. No. 217, 218, or Lowthorp’s Abr. vol. iii.) but chiefly to M. Bouverie and Mr. Dawkins, accompanied by Mr. It. Wood, who travelled thither in 1751. The result of their observations was published in 1753, in the form of an Atlas, containing fifty- seven copper-plates, admirably executed. Since this publication, it is universally acknowledged that antiquity has left nothing, either in Greece or Italy, to be compared with the magnificence of the ruins of Palmyra. PANEL, or PANNEL (from the Latin panel/um, a small pane) in joinery, a tympan, or square piece of wainscot, sometimes carved, framed, or grooved in a largev'piece, between two niounters or upright pieces, and two traverses or cross pieces. Hence also panels or panes of glass, are compartments, or pieces of glass of various forms; square, hex- agonal, Ste. PAN EL, in masonry, one of the faces ofa hewn stone. PANNIEH, see CORBEL. PANORAMA, a picture exhibiting a succession of objects upon a spherical or cylindrical surface, the rays of light being supposed to pass from all points of external objects, through the surface, to the eye in the centre of the sphere, or axis of the cylinder. The first application of the representation of na- tural objects on the surface of a cylinder, is due to the late Mr. Barker. As no express treatise on this subject has yet appeared, the following essay, by the Author of this Work, will, it is hoped, be acceptable to the reader. » PANORAMIC PROJECTION is the method of form- ing a panorama, from the geometrical considera- tion of the properties of vision. In the following principles of the panorama, the surface on which objects are supposed to be re- presented is that ofa cylinder; though a sphere may be considered still more perfect, as its sur- face is every where equally distant from the eye; but a cylindric surface is more convenient for the purpose of delineation; and if the objects are not very distant from the intersection of a plane passing through the eye perpendicular to the axis, the distortion will not be perceptible. We pre- mise the following definitions: 1. The cylindric surface on which objects are to be represented, is called also the panoramic sur- face; and the picture formed is called a panoramic mew, or panoramzc pzcture. 2. The point of‘sz’g/zt is the place where the organ of vision is placed, in order to receive the impres- sion of the images of the objects on the panora- mic picture. 3. An original object is any object in nature, or an object which may be supposed to exist, in a given position and distance, as a point, line, or solid. 4. An original plane is the plane on which origi~ nal objects are supposed to be placed. 5. The point where an indefinite original line cuts the picture, is called the intersection officat original line. PAN 6. The line on the picture where an original plane meets or intersects it, it is called the intersection of that original plane. 7. A line drawn through the point of sight paral- lel to an original line, is called theparallel of that original line. i 8. A plane passing through the point of sight parallel to any original plane, is called the paral- lel plane. 9. A swface of rays is that which proceeds from an original line, or from any line of the original object, by rays from all points of that line termi- nating in the eye. If the line in the original ob- ject be straight, the surface of rays is called a plane of rays, optic plane, or visual plane. 10. When the rays proceed from one or more sur- faces of an original object, the whole is called a ' pyramid quys, or opticpyramid; and if the base be circular, it is called a cone afrays, visual cone, or optzc cone. In every kind of projection from a given point, the projection of a straight line upon any surface is the intersection ofa plane of rays with the sur- face from all points of the straight line to the given point. Therefore the panoramic projec- tion ofa straight line is the intersection of the cylindric surface and a plane. If a right cylinder be cut by a plane perpendicular to its axis, the section is a circle; if out parallel to the axis, the section is a rectangle; and if cut obliquely to the axis, the section is an ellipsis. If the surface of the cylinder be extended upon a plane with the sections of the cylindric surface and a plane cut in each of the positions here stated, the section made by the plane perpendicular to the axis will be a straight line ; and the section made by cut- ting it parallel to the axis will also be a straight line; but the section made by cutting it obliquely will be a curve of similar properties with that known to mathematicians by the name of thefigure of the lines; therefore the projection of every straight line in a plane passing through the eye perpendicular to the axis of the cylinder, will also be a straight line on the extended surface; and every straight line in a plane passing through the axis will also be a straight line on the extended surface, perpendicular to that formed by the plane passing through the eye perpendicular to the axis. The panoramic projection of any straight line not in a plane passing through the eye perpendicular 42% W \ PAN to the axis, nor in a plane passing through the axis, is in the curve of an ellipsis; for in this case the optic rays which cut the cylinder will neither be in a plane parallel to the axis, nor in a plane perpendicular to it. The panoramic representation of any straight line in a plane perpendicular to the axis, but not pass- ing through the eye, is in the curve of an ellipsis, and the optic plane will be at right angles to an- other plane passing through the axis at right an- gles to the original line. In the panoramic representation of any series of parallel lines, the optic planes have a common intersection in a straight line passing through the eye, and the common intersection will be parallel to each of the original straight lines; therefore the indefinite representations will pass through the extremities of the common intersection. In the panoramic representation of any series of parallel lines in a plane perpendicular to the axis, but not passing through the eye, the common intersection of the optic planes is parallel to the plane on which the original lines are situated. In the indefinite representations of any number of straight lines parallel to‘the axis, the visual planes will have a common intersection in the axis, and will divide the circumference of the cy~ linder into portions which have the same ratio to each other as the inclination of the visual planes. If an original straight line parallel to the axis be divided into portions, the representations of the portions will have the same ratio to each other as the originals. If in any original plane there be a series of straight lines parallel to each other, and also an- other series of straight lines parallel to each other, and at any given angle with the former series, the common intersections of the visual planes will make the same angle with each other, which any line of the one series makes with any one of the other series, and the common intersections will be in a plane parallel to the original plane; and, therefore, if the original plane be perpendicular to the axis, the common intersections of the visual planes will also be in a plane perpendicular to the axis. Hence the common intersections of visual planes from any two systems of straight lines, pa- rallel to any two straight lines at a given angle with each other in a plane perpendicular to the axis, are also ina plane perpendicular to the axis, PAN 4:23 ‘PA’N “W and make the same angle with each other which the two lines in the original plane make with each other. . ll. rl‘he two points where the parallel of an ori— ginal line inclined to the axis ofthe cylindermects the panoramic surface, are called the vanishing points of that original line. 12. The intersection of the parallel of an original plane is called the vanishing line (fthat plane. 13. A straight line drawn from any point in the axis of the cylinder, at right angles to the same, to meet the panoramic surface, is called the dis- tance of the picture. 14. The centre ofa plane parallel to the axis, is the point where a straight line from the eye perpen- dicular to the plane meets it. 15. The panoramic centre ofa plane parallel to the axis, is the point where a straight line drawn from the eye perpendicular to the plane cuts the picture. 16. The station point, is the point where the axis intersects the original plane. 17. The centre of an original line, is the point where a straight line, drawn from the station point perpendicular to the original line, cuts the original line. 18. The panoramic centre of an original line, is the point where a straight line, drawn from the station point perpendicular to the original line, cuts the picture. 19. The distance (fan original plane parallel to the axisfrom the picture, is the straight line drawn from the panoramic centre to the centre of the original plane. 20. The distance ofan original line from the pic- ture, is the straight line drawn from the panora- mic centre to the centre of the original line. 21. The distance of an original plane, is the straight line drawn from the eye to the centre of the original plane. 22. The distance ofan original line, is the straight line drawn from the station point to the centre of the line. An original line parallel to the axis of the pano- rama has no vanishing points. An original plane parallel to the axis of the pa- norama has two vanishing lines. The vanishing line of a plane perpendicular to the axis of the panorama, is a circle on the pano- ramic picture; but if the panoramic surface be extended upon a plane, it becomes a straightline. The vanishing lines of all planes inclined to the axis are ellipses, and when extended upon a plane become sinical curves, which are also termed panoramic curves, as, being the only kind of curve which the cylindric picture produces when de- veloped. PROBLEM I. Plate I. Figure 1.—-To describe the panoramic curve to given dimensions—Let A B be the length of the curve; bisect AB'in C, draw C D perpendicular to A B; make C D equal to the deflection of the are from the chord A B; from the point C, with the distance C D, describe the quadrant DE; divide the are D E into "any number of equal parts (say four) also divide either half, C B, into the same number (four) of equal parts; let I, i, g, be the points of division in the quadrantal arc; draw l 15, i h, gf, perpen— dicular to A B, cutting it at k, h,f; and let K, H, F, be the points of division in C B; draw K L, H I, FG, perpendicular to A B; make K L, H I, F G, respectively equal to h l, h i,fg; con~ struct perpendiculars upon C A, in the same man- ner; through all the points G, I, L, D, describe a curve, which will be that of the panorama. The curve A DB is that which would be found by cutting a semi-cylinder, whose circumference is A B, at an altitude, C D, distant on the surface from a plane perpendicular to the axis, at a qua— drant distance from the point A or B in the ex- tremity of the diameter of the plane perpendi- cular to the axis. Therefore the whole panoramic curve will be double the length of A B; the other part beinga similar and equal curve above the line A B, produced, and consequently a curve of con- trary flexure. The panoramic curve takes place when the cylin- der is cut by a plane at oblique angles to the axis. PROBLEM [L—TO find the indefinite representa- tion of lines parallel to the original plane, in a plane parallel to the axis of the picture; given the height of the eye, the intersection of the original plane, and the distance of the original plane from the picture. Figure Q, No. l.—Let P be the station point; G K HI the intersection of the picture; and AB a line in the original plane, on which the plane parallel to the axis stands. In Figure 2, No. 5, draw PK, which make equal to P K, No. 1. In No. 5, draw P O and Kw per- pendicular to P K; make PO equal to the height of the eye; draw Ow parallel to PK; produce PAN 424 PAN PK to r; in No. I, draw Pr perpendicular to AB, cutting AB at r, and the intersection of the original plane with the panoramic surface at K; make Pr, No. 5, equal to P r, No. I; draw 1' s perpendicular to K P: in No. 5, make r t, tu, u 1), equal to the height of the several lines, whose indefinite representations are required, above the original plane; produce 0 to, meeting r s at s; produce K 2 to meet 0 s at a); draw 0 r Ot, O ii, and 0 v, cutting K at respectively at a, x, 2/, and z. In No. 2, make G H equal to the semircircumference G K H, No. l; bisect G H at it); draw w-v perpendicular to G H; make to a, war, trip, and zaz, respectively equal to a) v, w x, 20 y, and a) z, No. 5; then with the common length G H, and the deflections (012,70 x, zap, and w 2, describe the curves Gv H, G .rH, Gy H, G zH, which will be the developement of the re— presentation of the lines required, and G and H will be their vanishing points. ForO Prs, No. 5, may be considered as a plane passing along the axis of the cylinder; 0 P the axis, 0 the eye, P the station point, K to a section of the cylindric surface, and Or, O t, On, and 0 1), visual rays; and, consequently, the points '0, 13y, z, will be the representations of r, t, u, v; and since 7', t, u,v, may be considered as the centres of the ori- ginal lines, whose representations are required, and since the optic planes of these lines cut the cylinder obliquely, the sections will be elliptical, and, consequently, their envelope will be the figure of the sines, as here described. PROBLEM IlI.-—-To describe the representation of a line in a plane perpendicular to the axis of the cylinder, giving the seat of the line on. the original plane. In No. 9., draw G d perpendicular to G H; make G d equal to the descent or deflection of the curve, and describe the quadrantal sinical curve d w, and dw will be the representation of a line perpendicular to the plane, in which the origi- nals of G 12H, G x H, Gg/ H, and G 2 H, are situated. PROBLEM IV.——Gicen the indefinite representa- tion, Gz H, No. ‘2, qfa straight line, to determine the. finite portion, whose seat is A B, N o. 1. Draw PA and PB, No. 1, cutting the intersec- tion at a and I); make a) a, No. 2, equal to the ex- tension of Ka, No. l; and w b, No. 2, equal to the extension of Kb, No. 1; draw aa‘ and 66', No. 2, perpendicular to G H, cutting the curve GzH at a‘ and b', and a‘ z b‘ will be the finite portion required; a11 y b“, a’“ x b‘“, and a“ a b”, will be the same portions of the indefinite repre— sentations G 2/ H, G x H, and'G v H. The following examples shew the application of the principles in the representation of solid objects. Example 1. Figure 2, No. l.-—Let C I) E F, be the plan of a house, in contactwith the picture at C. Through the station point P,draw, GH, parallel to D C, cutting the intersection of the panoramic picture in the points G and H ; also through P draw K I, parallel to ED, or F C, cutting the picture in l and K ; then G and H are the vanish- ing points of all lines parallel to E F or I) C, and I and K the vanishing points of all lines parallel to C F or D E; draw F P and I) P, cutting the picture atfand (I. Let W V be the ridge of the building, bisecting E D at W, and E C at V; produce W V to Y, cutting I K at U; makeU Y equal to the height of the house, Nos. 3 and 4; and make the angle U Y Z equal to half the ver- tical angle of the roof, and let Y Z cut I K at Z; draw X Q parallel to Y Z, cutting K I, or K I produced at Q; draw Z .1" parallel to V W; pro- duce E D to x, and F C to meet .1“ Z at T; join Q at and Q T, which are the intersections of the optic planes formed by the inclined side of the roof, and the vertical planes standing upon I) E and C F; draw I N parallel to P O, and O N pa- rallel to I P. To find the inclination of the optic planes; draw P M perpendicular to xQ, cutting 5r Q at u, and the panoramic intersection at M; from P, with the distance P u, describe the are n J, cutting Plat J; join OJ; produce NI and OJ to meet each other in S. In like manner, draw P t perpendicular to T Q, cutting T Q at a, and the panoramic intersection at it; from P, as a centre, with the radius P 1;, describe the are *0 to, cutting I P at av; join Ow; produce N I and O a) to meet each other in R; then N O S is the inclination of the optic plane, whose intersec- tion is Q :r; and N O R is the inclination of the optic plane, whose intersection is Q T. Figure 9.,No. 6.—Upon any convenient line, I H, extend the panoramic intersection; according to the corresponding places of No. l, as shewn by similar letters; that is, I t, t G, G d’, d C’, C’f’, f’ K, and K H, No. (i, would cover It, tG, Gd', d’ C', 0]", f’ K, and K H, No. I. In No.6, draw t R, G o, d’ d, C' c, f'f, K It perpendicu- lar to I H. _ - .v.-r:'I»’- H’Iy‘w‘ ' m an}: - W PANORAMA. PLATE]. Fly. 2. M1. 'ihfgflm’ mm] \ \ F \ ‘ \ . \\~ i 4]? I f G_ d u ; I 4‘ J l I 1) \\ I j \ ‘x f f \ \ - 1 . ‘ I , l ' f r n , .1 . x ’ ‘“‘ 125;. 2. 2V.” 3. g ! _ I ( Q 5 k I R "i 51/ [fjrz'z‘fiu/wnu. lam/umf‘hblzlr/za/ 51/ If J'IQ‘fiu/Jun X' J. litll-tikld, Wlnlulu' $715615. [inf/rural [33/ J11. ’llwlul'. . We - ” 5., 1")”.n -t~e:aqm-¢rn~g. PAN 4Q 02 ‘ PAN In No. 5, produce K P to a,- make P a equal to the radius of the cylinder; througha draw 2' '0 parallel to O P; on P a make Pj equal to Pj, No. 1, and P q, No.5, equal to Pq, No. 1; draw 7‘ g and q k, No. 5, perpendicular to P a; make 9 h and jg each equal to the height of the walls, Nos.3 and 4; join 0g and O h,- produce 0g to l, and 0 It to 2', meeting 0 2'; produce Oj and Oq to meet G 0 at o and k. In No. 6, make if R equal to N R, No. 1; G 0 equal to G o, No. 5; G [equal to G]; K 1: equal to G: k; K 2' equal to G 2'; describe the panoramic curves IlK, I o~K, G k H, G 2' H; then the curves 1 0 K and G k H will cut each other at c, and the curves i l K, G i H, will cut each other at C, so that the points C', C, c, will be in the same perpendicular; C c will thus represent the angular line of the building. Let the perpendicu- lar d’ (1 cut the curve G i H at D, and the curve G /c H atd; and the intercepted portiOn D d is the angular line at one end; in like manner, let the perpendicular f’f cut the curve I lit at F, and the curve I 0 K atf; and the intercepted portion Ffof the perpendicularf’f, is the representation of the angular line at the other end; therefore c C Dd represent the front, and c C Ffthe end, exclusive of the triangular part adjoining the roof, which will be formed in the following‘ manner: make tr and a‘ at equal to GK each; describe the same panoramic curve, R C at; and if the other semi-panoramic curve, x cm, is de- scribed, and if k K be produced to c, 1) will be the vanishing point for the gable top; and if K n be made equal to K v, u will be the vanishing point of the other inclined plane of the roof; and thus the representation of lines and planes will have vanishing points and vanishing lines, as in the methods of describing the perspective represen- tation of objects upon a plane surface; and if the points (I, D, c, C,f, F, are found, and the lines c d, C D, and cf, C F, are made straight instead of being curved and produced, they will find their own vanishing points in the line I H; but more remote from each other than the points G and K. What is here observed, is exemplified in No. ’7, as will appear sufficiently clear by a little reflection. The example here shewn is very distorted, on ac- count of the smallness of the panoramic cylinder, and the size of the object, which was obliged to be very large, in order to give a clear elucidation of the principles. VOL. 11. Example 2.——Figure 3, shews the panoramic re- presentation of a row of houses, upon the surface ofa cylinder of greater radius than that of Figure 9., No. 1, where the pictural objects appear much more agreeable to the eye than that of Figure Q; the lines which form the roofs are in this ex~ ample represented as straight, though in reality they are curves, as a great deal: of trouble is saved, and the error occasioned by their intro- duction is too trifling to be observed. It remains to shew the truth of the operations used in the construction of Figure 2. Let it now be proved that x Q and T Q are the intersections of the optic planes, formed by the inclined lines of the gables. From the definition given, an optic plane is one passing along an original line, and through the eye; therefore, if a straight line be drawn through the eye parallel to the original line, the line, thus passing through the eye, and the original line, will both he in the same plane, that is, both in the optic plane; and if two planes be drawn along two parallel lines, their intersections with a third plane will be parallel; now the pa- rallels FT and K I are the intersections of two parallel planes; F T that of the vertical plane, in which the inclined original line is situated, and K I that in which the eye is situated, or in which the line parallel to the inclined line is situated; the point T is the intersection of the inclined line of the roof, and the point Q the intersection of the line drawn through the eye parallel to the inclined line of the roof; therefore the optic plane will pass through the points T and Q, and consequently T Q is the intersection of the optic plane and the original plane. In the same man- ner, it may be shewn that x Q is the intersection of the optic plane, formed by the other inclined line of the farther gable in the same plane with the former line. Next let it be shewn that the angles N O S and N O R, No. 1, are the inclinations of the optic planes, whose intersections are a‘ Q and T Q. The inclination of any two planes is measured by a third plane, perpendicular to their common inter- section; now T Q is the intersection of the optic ~ plane, and P v is perpendicular to T Q; and be cause P w is equal to P v, and 1’ 0 perpendicular to P w, and equal to the height of the eye; con- ceive the plane of the triangle :0 P O to be raised perpendicular to the original plane, so that the base P a" may coincide with P a; then 0 will re. 3 I PAN 426 / PAN present the eye in its true place, and the point a) will be upon 1),- and since the intersection TQ would be perpendicular to the plane of the tri- angle, every line drawn in the plane of the tri- angle from 1), would be perpendicular to the inter- section T Q, and consequently, the line drawn in this plane from 1; to 0, would also be perpen- dicular to the intersection; therefore the angle Pa) O is the inclination of the plane, and, conse- > quently, the alternate angle N O R. In the same manner, it may be shewn, that N O S is the incli— nation of the plane whose intersection is x Q. Now to shew that N R is the deflexion of the curve made by the optic plane, it only requires to be considered, that the transverse axis of the el- lipsis made by the optic plane, is in the plane which measures the inclination of the optic plane to the original plane: for this purpose, P O N R may be considered as a semi-section of the cylin- der along the axis, and N R a section upon the surface; therefore 0 R will represent half the greater axis, and N R the deflexion of the curve, or its descent below the vanishing line of the ho- rison. Figure 2, No. 5, is also to be considered as a section of the cylinder, of which 0 P repre— sents the axis, G 0 and a) K the sides; and be- cause the appearance of all points in the same plane perpendicular to the axis, at equal distances from the station point, will be at the same height on the surface from the original plane, or from the plane passing through the eye parallel to the original plane, their heightswill be found by set- ting their distances upon P a, then erecting lines perpendicular to P a, from each point of the sec- tion; then setting the heights of the points upon these lines, and drawing lines from 0, through the top of each perpendicular till they cut G 0,- then the distance from G, to each point of sec- tion, gives the distance of each point from the plane passing through the eye upon the panora- mic surface. Now let the cylinder be conceived to be enve- loped by No. 6, so that I H may fall upon the circumference of a circle in a plane perpendicu- lar to the axis; then every line will fall in its true position, and the representative object will pro- duce the same pyramid of rays as the original, the eye being supposed to be fixed at its true distance above the line I H; and, consequently, nothing more will be required to excite an idea of the existence of the object, than to give the re- presentative Surfaces their proper colours, light, and shade, according to the distance ofthe original. Hitherto straight lines have been represented by portions of the sinical curve when extended, or by portions of an ellipsis, when the sheet on which the objects are represented is brought in contact with the surface of the cylinder, as they ought properly to be; but if the radius of the cylinder is of sufficient extension, and the objects to be represented of proper magnitude, any attempt to represent straight lines by curves from the hands of an artist would be absurd, except when the object to be represented is very near to the pa- noramic surface, in which case a curvature in the line may be sensible, also at a moderate distance: the curve can only be observed in a series of ob- jects in a straight line; it will therefore be suflig cient to represent the straight lines of each indi«- vidual object by straight lines also, but to pre- serve the curve, or rather the polygonal figure in- scribed in the sinical curve in the series, as the inflexions or angles will hardly be visible. A straight line will therefore be represented by finding the representation of its extremities, and joining the representative points; but if it is of great extent, it may be obtained by finding a num- ber of points, and joining every two adjoining points in succession by a straight line, and the whole will assume the form of a curve, which will be the representative of the straight line. Plate II. shews a series of figures, such as may be supposed ,to constitute the whole of the prac— tice of representing panoramic objects. S is the station point; the objects are referred to in al- phabetical order from A, B, C, Ste. to H; each extreme point of the linear parts of the same ob- ject has the same letter affixed, with a numerical index, which increases, by unity, in tracing round the circumference in progressive order. The points where the optic lines cut the panoramic surface, are numbered with the same figure from the same object, each number having an index corresponding to that of the point ofthe object to. be represented. Thennmbers are placed in suc~ cessive order, agreeing with that ofthe alphabet. No. 1, the intersection of the panorama and the original plane, with the figures of the objects to be represented. No. Q, 3, 4, vertical sections of the panorama, passing along its axis, in order to ascertain the heights of the several places of each object; E F ‘ 1753;. , ' . “u " ' PANORAMA. PIA T 12’ II. Q E arm/(711a! by I). fiZ‘lmZm/z. Zulu/4m, [lull/(kind by l.’ JVI}'fiz’/.f(’ll X' f [fur/ir/zl, ”fin/0111‘ .Vh'.’ 181.47. Equrll Vt’d [I‘ll J B . n’.”"”' I‘ , ‘ ii.- “ ‘ ' - 7‘“ " PAN PAN J n - the point of sight, or place of the eye; S the sta- tion point; P Q a section of the cylinder, shew- ing the heights of the objects. The objects to be represented are, A, a point, the optic ray from which cutting the intersection at 1; B a straight line, the optic rays from which cutting the intersection at 21 2‘; C a line stand- ing upon C, the optic ray from which cutting the intersection at S; D an inclined line, whose seat is represented by D1, D2, the optic rays from which cutting the intersection at 4‘, 4“; Ban angle, the optic nys from which cutting the inter- section at 5‘, 52, 53; F a triangle, the optic rays from which cutting the intersection at 61, 6‘, )3; H a rectangle, the optic rays from which cut- ting the intersection at 71, 72, 7", 7*; and, lastly, G a circle, the optic rays from which cutting the ' intersection at 81, 81, 83. The distances of the objects are placed upon the panoramic section; No. ‘2, 3, 4, from S, upon the lines S P, or upon SP produced; then drawing lines from the points to E, give the heights upon P Q. The perpendicular standing upon C, No. l, is thus found: in No-3, draw C C from C, perpendicu- lar to 81’, equal to the height of the perpendi- cular upon C, No. 1, and draw the straight lines C E, C E, No. 3, cutting P Qat 33, then 3 3 is the panoramic length of CC. The upper ex- tremity of the inclined line, D, will be found by ascertaining the panoramic height of the perpen- dicular, from the elevated end to the original plane. No. 5 shews the panoramic representation of the several objects; V L the vanishing line of the horizon; the intersections of the optic rays are extended upon VL from No. i, the references upon the intersection No. l, and upon V L, No. 5, being the same. The heights of the several points are taken from the sections No. 9, 3, and 4, from Q downwards towards P, and placed from the corresponding points in V L, No. 5, also downwards upon the perpendiculars, gives the several points of the objects; thus a is the repre- sentation of the point A, No. 1 ; b’, If, of B1, 13‘, Ste. In the circle, the points for half the curve are found, the other half being repeated in the same order from the middle line, each line serv- ing for two points, so that the three lines give eight points; the extreme lines are tangents which are equivalent to two points. ' The points around the circumference of the inter- section No. l, are extended upon VW and XY, according to the principle of Renaldinus, by set— ting three-fourths of the radius, without the Cir- cle, upon the opposite side of the tangents V W, and X Y, and transferring the divisions of V W and X Y upon V L, No. 5, gives the points cor~ responding to the intersection. The panoramic surface being enveloped by No. 5, and the representations of the objects placed in their true position, will form the same picture at the point of sight, if correctly painted, as the objects themselves would in nature. A practical method of forming all straight lines on the panoramic surface in its place, without developement, is to ascertain the position of the objects, also the heights of the centres of the lines to be represented; then fixing the eye in its po- sition, and holding a straight-edge parallel to the line to be drawn in a plane with the point of sight and the point representing the centre of the line, mark several points in the same plane, on the panoramic surface; these points being join- ed, will give the representation of the line required. In preparing for panoramic projections, whatever objects are intended to be represented, a proper point of view should be chosen from this situa- tion; a sketch of all the surrounding objects should be made according to the developement of the panorama; for though the painting itself may be performed upon the eylindric surface, it is more eligible to sketch upon a plane. The next thing to be done is to take a survey of the objects, observing their positions to,each other; then with a plane table fixed on the point of view, quite level, take the successive angles of the sur- rounding objects by means of a moveable limb, which may carry two pieces, one at each ex- tremity, perpendicular to the surface of the plane table; one piece being fixed in the supposed axis of the panorama, containing a sight hole for the point of view, so that the moveable part will con- sist of three bars, the bottom one serving as a straight-edge for drawing the angles of position : the heights of the object may be marked upon the other limb parallel to that fixed in the axis; and let it be observed, that the point of view in the axis, the edge of the limb which gives the heights of the objects, and the edge of the bot- tom bar by which the angles are drawn, must be in a plane passing along the axis: mark the ver- tical lines on the sketch, and the lines on the 312 PAN , 428 PAN plane table, which shew their position, with cor- responding characters, otherwise it would be dif- ficult to distinguish what the numerous lines apply to. The movcable edge of the index, which describes the circumference of the cylin- der, should he of ivory, as the various heights may be marked with pencil, and rubbed out at pleasure, as these heights may be transferred to a piece of paper, marking them with the same cha- racter as that of the sketch, and with the addition of the words top of chimney, shaft, ridge of roof, top qf'zt‘ull, Ste. as the heights may be the termi- nations of such parts of the said objects, or, in— stead of writing any word, a slight representation may be drawn of the parts of the object. ’ Instead of the ivory edge of the bar, which de- scribes the panoramic surface, a slit, or very nar- row aperture, formed by a double bar, may be used. The tendency of every line, horizontal or inclined, may be found by a fifth bar, move-able round a centre, which centre must be also moveable upon the edge of the limb which gives the panoramic heights of the objects; the plane in which this fourth bar moves must be a tangent to the pano- ramic surface, at the line which is intersected by the plane passing along the axis, along the straight edge of the bottom bar, and along the edge where the heights of the objects are marked; then if the edge of this fourth moveable ,bar be brought in a plane with the eye and the original line, the angle which it forms with the edge of the vertical limb is the inclination of the line on the picture. PANTHEON (from the Greek way, all, and Snow, gods)'in architecture, a temple, or church, of a circular form, dedicated to all the gods, or to all the saints. The Pantheon of ancient Rome is of all these edifices the most celebrated, and that from which all the rest take their name. It was built by Agrippa, son-in-law to Augustus, in his third con- sulate, 25 years before the Christian aera; though several antiquaries and artists have supposed that the Pantheon existed long before, during the commonwealth, and that Agrippa only embel- lished it, and added the portico. To this purpose they allege the authority of Dion Cassius, who, speaking of Agrippa, says, he also finished or per— fected the Pantheon. It was dedicated by him to Jupiter Ultor, Jupi- ter the Aevenger, according to Pliny’s account; according to Dion Cassius, to Mars, Venus, and ‘fi Julius Caésar; but, according to the most p‘ro- bable opinion, to all the gods; and had the name Pantheon, on account of the great number of sta- tues of the gods, raised in seven niches all round it; and because it was built of a circular form, to represent heaven, the residence of the gods; or, because it was dedicated to all the gods (quasi “Iran/Troy Saar.) It had but one door. It was 144, or, as Fabricius says, 140 feet diameter within, and just as much in height, and of the Corinthian order. The roof was curiously vaulted, void spaces being left here and there for greater strength. The rafters, 40 feet long, were plated with brass. There were no windows in the whole edifice; but sufficient light was let in through a round hole in the top of the roof. Before each niche were two columns of antique yellow mar- ble, fluted, each of one entire block. The whole wall of the temple, as high as the grand cornice inclusive, was cased with divers sorts of precious marble in compartments: and the frieze was en- tirely of porphyry. The outside of the front was anciently covered with plates of gilt brass, and the top with plates of silver; in lieu of which lead was afterwards substituted. The gates were of brass, and of extraordinary size and workmanship. The eruption of Vesuvius, in the reign of Tibe- rius, and a great fire in the reign of Titus, da- maged the Pantheon very considerably; but it was successively repaired by Domitian, Adrian, and Septimius Severus: and having subsisted in all its grandeur till the incursion ofAlaric, in the reign of Honorius, it was then stripped of seve- ral of its statues and ornaments of gold and silver. About thirtymine years after this, Gen- seric, king of the Vandals, took away part of its marbles and statues: and, at length, Pope Boni- face lV. obtaining this Pantheon of the Emperor Phocas, converted it into a church, without any alteration in the building; and dedicated it to the Vll’glll and all the martyrs: but, in 1665, Con- stantius II. stripped it of its inside and outside brazen coverings, which he transported to Syra- cuse. It still subsists at Rome, under the title of Notre Dame de la Rotonda. The square of the Pantheon, or Piazza della Ru- tonda, is adorned with a fountain and an obelisk, and terminated by the portion of Agrippa. This noble colonnade consists of a double range of Corinthian pillars of red granite. Between the middle columns a passage opens to the brazen PAN 499 _ PAR — _ - _ _.._ portals, which, as they unfold, expose to view a circular hall of immense extent, crowned with a lofty dome, and lighted solely from above. It is paved and lined with marble. Its cornice of white marble is supported by sixteen columns, and as many pilasters of Giotto antico: in the circumference there are eight niches, and between these niches are eight altars, adorned each with two pillars of less size, but the same materials. The niches were anciently occupied by statues of the great deities; the intermediate altars served as pedestals for the inferior powers. The propor- tions of this temple are admirable for the effect intended to be produced; its height being equal to its diameter, and its dome not an oval, but an exact hemisphere. The Pantheon is the most noble and perfect specimen of Roman art and magnificence which time has spared, or the an- cients could have wished to transmit to posterity. It has served, in fact, as a model to succeeding generations, and to it Constantinople is indebted for Santa Sophia, and to it Rome, or rather the universe, owes the unrivalled dome ‘of the Vati- can. Upon the whole, this is the most ancient edifice that now remains in a state of full and al- most perfect preservation. There was also another Pantheonat Rome, dedi- cated to Minerva, as the goddess of medicine. It was in the form of a decagon, and the distance from one angle to another measured 22% feet. Between the angles there were nine chapels of a round figure, designed for so many deities: and over the gate there was a statue of Minerva. The Pantheon of Nismes, was a temple in that city, in which were twelve niches, for statues, supposed to have been destined for the twelve great gods. The Pantheon of Athens was, in many respects, little inferior to that of Rome, built by Agrippa. The Greek Christians converted it into a church, dedicated to the Virgin, under the name of Pa- negia: but the Turks changed it into a mosque. In the Escnrial is a magnificent chapel, called Pantheon, 35 feet in diameter, and 38 high, from the pavement, which is of marble and jasper in- laid. The whole inside of the chapel is of black marble, except the luthern, and some ornaments ofjasper and red marble. In this chapel are de- posited the bodies of the kings and queens: there are only places made for twenty-six; eightof which are already filled. PAN'l‘H EON, in England, a modern building in Ox- ford-street, London, begun in 1768, and finished in 177.1, for concertos and other musical perform- ances. It was built by Mr. James Wyatt, and, both by natives and foreigners, considered as the most elegant structure in Europe, if not on the globe. This splendid and elegant edifice was opened as a place of public entertainment, on Monday, January 27, 1772. During the first winter there were assemblies only, without danc— ing, or music, three times a week. On other days, each person paid five shillings for seeing the building only. But the great room, though spacious, was so crowded on all these occasions, that, in July, a general meeting of the proprietors was advertised, in order to take into consideration the enlarging of the building. After the opera-house in the Haymarket was burnt down, in 1790, this master-piece of architecture was transformed into atheatre, for the perform— ance of operas: when, though many of its inter- nal beauties were hidden and annihilated, it still was a perfect model of a complete theatre in its new form. But unhappily, before it had been thus used two seasons, it was burnt down by some fatal accident or design, which has neVer yet been divulged to the satisfaction of the public. The Pantheon, in its present state, as a theatre, retains nothing of its former grandeur, the fire having so completely destroyed the interior, ex- cept the rooms next to Oxford-street, which are the only remains of the former edifice. PARABOLA (from the Greek wapu, through, and fiaMw, to throw) in geometry, a curve line made by the common intersection of a conic surface and a plane which cuts it, and is parallel to an- other plane that touches the conic surface. A conic section made by a plane ever so little-in‘ clined to the parabola on the one side, is an ellip- sis; and a section made by a plane inclined ever so little on the other side, is an hyperbola: thus the parabola is the limit between these two curves, to which they both continually approach, while their transverse axes increase more and more; being, as it were, the passage from one of them to the other. PARABOLA, a plane figure, bounded by a curve and a straight line, possessing the property that ax 23/1; in which a: is the abscissa, and 3/ the ordinate. PARABOLIC ASYMPTOTE, in geometry, aparabolic PAR ' 43.0 PAR line approaching to a curve, but never meeting it; yet by producing both indefinitely, their distance from each other becomes less than any given line. There may be as many different kind of asymptotes as there are parabolas of different orders. When a curve has a common parabola for its asymptote, the ratio of the subtangent to the ab- scissa approaches continually to the ratio of two to one, when the axis of the parabola coincides with the base ; but this ratio of the subtangent to the abscissa approaches to that of one to two, when the axis is perpendicular to the base. And by observing the limit to which the ratio of the subtangent and abscissa approaches, parabolic asymptotes of various kinds may be discovered. PARABOLIC CONOID, see PARABOLOID. PARABOLIC CURVE, the curved boundary ofa pa~ rabola which terminates its area, except at the double ordinate. PARABOLIC SPIRAL, or HELICOID, a curve arising from a supposition of the axis of the com- mon parabola being bent into the periphery of a circle, while the ordinates are portions of the radii next to the circumfeience. PARA BOLOID (from waloafiohi‘y and 5:809) a solid formed by the revolution of a parabola about its axis. It is described by Harris as a parabolic firm curve, whose ordinates are supposed to be in subtriplicate, subquadruplicate, 8L0. ratio of their respective abscissas. PARADIGRAMMATICE (from the Greek ’wapa- daylua, an example, and map/ta, a letter) the act of forming all sorts of figures in plaster. The ar- ' tists themselves are called gypsochi. Neither term is much used. PARADOX (from the Greek wrapa, against, and 805a, opinion) in philosophy, a proposition seem- ingly absurd, because contrary to the received opinions ; but yet true in effect. The Copernican system is a paradox to the com- mon people; but the learned are all agreed as to its tiuth. Geometricians have been accused of maintaining paradoxes; and, it must be owned, that some use very mysterious terms in expressing themselves about asymptotes, the sums of infinite progres— sions, the areas comprehended between curves and their asymptotes, and the solids generated from these areas, the length of some spirals, 8m. But all these paradoxes and mysteries amount to no more than that the line or number may be conti- nually acquiring increments, and those incre— ments may decrease in such a manner, that the whole line or number shall never amount .to a given line or number. The necessity of admitting this is obvious from the nature of. the most common geometrical figures: thus, while the tangent of a circle in- creases, the area of the corresponding sector in- creases,but never amounts to a quadrant. Neither is it difficult to conceive, that if a figure be con~ cave towards a base, and have an asymptote pa- rallel to the base (as it happens when we take a. parallel to the asymptote of the logarithmic curve, or of the hyperbola, for a base) that the ordinate in this case always increases while the base is produced, but never amounts to the distance be- tween the asymptote and the base. In like man- ner, a curvilinear area may increase while the base is produced, and approach continually to a certain finite space, but never amount to it; and a solid may increase in the same manner, and yet never amount to a given solid. A spiral may in like mannei approach to a point continually, and yet in any number of revolutions never arrive at it; and there are progressions of fractions, which may be continued at pleasure, and yet the sum of the terms shall be always less than a given number. 111 Maclaurin’s Fluxions (book i. ch. 10. et seq.) various rules are demon- strated, andillustrated by examples, for deter- mining the asymptotes and limits of figures and progressions, without having recourse to those mysterious expressions which have of late years crept intothe writings of mathematicians. For, as that excellent author observes elsewhere, though philosophy has, and probably always will have, mysteries to us, geometry ought to have none. PARALLEL (from the Greek mdequg) in geo~ metry, a term applied to lines,figures, and bodies, which are every where equidistant from each other; or which, though infinitely produced, would never approach nearer to, nor recede farther from, each other. PARALLEL COPINGS, such copings as have their upper surface parallel to the bed of the stone, as in those which cover the gable of a house. PARALLEL RIGHT LINES, such lines as, though infinitely produced, could not meet at any finite distance. PARALLEL MOTION, among practical mechanics, denotes the rectilinear motion of a piston-rod, 8w. PAR 431 PAR Wm in the direction of its length; and contrivances, by which such alternate rectilinear motions are converted into continuous rotatory ones, or vice versa, for pumps, steam-engines, saw-mills, Sec. are usually called parallel motions or parallel levers. The object of the parallel motion is, to convert the motion of the end ofa reciprocating beam or lever, into a vertical or rectilinear mo- tion; or the continuous motion of a crank at once into a reciprocating motion. The simplest and most obvious method of pro- ducing either of these effects, is to connect the end of the piston-rod to the beam, or the crank, by means ofjoints, with a connecting rod of a proper length between them, and confine the former, to preserve its rectilinear movement, by sliding through a collar, or in grooves. Friction- wheels may beused to make it work easily; but in machines which have great strains, the con- stant wear of the grooves or wheels, would soon produce looseness, and destroy the parallelism of the motion: recourse must, therefore, be had to parallel levers. PARALLEL PLANES, those which if produced can- not meet at any finite distance. PARALLEL RULER, see INSTRUMENTS. PARALLEL CUT, in inland navigation, a counter drain, to carry ofl" water, and prevent the adjoin- ing lands from being flooded. PARALLELOPIPED (from the Greek wapakknxog, parallel) in geometry, one of the regular bodies, or solids, comprehended under six parallelograms, the opposite sides of which are similar, parallel, and equal. ' A parallelopiped is by some defined an upright prism, whose base is a parallelogram, and the planes of whose sides are perpendicular to the plane of the base. A rectangular parallelopiped is one whose bound- ing planes are all rectangles, and which stand at right angles to each other. Every rectangular pa- rallelopiped is said to be contained under the planes that constitute its length, breadth, and altitude. It is demonstrated, that if from one of the angu- lar points of any parallelogram, a right line be elevated above the plane of the parallelogram, so as to make any angles with the contiguous sides of it, and there be also drawn, from the three re- maining angular points, three other right lines parallel and equal to the former, and the extremes of these lines be joined, the figure thus described will be a parallelopiped. If the angle of the pa- rallelogram be right, and the elevated line be erected perpendicular to the plane of the base, then will the parallelopiped be a rectangular one. PARALLELOPIPED, Properties if the. All paral- lelopipeds, prisms, and cylinders, Eco. Whose bases and heights are equal, are themselves equal. Every upright prism is equal to a rectangular pa- rallelopiped of equal base and altitude. A diagonal plane divides the parallelopiped into two equal prisms : a rectangular prism, therefore, is halfa parallelopiped upon the same base, and of the same altitude. All parallelopipeds, prisms, cylinders, 8w. are in a ratio compounded of their bases and altitudes: Wherefore, if their bases be equal, they are in proportion to their altitudes; and conversely. All parallelopipeds, cylinders, cones, 8w. are in a triplicate ratio of the homologous sides; and also of their altitudes. Equal parallelopipeds, prisms, cones, cylinders, 8L0. are in the reciprocal ratio of their bases and altitudes. Rectangular parallelopi‘peds, contained under the corresponding lines of three ranks of proportionals, are themselves proportionals. To measure the surface and solidity of a parallelo- piped. — Find the areas of the parallelograms I LM K, LMON, and OM KP (see PARAL- LELOGRAM); add these into one sum, multiply that sum by 2, and the product will be the surface of the parallelepiped. It, then, the base,l L M K, be multiplied by the altitude, NI 0, the product will be the solidity. SupposeLM = 36, MK = 15, MO =12; then LIKM =36 x15=540;LMON= 36 x'12=432;1\10 K P=15 x12 =180. The sum of which is = 1152, which multiplied by ‘2, gives the superficies equal to 2304. And 540 x 12 gives the solidity equal to (5480. Or the solid content of a parallelopiped may be ob- tained by multiplying the area of the base by the altitude of the parallelopiped. Thus, if the two dimensions of the base be 16 and 12 inches, and the height of the solid 10 inches; then the area of the base being 192, the content of the solid will be 1920 cubical inches. The paralleloiriped with oblique angles is a figure very common to many kinds of stones, especially of the softer sort. PARALLELOGRAM (from the Greek wapaMnkog, PAR , 432 , PAR ‘I’ aparallel, and 'ypalu/ta, afigure) in geometry, a quadrilateral right-lined figure, whose opposite sides are parallel, and equal to each other. A parallelogram is generated by the equable mo- tion of a right line always parallel to itself. When the parallelogram has all its four angles right, and only its opposite sides equal, it/is called a rectangle, or an oblong. When the angles are all right, and the sides are all equal, it is called a square, which some make a species of parallelogram, others not. If all the sides are equal, and the angles unequal, it is called a rhombus, or lozenge. If both the sides and angles be unequal, it is call- ed a rhomboides. Every other quadrilateral, whose opposite sides are neither parallel not equal, is called a trapezium. See each of these articles. In every species of parallelogram, a diagonal di- vides it into two equal parts; the angles diago- nally opposite are equal; the opposite angles of the same side are, together, equal to two right angles ; and every two sides are, together, greater than the diagonal. Every quadrilateral, whose opposite sides are equal, is a parallelogram. Two parallelograms on the same, or on an equal base, and of the same height, or between the same parallels, are equal. Hence two triangles on the same base, and of the same height, are also equal; as ‘are all parallelograms or triangles whatever, .Whose .bases and altitudes are equal among them- selves. Hence, also, every triangle is half aparallelogram upon the same or an equal base, and of the same altitude, or between the same parallels. Hence also a triangle is equal to a parallelogram, having the same base, and half the altitude, or half the base, and the same altitude. Parallelograms, therefore, are, in a given ratio, compounded of their bases and altitudes. If then the altitudes be equal, they are as the bases; and conversely. In similar parallelograms and triangles, the alti- tudes are proportional to the homologous sides; and the bases are cut proportionally thereby. Hence, similar parallelograms and triangles are in a duplicate ratio of their homologous sides, also oftheir altitudes, and the segments of their bases: they are, therefore, as the squares of the sides, alti- tudes, and homologous segment-s of the bases. - In every parallelogram, the sum of the squares of the two diagonals is equal to the sum of the squares of the four sides : and the two diagonals bisect each other. This proposition M. de Lagny takes to be one of the most important in all geometry; he even ranks it with the celebrated forty-seventh of En- clid, and with that of the similitude of triangles; and adds, that the whole first book of Euclid is only a particular case of it. For if the parallelo- gram be rectangular, it follows, that the two dia- gonals are equal; and, of consequence, the square of a diagonal, or, which comeslto the same thing, the square of the hypothenuse of a right angle, is equal to the squares of the sides. If the parallelogram be not rectangular, and, of consequence, the two diagonals be not equal, which is the most general case, the proposition becomes of vast extent; it may serve, for in- stance, in the whole theory of compound mo- tions, Ste. There are three ways of demonstrating this pro- position; the first by trigonometry, which re- quires twenty-one operations; the second geome« trical and analytical, which requires fifteen. But I“. de Lagny gives a more concise one, in the IlIemoires (1e l’flcad. which only requires seven. PARALLELOGRAM, see PENTAGRAPH. PARAMETER (from the Greek wrapa, through, and per-pew, to measure) in conic sections, a constant right line in each of the three sections; called also lotus rectum. In the parabola, the rectangle of the parameter and an abscissa are equal to the square of the correspondent semi-ordinate. Sec PARABOLA. In an ellipsis and hyperbola, the parameter is a third proportional to a conjugate and transverse axis. See ELLIPSIS and HYPERBOLA. PARAPET (French) or BREASTWORK, in fortifica- tion, a defence, or screen, on the extreme of a ‘ rampart, or other work, serving to cover the sol- diers and the cannon from the enemy’s fire. The thickness of the parapet should be about eighteen or twenty feet, in order to be cannon- proof, and it should be about seven or eight feet high, when the enemy has no command above the battery; otherwise it should be raised high enough to cover the men while they load the guns. lts length depends on the number of guns to be employed in the battery: for one gun, it is common to allow eight yards in length, and six yards more for every other gun. The parapet PAR 4:33 PAR ' consists of two parts, the wall contained in one piece from end to end, and about two and a half or three feet high; and the merlons, which are de- tached pieces of the parapet, leaving openings, called embrasures, through which the cannon de- liver their shot. The parapet of the wall is sometimes of stone. The parapet of the trenches is either made of the earth dug up; or of gabions, fascines, barrels, sacks of earth, or the like. PARAPET is also a little wall, breast-high, raised on the brinks of bridges, quays, or high buildings; to serve as a stay, and prevent accidents from falling over. PARASTATA (Greek) in ancient architecture, a kind of pier, or piedroit, serving as adefence or support to a column or arch. Mr. Evelyn makes the parastata the same with pilaster; Barbaro and others the same with antae; and Daviler the same with piedroit, PARENT, ANTHONY, in biography, an eminent mathematician, born at Paris in the year 1666. Ata very early period, he discovered a strong propensity to the study of mathematics; for, at the age of fourteen, accidentally meeting with a dodecahedron, upon every face of which was delineated a sun-dial, excepting the lowest, upon which it stood, he attempted to imitate them, and was led from the practice to investi— gate the theory, and in a short time wrote a trea— tise upon Gnomonics, which, though said tobe extremely rude and unpolished, had the merit of being his own invention, as was a work on Geo- metry, which he wrote about the same time. At the earnest desire of his relations, he entered upon the study of the law, as a profession for his life; but he no sooner completed his studies in that faculty, than he betook himself, with in- creased ardour, to those pursuits which accorded best with his genius and inclination. . He attend- ed very diligently the lectures of M. de la Hire and M. Sauveur, and, as soon as he felt himself capable of teaching others, he took pupils; and fortification being a branch of study which the war had brought into particularnotice, he was called upon frequently to teach the principles of that science. In 1699, M. Fillau des Billets having been admitted a member of the Academy of Sciences at Paris, with the title of their acade- mician, nominated M. Parent for his eleoe, who particularly excelled in that branch of knowledge. VOL. II. It was soon discovered that he directed his atten— tion to all the subjects that came before the aca- demy, and that he was competent to the investi- gation of every topic which was recommended to their notice. In the year 1716, the king abo- lished the class of eleves, and on this occasion he made M. Parent an adjunct, or aSSistant member of the class of geometry. He lived but a short time to enjoy this honour, being in the same year cut off by the small-pox, when he was about fifty years of age. Although of a very irritable disposition, he is said to have possessed great goodness of heart; and though his means were extremely limited, he devoted much of his in— come to acts of beneficence. He was author of Elements of JlIechanics and Natural Philosophy, Mathematical and Physical Researches, a sort of journal, which first appeared in 1705, and which, in 1712, was greatly enlarged, and published in three vols. 4to.; and A Treatise on Arithmetic. Besides these, he wrote a great number of papers in the different French Journals, and in the vo— lumes of the .Memoirs of the Academy qucz'en‘ces, from the year 1700 to 1714, and he left behind him in manuscript many works of considerable research; among which were'some complete trea- tises on divers branches of mathematics, and a work containing proofs of the divinity of Jesus Christ, in four parts. PARG ET (from the Latin parses, a wall) in natu- ral history, a name given to the several kinds of gypsum or plaster-stone, which, when slightly calcined, make what is called plaster of Paris, used in casting statues, in stuccoing floors and ceilings, Ste. The word parget, though generally applied to all the gypsums, is, however, given by the workmen principally to the two species which make up the first genus of that class, called by Dr. Hill the pholides. These are the Montmartre kind, and that of Derbyshire. - PARGETING, in building, a term used for the plas~ tering of walls; sometimes for the plaster itself. Pargeting is of various kinds; as, 1. White lime and hair mortar laid on bare walls. 9. On bare laths, as in partitioning and plain ceiling. " 3. Rendering the insides of walls, or doubling pari- tition walls. 4. Rough-casting on heart-laths. 5. Plastering on brick-work, with finishing mor- tar, in imitation of stone-work; and the like upon heart-laths. PAS 4334 a L PARTITION (from the Latin partitio, to divide) a wall which divides and separates one apartment f1om another. It may be eithe1 of brick, stone, or timber. When a partition wall has no support from below, it ought to be so constructed as to lay no stress upon the floor; and theretbreatruss- partition should be employed, to discharge the weight. See TRUSS. PARTY-VVALLS, in building, partitions of brick made between buildings in separate occupations, for preventing the spread of fire. For the regu- lations prescribed by an act of 14 Geo. HI. see BUILDING ACT. PASCAL, BLAISE, a celebrated mathematician and philosopher, born at Clermont, in Auvergne, in the year 169.3. great consideration in his province, was also illus- trious as a general scholar, as well as an able ma— thematician. To promote the studies of his only son Blaise, he relinquished his official situation, settled at Paris, and undertook the employment of being his tutor. The pupil was, from a very early period, remarkably inquisitive, and desirous of knowing the principles of things; and when goodleasons were not given to him, he would search for better, nor would he rest contented with any that did not appear to his mind well founded. His father soon discovered that the bent of his genius was decidedly to mathematics, from which he was determined, if possible, to keep him, lest he should, by this pursuit, be prev vented from learning the languages. He accord- ingly locked up all the books that treated of geo— metry and the sciences properly so called, and refrained even from speaking of them in his pre- sence. On one occasion, however, the youth asked, with an importunity not to be put off, what was geometry? to which the father replied, “Geometry is a science which teaches the way of making exact figures, and of finding out the pro- portions between them ;” but, at the same time, he forbade him to speak or think of the subject any more; which was perhaps the very readiest way to excite in him an earnest desire to become ac- quainted with it. Accordingly the science soon occupied all his thoughts; and though but twelve years of age, he was found, in the hours of re- creation, making figures on the chamber-floor, with charcoal, the proportions of which he sought out by means of a regular, though perhaps un- couth, series of definitions, axioms, and demon- His father, who was a man of PAS strations. It is said, apparently upon unques- tionable authority, that he had proceeded with his inquiries so far as to have come to what was just the same with the thirty-second proposition of the first book of Euclid, and that without any assistance either from living instructors, or the works of the illustrious dead. From this time, young Pascal had full liberty to indulge his ge- nius in mathematical pursuits, and was furnished by his father with Euclid’s Elements, of which he made himself master in a very short time. So great was his proficiency in the sciences, that, at the age of sixteen, he wrote a Treatise on Conic Sections, which, in the judgment of the most learned men of the time, was considered as a great effort of genius. At the age of nineteen, he con- trived his admirable arithmetical machine, fur- nishing an easy and ex peditious method ofmaking a1ithmetical calculations, 1n the fundamental rules, without any other aid than that of the eye and the hand. About this time, owing to ill health, he was obliged to suspend his studies, which he was unable to renew for four years; when having been witness to the famous Torricellian experi— ment respecting the weight of air, he instantly directed his attention to discoveries in the science of pneumatics. He made a vast number of ex- periments, of which he circulated a printed ac- count through the whole of Europe. He soon ascertained the fact of the general pressure of the atmosphere, and composed a large treatise, in which he fully explained the subject, and an- swered the objections which were advanced against his theory: afterwards, thinking it too prolix, be divided it into two small treatises, one of which he intitled, A Dissertation on the Equi- librium (f Fluids,- and the other, An Essay on the Weight of the Atmosphere. These treatises were not published till after the author’s death. The high reputation which M. Pascal had ac- quired, caused him to be looked up to by the most considerable mathematicians and philoso- phers of the age, who applied for his assistance in the resolution of various difficult questions and problems. Among other subjects on which his ingenuity was employed, was the solution of a problem suggested by Mersenne, which had baf- fled the penetration of all who had attempted it: this was to determine the curve described in the air by the nail of a coach-wheel, while the ma- chine is in motion; which curve was at that W PAS - 435 m, I time known by the name of the roullette, but is now designated the cycloz'd. Before this time he had drawn up a table of num- bers, which, from the form in which the figures were disposed, he called his Arit/tmetical Tri- angle. He might perhaps have been an inventor of it, but it is certain that it had been treated of, a century before Pascal’s time, by Cardan, and other arithmetical writers. When M. Pascal was in the twenty-fourth year of his age, and the highest expectations were formed of the advantages to be attained in science from his labours, he on a sudden renounced the study of mathematics, and all human learning; devoted himself wholly to a life of mortification and prayer; and became as great a devotee as almost any age has produced. He was not, how- ever, so completely abstracted from the world, as to be wholly indifferent to what was passing in it; and in the disputes between the Jesuits and the Jansenists, he became a partisan of the latter, and wrote his celebrated Provincial Letters, pub- lished in 1656, under the name of Louis de Mont- alte, in which he only employed his talents of wit and humour in ridiculing the former. These letters have been translated into almost all the European languages, and probably nothing did more injury to the cause of the Jesuits. The course of life which he prescribed to himself, proved unfavourable to his health of body and mind. His reason became in some measure af- fected, and, in these circumstances, an accident produced on his mind an impression which could not be efi‘aced. In 1654, while he was crossing the Seine in a coach and four, the two leading horses became unmanageable at a part of the bridge where the parapet was partly down, and plunged over the side into the river. Their weight fortunately broke the traces, by which means the other horses and the carriage were extricated on the brink of the precipice. From this fright it was difficult to excite the feeble Pascal, and he never afterwards had the possession of his mental faculties. He always imagined that he was on the edge of a vast abyss on the left side of him, and he would at no time sit down till a chair was placed there, to assure him there was no real dan- ger. After languishing some years in this miserable state, he died at Paris in 1669, at the age of 39. PASSAGES, the avenues or accesses which lead to the various apartments of a buildincr. PAT Passages must always be convenient to give ready access, and proportional in width and height to the magnitude of the other apartments, and with suitable decorations. PASTIL, or PASTEL (from the Latin pastillus) among painters, 8tc. a sort of paste, made of se- veral colours, ground up with gum-water, either together or separately, in order to make crayons, to paint with on paper or parchment. PASTOPHORIA (Greek) in antiquity, apartments near the temples, for lodging the pastopkorz', or priests, whose business it was, at solemn festivals, to carry the shrine of the deity. Clemens Alexandrinus, describing the temples of the Egpytians, says, that, “ after having passed through magnificent courts, you are conducted to a temple, which is at the farther end of these courts, and then a pastop/torus gravely lifts up the veil, which is the door, to shew you the deity within; which is nothing but a dog or a cat, or some other animal.” Apuleius speaks of the pas- top/zori that carried the Syrian goddess. In the temple of Jerusalem,there were two courts surrounded with galleries, and round about were several lodging-rooms for the priests to lay up wood, wine, oil, salt, meal, spices, incense, vest- ments, valuable vessels, and provisions necessary for the sacrifices and lamps, as also for the sup- port and maintenance of the priests. See I Citron. ix.Q6,33. xxvi. 16. Ezek. x1. 17, 18. PATE, in fortification, a kind of platform, like what they call a horse-shoe; not always regular, but generally oval, encompassed only with a pa- rapet, and having nothing to flank it. It is usually erected in marshy grounds, to cover the gate of a town, or the like. PATERA (from pateo, to be open) among anti- quaries, a goblet, or vessel, used by the Romans in their sacrifices, in which they received the blood of their victims, offered their consecrated meats to the gods, and made libations. ()n medals, the patera is seen in the hands of se- veral deities; and‘ frequently in the hands of princes, to mark the saeerdotal authority joined with the imperial, Ste. Hence F. Joubert ob- serves, that besides the patera, there is frequently. an altar, upon which the patera seems to be pour- ing its contents. The patera is an ornament in architecture, fre- quently introduced in friezes, fascias, and im- posts, over which are hung festoons of husks or 3 1; 2 ' PAT 436' PAV flowers; or they are sometimes used by them- selves, to ornament a space; and in this case it is common to hang a string of husks or drapery over them; sometimes they are much enriched with foliage, and have a mask or ahead in the centre. - In vol. xiv. of the Archaeologia, a description and plate are given of a Roman patera and vase dug ' up when sinking a ditch in Essex, in June 1800. They were found near an ancient Roman road, between Camulodunum and Camboritnm. “The metal vase and patera merit attention, as none similar to the first have been figured or described in the works of the society; nor do I know that any like either have been presented for their in- spection. The vase is of that fdrm which Mont— faucon has figured in his 2d vol. pl. 19, fig. 10. and calls a pm’fericuhmz, used by the Romans at their sacrifices, for pouring wine into the patera. See p. 88, where he controverts Festus’s opinion that the prasfericula were without handles. An- other, more nearly resembling that here repre- ' sented, is given in his 3d vol. pl. 24. fiat. 9, and called by Beger an epic/zysis, but not allowed to be such by Montfaucon. The metal patera which belongs to the above, differs from the earthen paterte, in general, by being bossed in the centre, a circumstance not easily to be accounted for, unless it was for the firmer fixing the praefericu- lum upon, when placed with the body at the time of interment.” With the above Roman antiqui- ties were found several little cups of Samian ware. “ The-uses of these elegant little cups have not,” the antiquary continues, “ that I know of, been ascertained by any author. The real purposes to which they were applied must remain at present in obscurity.” The learned author of this communication, Thos. Walford, Esq. F.A.S. earnestly invites an explana- tion of these several Roman antiquities. It is, perhaps, no explanation to state, that the IIin- (1005, in their sacrifices and ceremonies, have 1m- memorially used, and still use, articles exactly similar to those exhibited, with the above com- munication, in vol.xiv. of the Arc/twologia, Plates 4 and 5. But it is curious to see how nearly they agree in form. A comparison of the article in the platesjust adverted to, with those in Plates 83, 86, and 105, of the Hindoo Pantheon, will strikingly evince this. The sacrificial ease, in the latter plate, has the same form, though more elaborately ornamented, as the above described praefericulum; and the others exhibit metallic circular paterze, and the central embossment, which, though “not easily accounted for,” is found among Hindoo mystics to have very pro- found allusions. The Roman patera has also the mysterious rim or yoni, respecting which the reader may consult the work last referred to. Dr. Clarke, in his recently published Travels, notices that “ the patera used by priestesses in the rites of Ceres, had this pyramidal node or cone in the centre. A priestess is represented holding one of these, on a has-relief, in the vestibule of Cam— bridge University library.” Vol. ii. p. 334. Greek marbles, No. xv. p. 37. Similar articles are still .used in the rites of the Hindoo Ceres; as are also the “little cups” described and exhibited in the Arcfiwologia, as above referred to, and in many of the plates of the Hindoo Pant/lean. In India, they are used for holding clarified butter,_ca common ingredient in the frequent oblations to fire; and unguents, and holy water, in the sradlza, or fune- ral obsequies, and in other rites and ceremonies. PATERNOSTERS, in architecture, a sort of or- naments in form of beads, either round or oval, used on baguettes, astragals, Ste. PAVEMENT (from the Latin pavimentum, derived from pavire, to make the earth firm and strong by beating) a layer or stratum of stone, or other matter, serving to cover and strengthen the ground of divers places, for themore com modious walking on, or for the passage of carriages. In England, the pavements of the grand streets, 8w. are usually of flint or rubble-stone; courts, stables, kitchens, halls, churches, 810. are paved with tiles, bricks, flags, or fire-stone; sometimes with a kind of free-stone, and rag-stone. In some cities, e. gr. Venice, the streets, Ste. are paved with brick; churches sometimes are paved with marble, and sometimes with mosaic work, as the church of St. Mark, at Venice. In France, the public roads, streets, courts, &c. are paved with gres or grit, a kind of free-stone. In Amsterdam, and the chief cities of Holland, they call their brick pavement the burglzer-mas- ter’s pavement, to distinguish it from the stone or flint pavement, which usually takes up the middle of the street, and which serves for carriages; that which borders it being for the passage of people on foot. Pavements of free-stone, flint, and flags, in streets) PAV 4,37. 1‘ Ste. are laid dry, 2'. e. in a bed of sand; those of courts, stables, ground-rooms, Ste. are laid in a mortar of lime and sand; or in lime and cement, especially if there be vaults or cellars underneath. Some masons, after laying a floor dry, especially of brick, spread a thin mortaroverit; sweeping it backwards-and forwards to fill up thejoints. The several kinds of pavement are as various as the materials of which they are composed,and whence they derive the name by which they are distin- guished; a l. Pebble-paving, which is done with stones col- lected from the sea-beach, mostly brought from the islands of Guernsey and Jersey; they are very durable, indeed the most so of any stone used for this purpose. They are used of various sizes, but those which are from six to nine inches deep, are esteemed the most serviceable. When they are about three inches deep, they are denominated bolders, or bowlers,- these are used for paving court—yards, and other places not accustomed to receive carriages with heavy weights; when laid in geometrical figures they have a very pleasing appearance. 2. Rag paving was formerly much used in Lon- don, but is very inferior to the pebbles; it is dug in the vicinity of Maidstone, in Kent, from whence it has the name of Kentish rag-stone; there are squared stones of this material for pav- ing coach-tracks and foot-ways. 3. Parbeclc pin-liens; squared stones used in foot- ways; they are brought from the island of Pur- beck, and also frequently used in court-yards; they are in general from six to ten inches square, and about five inches deep. 4. Squared paving, for distinction by some called Scotch paving, because the first of the kind paved in the manner that has been and continues to be paved, came from Scotland; the first was a clear close stone, called blue wynn, which is now dis- used, because it has been found inferior to others, since introduced, in the order they are hereafter placed. 5. Granite, a hard material, brought also from Scotland, of a reddish colour, very superior to the blue wynn quarry. 6. Guernsey, which is the best, and now almost the only stone in use”; it is the same stone with the pebble before spoken of, but broken with iron hammers, and squared to any dimensions re- quired, of a prismoidical figure, set with its PAV w smallest base downwards. The whole of the fore- going paving should be bedded and paved in small gravel. 7. Purbeck paving, for footways, is in general got in large surfaces, about two inches and a half thick; the blue sort is the hardest and the best of this kind of paving. 8. Ymkslzire paving, is an exceeding good mate- rial for the same puipose, and 18 got of almost any dimensions, of the same thickness as the Purbeck; this stone will not admit the wet to pass through it, nor is it affected by the frost. 9. Ryegate, or fire-stone paving, is used for hearths, stoves, ovens, and such places as are liable to great heat, which does not affect this stone, if kept dry. 10. Newcastle flags, are stones about two feet square, and one and a half, or two inches thick; they answer very well for paving out~oflices; they are somewhat like therYorkshire. 11. Portland paving, with stone from the island of Portland; this is sometimes ornamented with black marble dots. - 12. Sweedlandpaving, is a black slate, dug in Lei- cestershire, and looks well for paving balls, or in party-coloured paving. 13. Marble paving, is mostly variegated with different marbles, sometimes inlaid in mosaic. 14-. Flat brie/c paving, done with brick laid in sand, mortar, or grout, as when liquid lime is poured into the joints. 15. Brick-on-edge paving, done with bricks laid edgewise in the same manner. 16. Bricks are also laid flat or edgewise in her- ring-bone. 17. Bricks are also sometimes set endwise in sand, mortar, or grout. 18. Paving is also performed with paving bricks. 19. With ten-inch tiles. 20. VVith foot tiles. ‘21. With clinkers, for stables and outvoflices. 22. With the bones of animals, for gardens, Ste. And, ‘23. We have knob-paving, with large gravel- stones, for porticoes, garden-seats, 8L0. Paviours’ work is done by the square yard; and the content is found by multiplying the length by the breadth. Pavements of churches, 3w. frequently consist of stones of several colours; chiefly black and white, and of several forms, but chiefly square, and loc- PAV 438 PAV z'enges, artfully disposed. Indeed, there needs no great variety of colours to make a surprising diversity of figures and arrangements. M.. Truchet, in the Memoirs of the French Academy, has shewn, by the rules of combination, that two square stones, divided diagonally into two co- lours, may be joined together chequerwise sixty- four different ways: which appears surprizing enough ; since two letters, or figures, can only be combined two ways. The reason is, that letters only change their situation with regard to the first and second; the top and bottom remaining the same: but in the arrangement of these stones, each admits of four several situations, in each of which the other square may be changed sixteen times, which gives sixty-four combinations. Indeed, from a farther examination of these sixty- four combinations, he found there were only thirty- two different figures; each figure being repeated twice in the same situation, though in a different combination; so that the two only differed from each other by the transposition of the dark and light parts. The paving of streets is one of the most beneficial regulations of police that have been transmitted to us from our ancestors. Several cities had paved streets before the commencement of the Christian aera; nevertheless those which are at present the ornament of Europe, Rome excepted, were des- titute of this great advantage till almost the 12th or 18th century. It is probable that those people who first carried on the greatest trade, were the first who paid attention to have good streets and highways, in order to facilitate that intercourse which is so necessary to keep up the spirit of commerce. Accordingly, we are told by Isidorus (Origin. lib. xv. cap. 16.) that the Carthaginians had the first paved streets, and that their example was soon copied by the Romans. Long before that period, however, Semiramis paved highways, as appears by the vain-glorious inscription which she herselfcaused to be put up. (Strabo, lib. xvi. Diod. Sicul. lib. ii. v. 13. Polyzeni Stratagem, lib. viii. cap. 26.) The streets of Thebes, and probably those of Jerusalem, were paved. But neither the streets of Rome, nor the roads around it, were paved during the time of its kings. In the year U.C. 188, after the abolition of the mo- narchical form of government, Appius Claudius, being then censor, constructed the first real high- way, called after him the Appian way, and, on ac- count of its excellence, the queen (f roads. The time when the streets were first paved cannot be precisely ascertained; some have referred this improvement to the,year 578, after the building of the city; others to 584; and others to 459; at which several periods some parts of the city and suburbs might have been paved. That streets paved with lava, having deep ruts made by the wheels of carriages, and raised banks on each side, for the accommodation of foot-passengers, were found both at Herculaneum and Pompeii, is well known. Of modern cities, the oldest pavement is com— monly ascribed to that of Paris; but it is certain that Cordova, in Spain, was paved so early as the middle of the 9th century, or about A.D. 850. The capital of France was not paved in the 12th century, but the orders for this purpose were issued by the government in the year 1184, on which occasion it is said that its name of Lute- tia, deduced from its dirtiness, was changed into that of Paris. Nevertheless, in the year 1641, the streets in many quarters of Paris were not paved. That the streets of London were not paved at the end of the 11th_century, is asserted by all historians. It does not appear when paving was first introduced; but it was gradually ex- tended as trade and opulence increased. Several of the principal streets, such as Holborn, which are at present in the middle of the city, were paved for the first time by royal command in the year 1417; others were paved under Henry VIII. some in the suburbs in 1544, others in 1571 and 1605; and the great market of Smithfield in 1614. i PAVEMENT OF TERRACE, that which serves fora covering, in manner of a platform; whether it be over a vault or a wooden floor. Those over vaults are usually stones, squared, and bedded in lead. Those on wood, called by the Latins pavimeuta contignata, are either stones with beds for bridges, tiles for ceiling of rooms, or lays ofmortar made of cement and lime, with flints or bricks laid flat: as is still practised by the Eastern and Southern people, on the tops of their houses. All those pavements which lie open were called by the Latins pavimenta subdialia. PAVEMENT, Diamond, those pavements of which the stones, flags, or bricks, are laid with their diagonals parallel and perpendicular to the sides of the apartment. PAVILION (French, from the Italian padiglioue, PEI) 439 PED Pi =— . a tent,- derived from the Latin papilio) in archi- tecture, a kind of turret, or building, usually in- sulated, and contained under a single roof; some- times square, and sometimes in form of a dome; ' thus called from the resemblance of its roof to a = tent. Pavilions are sometimes also projecting parts, in the front of a building, marking their middle. Sometimes the pavilion flanks a corner, in which ' case it is called an angular pavilion. The Louvre is flanked with four pavilions. They are usually highm than the rest of the building. There are pavilions built in gaidens, popularly called summer-houses, pleasure houses, 8tc. Some castles, or forts, consist only of a single pavilion. PAUTRE, ANTONY LE, in biography, an emi- nent French architect, born at Paris in 1614, who distinguished himself by his taste in the decora- tion of buildings. Several edifices from his de- signs were erected in the capital and its neigh- bourhood, of which the most noted new the wings of St. Cloud, the church of the nunnery of Port-Royal, and the hotels of Gevres and Bean- vais. He was appointed architect to the king’s brother, and afterwards to the king himself. He was a member of the Academy of Architecture from its first institution, and published a work on that art, intitled, Les Gfiuvres d’Ar-ahitecture d’JJn- toine le Pautre, of which the first edition appear- ed in 1652. He died in 1691. His son, Peter, was eminent as a sculptor. PEDESTAL (from the Latin pes, pedis, foot, and qukog, column) in architecture, the lowest part of an order of columns; being that which sustains the column, and serves it as a foot to stand on. The pedestal, called by the Greeks stylobates, and stereobates, consists of three principal parts: 'vzz.asquare trunk, or die, which makes the body , a cornice, the head; and a base, the foot of the pedestal. The pedestal 1s properly an appendage to a co- lumn; not an essential part ther,eof though M. Le Clerc thinks it is essential to a complete order. The proportions, or ornaments of the pedestal are different in the difi'erent orders: Vignola, indeed, and most of the inoderns, make the pedestal, and its ornaments, in all the orders, one-third of the height of the column, including the base and ca- pital: but some deviate from this rule. M. Perrault makes the proportion of the three I constituent parts of pedestals, the same in all the orders, viz. the base one-fourth of the pe- destal; the cornice an eighth part; and the socle, or plinth, of the base, two-thirds of the base itself. The height of the die is what remains of the whole height of the pedestal. PEDESTAL, Tuscan, is the simplest and the lowest of all. Palladio and Scamozzi make it three mo- dules high; Vignola five. Its members, in Vig- nola, are only a plinth, for a base; the die; and p a talon crowned, for a cornice. This has rarely any base. PEDESTAL, Doric. Palladio makes four modules five minutes high; and Vignola five modules four minutes. In the antique, we not only do not meet with any pedestals; but even not with any base, in the Doric order. The members in Vignola’s Doric pedestal, are the same with those in the Tuscan, with the addition. ofa mouchette in its cornice. PEDESTAL, Ionic, in Vignola and Serlio, is six modules high; in Scamozzi five; in the temple of FortnnaVirilis, it is seven modules twelve minutes. Its members and ornaments are mostly the same with those of the Doric, only a little richer. The pedestal now usually followed, is that of Vitru- vius, though we do not find it in any work of the antique. Some, in lieu hereof, use the Attic base, in imitation of the ancient. PEDESTAL, Corinthian, is the richest and most delicate of all. In Vignola, it is seven modules high; in Palladio, five modules one minute; in Serlio, six modules fifteen minutes; in the Coli- seum, four modules two minutes. Its members, in Vignola, are as follow: in the base are a plinth for a socle, over that a torus carved, then a reglet, a gula inverted and enrich- ed, and an astragal. In the die are a reglet, with a conge over it; and near the cornice a reglet, with aconge underneath. In the cornice is an astragal, a frieze, fillet, astragal, gorge, and a talon. See each under its proper article. PEDESTAL, Composite, in Vignola, is of the same heightwith the Corinthian, viz. seven modules; in Scamozzi six modules two minutes, in Palladio six modules seven minutes, in the Goldsmiths’ arch, seven modules eight minutes. . Its members, in Vignola, are the same with those of the Corinthian; with this difference, that, whereas these are most of them enriched with PED , 440 PED carvings in the Corinthian, they are all plain‘ in the Composite. Nor must it be omitted, that there is a difi'erence in the profiles of the base and cor- nice, in the two orders. The generality of architects, Daviler observes, use tables, or panels, either in relievo or creux, in the dies of pedestals, without any regard to the character of the order. Those in relievo, he ob- serves, only fit the Tuscan and Doric; the three others must be indented: but this, he adds, is a thing the ancients never practised, as being con- trary to the rules of solidity and strength. PEDESTAL, Square, that whose height and width are equal ; as that of the arch of the lions at Ve- rona, of the Corinthian order; and such some followers of Vitruvius, as Serlio, Philander, Ste. have given to their Tuscan orders. PEDESTAL, Double, that which supports two co- lumns, and is larger in width than height. PEDESTAL, Continued, that which supports a row of columns without any break or interruption; such is that which sustains the fluted Ionic columns of the palace of the Thuilleries, on the side of the garden. PEDESTALS OF STATUES, are those serving to sup- port figures or statues. Vignola observes, there is no part of architecture more arbitrary, and in which more liberty may be taken, than in the pedestals of statues; there being no laws prescribed for them by antiquity, nor any even settled by the modems. There is no settled proportion for these pedestals; but the height depends on the situation, and the figure they sustain. Yet, when on the ground, the pedestal is usually two-thirds, or two-fifths, of‘that of the statue; but always the more mas- sive the statue, the stronger must be the pedestal. Their form, character, Sec. are to be extraordi- nary and ingenious, far from the regularity and simplicity of the pedestals of columns. The same author gives a great variety of forms, oval, tri— angular, multangular, 81c. PEDIMENT, in architecture, a kind of low pin- nacle, serving to crown porticos, or finish a fron- tispiece; and placed as an ornament over gates, doors, windows, niches, altars, Ste. The pinnacles of the ancient hous€s,Vitruvius ob- serves, gave architects the first idea of this noble part; which still retains the appearance of its original. The parts of the pediment are, the tympanum and its cornice. The first is the panel, naked, or area of the pediment, enclosed between the cornice, which crowns it, and the entablature, which serves as a base, or socle. Architects have taken a great deal of liberty in the form of this member; nor do they vary less as to the proportion of the pediment. The most beautiful, ' according to Daviler, is that where its height is about one—fifth of the length of its base. The pediment is usually triangular, and sometimes an equilateral triangle; this is also called a pointedpediment. Sometimes it is circular; though Felibien observes, that we have no instances of round pediments in the antique, beside those in the chapels of the Rotunda. Sometimes its upper cornice is divided into three or four sides, or right lines; sometimes the cornice is cut, or open at. top, which is an abuse introduced by the mo- derns, particularly by Michael Angelo. For the design of this part, at least over doors, windows, Ste. being chiefly to shelter those underneath from the rain, to leave it open in the middle is to frustrate its end. Sometimes the pediment is formed of a couple of' scrolls, or wreaths, like two consoles joined to- gether. See CONSOLE. Sometimes, again, the pediment is without base, or its lower cornice is cut out, all but what is be— stowed on two columns, or pilasters, and on these an arch or sweep, raised in lieu of an entablature; of which Serlio gives an instance in the antique, in a Corinthian gate at I’oligny, in Umbria; and Daviler, a more modern one, in the church of St. Peter at Rome. Under this kind of pediments, also come those little arched cornices, which form pediments over doors and windows, supported by two consoles, in lieu either of entablature or columns. Sometimes the pediment is made double, 1'. e. a less pediment is made in the tympanum of the larger, on account of some projecture in the mid- dle; as in the frontispiece of the church of the Great Jesus, at Rome: but this repetition is an abuse in architecture, though authorised by some very good buildings; as the large pavilion of the Louvre, where the Caryatides support three pediments, one in another. ' Sometimes the tympanum of the pediment is cut out, or left open, to let in light; as we see under the portieo of the Capitol, at Rome. Lastly, this open pediment is sometimes triangular, and enriched PEL 441 PEN with sculpture, as roses, leaves, 8tc. as we find in PENDENT,01‘PH1LOSOPHICALBRIDGE,a wooden most of the Gothic churches. In all the remains of Grecian architecture, the horizontal cornice is never interrupted or broken, nor is there any instance of a circular pediment, nor of any open at the top. The proportion of the tympanum is from one-fifth to one-ninth part of the span, in the pediments which remain of Grecian edifices. In the Doric tetrastyle por- tico, at Athens, the height of the tympanum is about one-seventh part ofits triangular base. The proportion of the tympanum of the Ionic temple, which is also tetrastyle, is likewise one-seventh part of its triangular base. The portico of the temple of Theseus is hexastyle; and the height of the tympanum of the pediment is about an eighth part of the span of its triangular base. The por- tico of the temple of Minerva is octostyle; and the height of the triangular tympanum about one- ninth of its base. So that the higher the pedi— ment, the less is the height in proportion. And thus the pediments of doors and windows ought to be still higher, as is verified in the frontis- piece of the entrance door of the tower of the winds, at Athens, where the height of the tym- panum is only one-fifth part of the triangular base. Vitruvius expressly disapproves of the use of den- tils, modillions, or mutules, in pediments, for this reason: that as mutules and modillions were the representations of rafters, and dentils the re- presentations of laths, and as these essential parts were always placed in the inclined sides of the roof from the ridge, to overhang the eves, it would certainly have been improper to use mutules, mo— dillions, or dentils, in a situation where the origi- nals themselves never existed. bridge supported by posts and pillars, and sus- tained only by butments at the ends. See BRIDGE, Vol. I. p. 133. PENDENTIVE, in architecture, the whole body of a vault, suspended out of the perpendicular of the walls, and bearing against the arc-bou- tants. Daviler defines it, a. portion of a vault between the arches of a dome, usually enriched with sculpture; Felibien, the plane of the vault con— tained between the double arches, the forming arches, and the ogives. The pendentives are usually of brick, or soft stone; and care must be taken that the joints of the masonry be always laid level, and in right lines proceeding from the sweep whence the rise is taken. Thejoints too must be made as small as possible, to save the necessity of filling them up with slips of wood, or of using much mortar. PENDENTIVE BRACKETING, a cove bracketing, springing from the rectangular walls of an apart- ment upwards to the ceiling, so as to form the horizontal part of the ceiling into a complete circle, or ellipsis. The proper criterion for such bracketing is, that if the walls are cut by horizontal planes through the coved parts, all the sections through such parts will be portions of circles, or portions of ellipses, having their axes proportional to the sides of the apartment: so that each section will bea compound figure. Besides having four curvi- linear parts, it will have four other parts, which are portions of the sides of the rectangular apart- ment; and the axis of the ellipsis will bisect each side of the rectangle. Arches under pediments is an abuse in archi- tecture. PELECOIDES (from the Greek mkexug, a hatchet, PENITENTIARY HOUSE, see PRISON. PENTAGON, (from the Greek myrayoyog, quin- and udog‘, form) a figure in the form ofa hatchet. Such is the figure B C DA, contained under the 5 inverted quadrantal arcs AB and A D, and the F semicircle B C D. The area of the pelecoides is demonstrated to be ‘ equal to the square A C; and that, again, to the rectangle E B. It is equal to the square A C, be- cause it wants, of the square on the left hand, the two segments A B and AD, which are equal to t the two segments BC and CD, by which it ex- ceeds on the right hand. VOL. I]. quangulus, compounded of arm/re, jive, and 70mm, an angle) in geometry, a figure of five sides and five angles. If the five sides are equal, the angles are so too; and the figure is called a regular pentagon. Most citadels are regular pentagons. , The most considerable property of a pentagon is, that one of its sides, 12. gr. D E, is equal in power to the sides of a hexagon and a decagon inscribed in the same circle, A B C D E;,that is, the square of the side D E is equal to the sum of the squares of the sides D a and D b. 3 L PEN 44 0 M PEN ._._-—" ' A ,v .. __ A pentagon, and al-so a decagon, may be in- scribed in a circle, by drawing the two diame- ters A P, m n, perpendiculal to each other, and bisecting the radius 0 n at q. With the centre q, and distance qA, describe the alc Ar, and with the centre A, and 1adius A r, desc1ibe the arc TB. Then A B is one-fifth of the circumference, and A B, carried five times over,will form the pen- tagon; and the arc AB bisected in s, will give As, the tenth part of the circumference, or the side of the decagon. If tangents be d1awn th1ough the angula1 points, they will form the ci1cums01ibing pentagon, o1 decagon. See POLYGON, and . REGULAR FI- GURE. Pappus has also-demonstrated, that twelve regu- lar pentagons contain more than twenty triangles inscribed in the same circle, lib. v. probl. 45. The dodecahedron, which is the fourth regular body, consists of twelve pentagons. PENTAGRAPH, or PARALLELOGRAM, an instru- ment for copying plans, maps, designs, Ste. with expedition, even by a person unskilled in the art of drawing. This instrument consists of four brass or wooden rulers, in the form ofa parallelogram, with move- able joints at the angles; two of the rulers are extended beyond the parallelogram, one for the pu1pose of car1ying a fixed socket, called C, with a metal t1ace1, in orde1 to tiace ove1 the outlines of the original thawing, 01 print, and the othe1, called B, for carrying a moveable socket, also called B, with a pencil, in order to trace out a drawing similar to the original. The parts, B and C, of the rulers thus extended, being upon the same side of one of the diagonals, the side of the parallelogram, called D, which adjoins the ruler with the moveable socket, has another moveable socket, also called D, in order to insert a vertical pin, which is fixed in a flat piece of lead; both of the moveable sockets, B and D, are clamped by means of a screw. As the metal tracer, C,tl1e pinin the socket D, and the pencil in the socket'B, are cylindrical, in fixing the instru- ment, the axes of the three cylinders must be set all in the same plane, and they will remain so th1oughout every movement of the inst1ument. The pins which fasten the parallelogram at the angles being also ve1tical cylinde1s to the plane of the instrument, the axis of the metal tracing point, in the socket C, and those of the Mo pins in the sockets of B and D, must be in the same plane; also the axis of the pin, in the socket D, and those of the ruler D at the joints, must also be in a plane. In order to make the movement of the instrument easy, it is provided with casters, or rolle1s, each of which turns on an axis in the same line with the axis at the joints or angles. The extended part of the idler B, on which the socket and pencil a1e ca1ried, has seve1a1g1adua- tions, or divisions, which shew the proportion of the drawing to be made to the original; and thus calling the centre of the joint connecting the extended bars the apex of the instrument, the first division 011 the extended pa1t, B, is equally distant f1om the apex with the axis of the txacing point on the other extended part, C; and the ruler, D, which has the steel pin, has a cone.» sponding division, exactly opposite the vertex, when the extended rulers, B and C, are brought into a straight line, and, consequently, the instru- ment is divided thereby into two equal parts; and thus it becomes necessary to have the two opposite sides of the parallelogram, which has the side marked D, longer thau~the other two sides, one of which has the extended part B. The divisions upon the extended part, B, being fixed upon, and numbered from 1—1, 1-2, 1-3, 1-4, to 1-12; that is, 1, %, ii, i, 8m. towards the vertex, the other divisions upon the side of the parallelogram, D, are marked with corresponding figures, 1-], 1-2, 1-3, 8m. in such a manner, that when the extended sides are brought into a straight line, the division marked 1-2, on the side D, divides the instrument into three equal parts, from the division 1-2 on B, to the point C, 011 the axis of the tracing point on the othe1 extended leg C; and thus the distance f1o1n 1-0 ., 011 the side D, to 1—2 on the side B, will be half the dis- tance between 1—2 on the side D and the point (, on the extended pa1t C. In like manner, the division marked 1-3, on the side D, divides the instrument into four equal parts, from 1-3 on B, to the tracer 011 C; and thus 1-3 on D will be distant from 1-3 on B, and one-third of the distance from 1-3 011 D to the axis of the tracer on C. The other proportions are found in a similar manne1. The fiducial edges of the clamps, which can} the socket f01 the steel pin, and the socket for PEN 443 PER J holding the pencil, cross the rulers, to which they are attached, at right angles, and would, if pro- duced, cut the axis of the cylindrical socket in eaclrof the said rulers. The upper part of the cylindrical case, which holds the pencil, is pro- vided with a cup, to contain shot, or a small weight, in order to make the pencil press suffi— ciently, so as to mark the paper. In order to pre- vent the pencil from tracing the same path it has already described, a silk thread, or catgut string, connected with the pencil, passes through an eye at the vertex, returns to the hand of the operator, and being drawn tight, raises the pencil from the paper. To use the instrument, suppose the drawing re- quired to be one-half of the original; set the fiducial edge of the clamp B upon 1-2 in the ex- tended part B, and the fiducial edge of the clamp D, upon 1-2 of the ruler D; slide the socket D upon the pin fixed into the lead weight, then having adjusted the original drawing, or print, under the tracer, and the paper under the pencil, trace overall the lines of the original, and the pencil at the remote extremity will trace out a similar figure. Again, let us take another example: suppose the drawing required to be one-third of the original; set the fiducial edge of the clamp B upon 1-3 in the extended part B, and the fiducial edge of the clamp D upon 1-3 of the ruler D; slide the socket D Upon the pin fixed into theleaden weight, then proceed as before. In the same manner the draw- ing may be reduced to 7}, % 8L0. of the lineal dimensions, as shewu by the graduations: but if any intermediate proportion is required, as between a third and a fourth ; bring the fiducial edge of the clamp B to the intermediate point, and the fiducial edge of the clamp D in a straight line, then proceed as above. And should it be required to enlarge the drawing, it is only neces- sary to change the pencil in the socket or tube of the clamp B, for that of the metal tracer, and the paper for the original, and proceed as before. PENTASTYLE (from 71'61/7'5, five, and arr/hag, a CO- Iumn) in architecture, a work containing five rows of columns. Such was the portico begun by the Emperor Gallienus, and which was to have been con- tinued from the Flaminian gate to the' bridge Milvius, z'. e. from the Porto del Popolo to the Form Mole. ““ ‘A- " w‘ PERA MBULATOR, (from the Latin perambulo, to travel) an instrument for the measuring of dis— tances; called also pedometer, way-wiser, and surveying-wheel. Its advantages are its handiness and expedition: its contrivance is such, that it may be fitted to the wheel ofa coach; in which state it performs its office, and measures the road without any farther trouble. PERIDROME, PERIDROMUS, in ancient archi- tecture, the space, or an aisle in a periptere, be— tween the columns and the wall. Salmasius observes, that the peridromes served for walks among the Greeks. PERIMETER (from the Greek WEPL, about, and ,uerpéw, measure) in geometry, the ambit or extent that bounds a figure or body. The perimeters of surfaces, 01' figures, are lines; those of bodies are surfaces. In circular figures, Ste. instead of perimeter, we say circumference, or periphery. PERIPHERY (from the Greek rsptgbtpw, I surround, or 'n'flOt, about, and (pepw, I bear, or carry) in geo. metry, the circumference or bounding‘line of a circle, ellipsis, parabola, or other regular curvi- linear figure. The periphery of every circle is supposed to be divided into three hundred and sixty degrees; which are again subdivided, each into sixty mi- nutes, the minutes into seconds, 8w. The division of degrees, therefore, are fractions, whose denominators proceed in a sexagesimal ratio; as the minute, {5-, second, 5335?, third, 31—31—655. See SEXAGESIMAL. But these denominators being troublesome, in their stead are used the indices of their loga- rithms; hence the degree, being the integer, or unit, is marked by °, the minute by', second by ”, 8Lc. See CIRCLE. PERIPTERE (from the Greek mpmreloog, formed of Wépt, about, and m-r'pwv, wing, q. d. winged on every side) in ancient architecture, a building encom- passed on the outside with a series of insulated columns, forming a kind of aisle, or portico, all round. Such were the basilica of Antonine, the septizon of Severus, the portico of Pompey, 81c. Peripteres were properly temples with columns on all the four sides, by which they were distin- guished from prostyles and amphiprostyles, the one of which had no columns before, and the other none on the sides. 3 L 2 PER 444 PER M. Perranlt observes, that periptere, in its gene- ral sense, includes all the species of temples which have 'porticoes of columns all around, whether the columns be diptere, or pseudo-diptere, or sim- ple periptere; which is a species that bears the name of the genus, and has its columns dis- tant from the wall by the breadth of an inter- columniation. For the difference between perip- tere and peristyle, sec PERISTYLE. ‘PERISTYLE (from the Greek rapist/Rog, formed from 7.59;, about, and svkog, column) in ancient archi- tecture, a 'place or building, encompassed with a row of columns on the inside; by which it is dis- tinguished from the periptere, where the columns are disposed 'on the outside. Such was the hypaethral temple of Vitruvius, and such are now some basilicas in Rome, several places in Italy, and most Cloisters of reli- gious houses. PERISTYLE is also used by modern writers for a range of columns, either within or without a building. Thus we say, the Corinthian peristyle of the portal of the Louvre, 8L0. PERISTYLION (from the Greek 7r£pt€vluov) among the Athenians, a large square place, though some- times oblong, in the middle of the gymnasium, designed for walking, and the performance of those exercises which were not peculiar to the alaastra. PERITROCHIUM (from wept, about, and rpomkog, a circle) in mechanics, a wheel, or circle, concen- trio with the base of a cylinder, and moveable together with it, about an axis. The axis, with the wheel and levers fixed in it, to move it, con- stitutes that mechanical power called axis in peritrochio. PERPENDICULAR (from the Latin perpendicu- larz's) in geometry, a line falling directly on an- other line, so as to make equal angles on each side; called also a normal line. From the very notion of a perpendicular, it fol- lows, 1.That the perpendicularity is mutual; i. e. if a line, as I G, be perpendicular to another, K H; that other is also perpendicular to the first. 2. That only one perpendicular can be drawn from one point in the same plane. 3. That if a perpendicular be continued through the line} to which it was drawn perpendicular, the continuation will also be perpendicular to it. 4. That if there be two points of a right line, each of which is at an equal perpendicular distance from two points of another right line, the two lines are parallel to each other. 5. That two right lines perpendicular to one and the same line, are parallel to each other. 6. That a line, which is perpendicular to another, is also perpendicular to all the parallels of the other. 7. That perpendiculars to one of two parallel lines, terminated by those lines, are equal to each other. 8. That a perpendicular line is the shortest of all those which can be drawn from the same point to the same right line. Hence the distance of a point from a line, is a right line drawn from the point perpendicular to the line or plane; and hence the altitude of a figure is a perpendicular let fall from the vertex to the base. Perpendiculars are best described in practice by means ofa square; one of whose legs is applied along that line, to or from which the perpendi- cular is to be let fall or raised. A line is said to be perpendicular to a plane, when it is perpendicular to all right lines, that can be drawn in that plane, from the point on which it insists. A plane is said to be perpendicular to another plane, when all right lines drawn in the one, per- pendicular to the common section, are perpendi— cular to the other. Ifa right line he perpendicular to two other right lines, intersecting each other at the common sec: tion, it will be perpendicular to the plane passing by those two lines. Two right lines perpendicular to the same plane are parallel to each other. If, of two parallel right lines, the one is perpendi- cular to any plane, the other must also be perpen- dicular to such plane. If a right line he perpendicular to a plane, any plane passing by that line will be perpendicular to the same plane. Planes, to which one and the same right line is perpendicular, are parallel to each other: lient't' all right lines perpendicular to one of two parallel planes, are also perpendicular to the other. If two planes, cutting each other, be both perpetr dicnlar to a third plane, their common section will also be perpendicular to the same plane. PERPENDICULAR TO A CURVE, is a right line cut» ting the curve in the point in which any other PER. 44 PER W right line touches it, and is also itself perpendi- cular to that tangent. PERRAULT, CLAUDE, an eminent architect, born at Paris in 1613. He was brought up to the medical profession, and took his degree as doctor of the faculty of Paris in 1641. He practised little, however, excepting among his friends and the poor; and having a decided taste for draw- ing, and the fine arts, he turned his attention to the science of architecture, in which he became greatly distinguished. When the Academy of Sciences was founded, under the patronage of Colbert, in the year 1666, Perrault, who was one of the first members, was appointed to selecta spot for an observatory; and he also gave a: plan of the building, which was to be executed. When it was resolved, under Louis XIV. to pro- ceed in completing the palace of the Louvre, all . the eminent architects were invited to give in de- signs of the fagade; and that of Perrault was preferred. This is accounted the master-piece of French architecture, and it would alone suffice to transmit his name with. honour to posterity. It was in vain that persons, jealous of his reputation, endeavoured to make the public believe that the real designer was Le Veau: they entirely failed in their proof, and the glory of Perrault remained untarnished. When- Colbert, after the king’s first conquests, proPosed to construct a grand tri- umphal arch to his honour, Perrault’s design had the preference, and the edifice was commenced. It was, however, never finished. In its masonry, Perrault employed the practice of the ancients, of rubbing the surface of the stones together, with grit and water, soas to make-them cohere with- out mortar. Other works. of this architect were the chapel at Sceaux, that of Notre Dame, in the church of the Petits Peres, in Paris, the water- alley at Versailles, and most of the designs of the vases in the park. of that palace- By the king’s command, he undertook a translation of Vitru- vius, with notes, published in 1673. All the de- signs for the plates of thiswork were drawn by himself, and have been esteemed as master-pieces of the kind. He afterwards published an. abridg- ment of that author, for the use of. students. He likewise facilitated the study of architecture by a work, intitled, ,Ordomzance des Cinq Espéces de Colonnes, selon la Méthode des Anciens. In the preface to this work, he maintains that there is no natural foundation. for. the architectural pro- portions; but that they may be infinitely varied, according to taste and fancy; an opinion which , gave much offence, though justified by the‘prac- tice 0f the ancients themselves. A collection of the drawings of several machines, which he at different times invented, was published after- his death, inv4to. This excellent artist holds a re- spectable place among writers in his original pro- fession, and, besides various memoirs on this sub- ject, communicated to the Academy of Sciences, he published Memoires pour servir ti l’Hz'stoire Naturelle des Animaur, in 2‘ vols. His other writings of this class are contained in his Essais de Physique, 4- vols. One of these volumes relates entirely to the organ of hearing, under the title of Traité de Bruit. Another relates to the me- chanism of animals, in which be anticipated Stahl in some of his opinions respecting the functions of the animal soul. In other parts of these essays, he treats on the peristaltic- motion, on the senses, on nutrition, 8w. He died in Paris, in 1688, aged 75. Perrault published a Dissertation upon the Music of the Ancients, in 1680. He had indeed given his opinion upon the subject very freely, in the notes to his translation of Vitruvius, in T673; where, in his commentary of the chapter upon Harmonic Music, according to the Doctrine of" Aristoxenus he declares that “ there is nothing in: Aristoxenus, who was the first that wrote upon concords and discords, nor in any of the Greek authors who wrote-after him, that manifests the ancients to have had the least idea of the use of concords in music of many parts.” PERR-ON (French) in architecture, a' staircase lying open, or withoutside the building; pro- perly, the steps before the front of the building, leading into the first story, when raised a little above the level of the ground. Perrons are of different forms and sizes, according to the space and height they are to lead to. Sometimes the steps are round, or oval; more usually they are square. PERRONET, JOHN RODOLPHUS, director of the bridges and roads of France, born in 1708. He was brought up to the profession of architec- ture in the city of Paris, and made great progress in the art. In 1745, he became inspector of the school of engineers, of which he was afterwards a director. France is indebted to him for several ofits finest bridges and best roads, the canaliof PER 446 PER Burgundy, and other great works. He was, for his public services, honoured with the order of St. Michael, and admitted a member of the Aca- demy of Sciences at Paris; of the Royal Society of London, and of the Academy of Stockholm. He died at Paris in 1794. He wrote a Descrip- tion of the Bridges which he had constructed, 2 vols. 12mo. and Memoirs on the Method of con- structing Grand Arches of Stone from 200 to 500 Feet in span. PERSEPOLIS, a town of Persia, formerly called Elymai's, now known only by its ruins and mo— numents, which have been described by many travellers, from Chardin to Niebuhr and Franklin. They. are situated at the bottom of a mountain, fronting the south-west, about forty miles to, the north of Shirauz. They command a View of the extensive plainof Merdasht, and the mountain of Rehumut encircles them, in the form of an amphitheatre. Here‘are many inscriptions, in a character not yet explained; but which Niebuhr seems to have represented with great accuracy. The letters somewhat resemble nails, disposed in various directions, in which singularity they ap- proach to what are called the Helsing Runes of Scandinavia, but the form and disposition seem more complex. Behind the ruin, to the north, is a curious apartment cut in the rock, and a sub- terraneous passage, apparently of considerable extent. The front of the palace is 600 paces north to south, and 390 east to west; and the mountain behind has been deeply smoothed\to make way for the foundation. About three miles and a half to the north-east of these ruins is the“ tomb of Rustan, the ancient Persian hero. The temple, or palace, at Persepolis, now called the throne of Jemshid, is supposed to have been erected in the time of Jemshid, and to have been posterior to the reign of the Hindoo monarchs. The figures at Persepolis differ from those at Elephanta, which are manifestly Hindoo; and Sir William Jones conjectures, that they are Sabian, which conjecture is confirmed by a circumstance, which he believes to have been a fact, viz. that the' Talchti J‘emshid was erected after the time of Cayfimers, when the Brahmans had migrated from Iran, and when their intricate mythology had been . superseded by the simpler adoration of the pla- nets and of fire. Chardin, who observed the in- scriptions on these ancient monuments on the spot, observes, that they bear no resemblance whatever to the letters used by the Guebres, in their copies of the Vendidad; whence Sir VVil- liam Jones inferred that the Zend letters were a modern invention; and in an amicable debate with a friend, named Bahman, that friend insisted that the letters, to which he had alluded, and which he had often seen, were monumental cha- racters, never used in books, and intended either to conceal some. religious mysteries from the vulgar, or to display the art of the sculptor, like the embellished ‘fifick and Nagari on several Arabian and Indian monuments. PERSIANS, or Pansxc ORDER, in architecture, a name common to all statues of men, serving instead of columns, to support entablatures. They only differ from Caryatides, in that the latter re- present women. The Persian is a kind of order of columns, first practised among the Athenians, on occasion of a victory their general Pausanias obtained over the Persians. As a trophy of this victory, the figures of men dressed in the Persian mode, with their hands bound before them, and other characters of slavery, were charged with the weight of Doric entablatures, and made to supply the place of Doric columns. Persian columns, M. le Clerc observes, are not al- ways accompanied with the marks of slavery; but are frequently used as symbols of virtues, vices, joy, strength, valour, 8L0. as when made in the figures of Hercules, to represent strength; and of Mars, Mercury, fauns, satyrs, See. on other occasions. See CARYATIC ORDER. PERSPECTIVE (from the Latin perspicio, to see) the art of representing objects on a definite sur- face, so as to affect the eye, when seen from a certain position, in the same manner as the object itself would, when the eye is fixed on the point in View. . The art of perspective owes its birth to painting, and particularly to that branch of it which was employed in the decorations of the theatre, where landscapes were principally introduced, and which would have looked unnatural and horrid, if the size of the objects had not been pretty nearly pro- portioned to their distance from the eye. The ancients must, therefore, have had considerable knowledge of this art; though the only ancient author from whom we can obtain any information relative to its antiquity, is Vitruvius; who, in the proem to his seventh book, informs us, thatAga- PER 447 4 tharcus, at Athens, was the first who wrote on this subject, on occasion of a play exhibited by JEschylus, for which he prepared a tragic scene; and that afterwards the principles of the art were more distinctly taught in the writings of Demo- critus and Anaxagoras, disciples of Agatharcus, which are no longer extant. ' The perspective of Euclid and of Heliodorus La- risseus contains only some general elements of optics, that are by no means adapted to any particular practice; though they furnish some materials that might be of service even in the linear perspective of painters. Geminus of Rhodes, who was acelebrated mathe- matician in the time of Cicero, hath likewise written on the subject. We may also infer, that the Roman artists were acquainted with the rules of perspective, from the account which Pliny, (Natural History, lib. xxxv. cap. 4.) gives of the representations on the scene of those plays given by Claudius Pul- cher; by whose appearance, he says, the crows were so deceived, that they endeavoured to settle on the fictitious roofs. However, of the theory of this art among the ancients we know nothing ; as none of their writings have escaped the general wreck of ancient literature during the dark ages. Perspective must, without doubt, have been lost, when painting and sculpture no longer existed. Nevertheless, we have reason to believe, that it was practised much later in the eastern empire. John Tzetzes, who lived in- the twelfth century, speaks of it as if he was well acquainted with its importance in painting and statuary: and the Greek painters, who were employed by the Ve- netians and Florentines, in the thirteenth century, seem to have brought some optical knowledge with them into Italy: for the disciples of Giotto are commended for observing perspective more regularly than any of their predecessors in the art had done; and they lived in the beginning of the fourteenth century. The Arabians were not ignorant of this art; as we may presume from the optical writings of Al- hazen, who lived about the year 1100, cited by Roger Bacon, when treating on this subject. Vitellus, a Polander, about the year 1970, wrote largely and learnedly on optics. Our own Friar Bacon, as well as John Peckham, archbishop of Canterbury, treated this subject PER M with surprizing accuracy, considering the times in which they lived. The most ancient authors who professedly laid ‘down rules of perspective, were Bartolomeo Bra- mantino, of Milan, whose book, intitled Regole di Perspettiva, e Misure delle Azztic/iita dz' Lom- bardia, is dated 1440-; and! Pietro del Borgo, likewise an Italian, who was the most ancient author met with. by Ignatius Dante, and is sup-1 posed to have died in- 14,43. The last writer supposed objects to be placed beyond atransparent tablet, and endeavoured to trace the images, which. rays of light, emitted from them, would make upon it. But his work is not now extant. How- ever, Albert Durer constructed a machine upon the principles of Borgo, by which he could trace the perspective appearance of objects. Leon Battista Alberetti, in 1450, wrote his trea- tise De Pittura, in which he treats principally of perspective. Balthazar Peruzzi, of Sienna, who died in 155 , had diligently studied the writings of Borgo ; and his Method of Perspective was publishedby Serlio- in 1540. To him, it is said, we owe the discovery of points of distance, to which all lines that make an angle of 45° with the groundline are drawn. Guido Ubald-i, another Italian, soon after disco- vered that all lines parallel to each other, if in-A clined to the ground line, converge to some point in the horizontal line; and that through this point, also, a line, drawn from the eye, parallel to them, will pass. His Perspective was printed at Pessaro in 1600, and contained the first principles of the method afterwards discovered by Dr. B. Taylor. In 1583, a book was published by Giacomo Ba— rozzi, of Vignola, commonly called Vignola, inti- tled, The T woRuZes of Perspective; with a learned . Comment, by Ignatius Dante. In 1615, the work of Marolois was printed, in Latin, at the Hague, and engraved and published by Hondius. And in 1 Q5, Sirigatti published a treatise of perspective, which is little more than an abstract of Vignola’s. The art of perspective has been gradually im- proved by subsequent geometricians, particularly by professor s’Gravesande, and in a much greater degree, by Dr. Brook Taylor, whose principles {are in a considerable manner new, and far more general than those of any of his predecessors. He did not confine his rules, as they had done, to the horizontal plane only, but made them; PER 4'48 .— k general, so as to affect every species of planes and lines, whether they were parallel to the horizon or not; and thus the principles were made ufl-lversal. Farther, from the simplicity of his rules, the whole tedious process of drawing out plans and elevations for any object is rendered entirely useless, and therefore avoided : for by this method, not only the fewest lines imaginable are required to produce any perspective representa- tion, but every figure, thus drawn, will bear the nicest mathematical examination. Indeed, his system is the only one calculated for answering .every end of practitioners in the art of design; because from hence they may be enabled to pro- duce the whole, or only so much of an object as is wanted, and by fixing it in its proper place, may determine its apparent magnitude in an instant. It explains also the perspective of sha- dows, the reflections of objects from polished planes, and the inverse practice of perspective. ‘His Linear Perspective was first published in 1715; .and his New Principles of Linear Perspective in 1719, which he intended as an explanation of .his first treatise. In 1738, Mr. Hamilton pub- lished his Stereography, an original and learned work, in 2 vols. folio, after the manner of Dr. Taylor. Maroloi’s, printed at the Hague, Latin, fol. 1615. Verdeman Friese’s, French, fol. 1619. Andrea Pozzo, first book, Latin and English, fol. 1700; and his second book, Latin, fol. also, 1707. Desargues, French, 1647. We have also treatises on this subject, by the Jesuit, originally written in French, at Paris, translated by Mr. Chambers, and printed at London, in 1726; as likewise by Highmore, Ware, Cowley, Kirby, Priestley, Fer- gusson, Sic. Vanishing points in every position were known to Guido Ubaldi, and s’Gravesande not only understood the use of vanishing points, but the use of directors also, in the representation of a point, prior to the appearance of any thing pub- lished by Brook Taylor; but the latter has extended his theory not only to vanishing points, but to the vanishing lines of planes in every situ- ation, which, when once ascertained, the repre- sentation of an object is found by the same means in each plane, consequently with the same facility. Hamilton seems to be the first writer who intro- duced the practice ofsetting the radial, or parallel of the original line from the vanishing point, upon the vanishing line, and the original line ' PER from the intersecting point upon the intersecting V line, in order to ascertain the representation of any point, or any part or parts of the original line, and to find the originals from the representations given. (See Problems 8 and 9, Book II. Sect. 2, of his Stereograpby, and the following Corollaries from Problem 8.) This author is the first who has applied the harmonical division of lines to per- spective. Noble’s Perspective contains several inventions : his methods of drawing. indefinite re- presentations to inaccessible vanishing points, both by scales and other means, are new. Thomas Malton’s treatise on this subject is an able per- formance. His theory is well arranged, and de- monstrated with true geometrical spirit. The choice of his examples in the component parts of architecture, before uniting the whole into a complete edifice, are excellent. The works on perspective of the following gen- tlemen, among the authors already enumerated, are performed strictly upon the principles of Dr. Brook Taylor: Hamilton, Kirby, Highmore, Fournier, Priestley, Noble, Thomas Malton, J. Wood, Edward-s, J. G. VVood, Cresswell, A. M. Though Mr. James Malton pretends to unite the principles of Dr. Brook Taylor with those of Vig-n nola and Sirigatti, he might have referred them with more propriety to s’Gravesande’s invention of directors; as the use of the station point, which is only a directing point, can be more easily explained upon the principles of the direct- ing line, director, and directing point, than by any mechanical notion ; so that the methods which he uses may be referred entirely to the principles of Dr. Brook Taylor. In the method used in James Malton’s Perspective, every point of an object in the original plane is found in the picture, by a line drawn between the intersecting and vanishing point, or drawn from some point already found, and the vanishing point, and another line drawn by the directing point and the director; for when the director of an original line coincides with the intersection of the vertical plane, the representations directed will be perpendicular to the intersection,or to the vanishing line; therefore, lines thus drawn in the picture will fall in the same straight lines with original lines parallel to the picture, and to the vertical plane, insisting upon the remote extremities of the lines drawn to the directing p int. This, therefore, admits of the plan of the object either being connected with PER ’4th PER the picture, or separated from it, as conveniency may require. This circumstance has even been overlooked in the more excellent treatise of the father of the gentleman, u'pon whose work the remarks are now made. It is something remarkable, that in Brook Taylor’s Perspective, he no where directs the radial to be placed upon the vanishing line, except in prob- lem 10, inverse perspective, notwithstanding the very near affinity shewn in problems 3, and ,4, which one would have thought might have led to that application; particularly, considering the great use which Kirby, Highmore, Fournier, Priestley, E. Noble, Thomas Malton, J. Wood, Edwards, and others of inferior note, have made ofit, in representing original measures without the use of the plan. It is to be observed, that in Brook Taylor’s Perspective, when he finds the re- presentation of an original figure without the plan, he first finds the representation of a side of the figure; then the representation of a line, whose original will make an angle of the figure with the original side of the projection given; he then determines the proportion of the last line, found by supposing the two sides to be joined by a third line, making a triangle; and then he finds the vanishing point of the third side. He next proceeds with another side, if more than three, in the same manner; so that he supposes the original figure divided into triangles, by drawing diagonals, and constructs angles at the eye, equal to those of the originals”; he then finds the vanishing points of the sides, and of the diagonals; and, by drawing the suc- cessive lines to the respective vanishing points, completes the whole representation. Or, he finds the projection of each triangle, if more than one, in the succession in which they adjoin each other, until the whole representation is completed. Now, by placing the length of the radials upon the vanishing line, the originals may be represented, without supposing the figure to be resolved into triangles. But, what is still more to be wondered at, in respect to Brook Taylor, in problem 10, of the edition 1719, the intersectioan a plane, its vanishing line, with the centre and distance of the vanishing line, are given, to ”find only the length of the original ofa projection given, which is a problem in inverse perspective; he absolutely sets the length of the radial on the vanishing line: and had he done so, in findin g the representations VOL. II. 1 of original figures, he would have been the sole inventor of the practice, without the use of the ground plan, or the figure to be represented being placed in its true situation. The writers on perspective are very numerous: the following (some of whom have been already mentioned) are the principal, with the dates of their performances, as near as they can be ascer- tained. .Guido Ubaldus, 1600, Latin folio; Bernard La- . my, 1701, 8vo.; s’Gravesande, 1711, 8vo. trans- lated into English by Stone, 1724; Marolois, Vredeman, Friese, the Jesuit, 4to. Pozzo, folio. The Jesuit, translated into English by E. Cham- bers, 17016. Ozenam’s lilathematics contain also a Treatise on Perspective. These are all foreign works. The following list contains all, or nearly all, the English authors, or their w01ks, that hai’e written on this subject. Humphry Ditton, 1712, 8vo; Moxon, folio; Brook Taylor, two t1eatises, one in 1715, and the other in 1719, both 8vo.; Langley, 1730, 4to.; ()akley’s Magazine of Architecture, Per- spective, and Sculpture, 1730, folio; Halfpenny, 1731; Hamilton, 1738, folio; Ur. Brook Taylor’s IlIethod of Perspective, by Kirby, 1754, letter- p1css, 4to., and plates, folio; Sirigatti, by \Vare, 1754, folio; Kir’shy Parallel suppressed, Kir"sby Perspective of Architecture, 1760, large folio; Highmo1e, 1763, 4to. , Fournier, 1764, 4to. ; Cowley s JlIoveable Schemes for illustrating the Principles of Perspective, 1765, 4to. , Fe1gus‘son, 1765, 8vo.; \Vare’s Complete Body offlrchitecture contains a Treatise on Perspective, 1768, folio; Priestley, 1770, 8vo.; Edward Noble, 1771, 8vo.; Thomas Malton, 1775, folio; Bradberry; Shira- ton, in his Cabinet and Upholsterer’s Drawing- Book, 410.; \Vood, of Edinburgh, 1797, 8110.; The Painter’s llIaulstick, by James Malton, 1800, 4to.; Douglas, 1805, letter-press, 8vo. and plates, folio; Edwards, 1806, 4t0.; Thomas Noble, se- cond edition, 1809, 4to.; \Vood’s Lectures, Len- don, second edition, 1809, 4to.; \V. Daniel, 1810, small 81/0. for children; a thin quarto without the name of the author, the title being “A new Trea-.. tise on Perspectite, founded on. the simplest Prin- ciples, containing universal Rules for drafting the Representation (y any Object on a vertical Plane, 1810, thin 4to. , D. Cressw,ell A M. 1811, 8vo.; Milne, in his Elements ofArchitecture, 1819, 4to.; and Mr. Hayter, 1813, 8vo. Besides ‘the above 3M PER 450 PER authors and treatises, are Muller, Martin, and Emerson, who have written octavo treatises in their mathematical courses. A thin quarto was written by Bardwell, a painter. The Artists’ Re- pository, published by C. Taylor, Hatton Garden, contains also an article on perspective. The instruments necessary for drawing according to the rules of perspective, are a T square, :1 pa— rallel ruler, a drawing board (which is only a smooth board make exactly square) a sector, a protractor; to which may be added a drawing- pen, and a blaclclead pencil. Proposition.-—lt is a well-known fact, founded on experience, that objects reflect their lights, shades, and colours, in straight lines, and describe an image in the eye which produces that sensation of the object called vision. Corollary 1.——If a straight line be opposed to the eye, and not directed to it, the rays or straight lines which issue from all points of it to the eye, form a plane. 'Corollazy_Q.—-—If any plane 01' solid be opposed to the eye, the straight lines or rays which issue from all points of the surface to the eye, form a pyramid, provided that, with respect to the plane, the eye is out of its surface. The following are definitions of the terms employed. 1. The straight line reflected from any point ofa line or surface, is called a visual ray. 9.. A plane composed of visual rays is called an optic plane. 3. A pyramid composed of visual rays is called an optic pyramid. 4-. An optic plane, or pyramid, is called a system qfrays. 5. If a system of rays be intercepted by a plane, the common section is called the scenographic, or perspective representation of the body. Corollary—Hence the representation of any right line, or rectilinear figure, or solid, is also rectili- near. 6. The plane on which the section is made is called the picture. 7. The point, line, surface, or body, from which the rays proceed to the eye, is called the original object. Corollary 1 .-—Hence, if the original object be a plane, and the picture parallel to it, the represen- tation will be a figure similar to the original. Corollary 2. -—It any part of an original object touch the picture, the part which 15 thus 1n con- tact will be the scenographic representation of that part. 8. The vertex, or point, of the pyramid, where the eye is placed, is called the point of sight, or point ofviea'. 9. 1f the original object be situated on a plane, such plane is called the original orprimitiveplane. 10. If a plane be supposed to pass through the eye parallel to the picture, it is called the directing plane. 11. The intersection of the picture and the ori‘ giual plane is the intersection, or intersecting line, of that plane. 12. The intersection of any original line with the picture, is the intersecting point of that original line. Corollary. —Hence the intersecting points of all lines in any original plane, a1e in the intersecting line of that plane. 13. If a straight line be supposed to be drawn through the eye parallel to any original line, the. line so drawn is called the parallelor radial of that original line. Corollary-Hence, if any number of original lines be parallel among themselves, one line only can pass through the eye parallel to them all. 14.1f a plane be supposed to pass through the ey e palallel to any original plane, or theD plane of an original obJect, the plane thus passing through the eye is called the parallel or radial of that original plane. Corollary.——Hence, if any number of original planes 'be parallel among themselves, one plane only can pass through the eye, which will be pa- rallel to them all. 15. The intersection of the parallel of any original plane and the picture, is called the vanishing line of that plane. Corollary l.——Hence the intersecting and vanish- ing lines are parallel to each other. Corollary 9..——Hence all original parallel lines have the same vanishing line. Corollary 3.——Hence the parallels of every two original planes have the same inclinations as the originals. Corollary 4-.——Tl1e vanishing point of the common intersection of any two planes, is the intersection of the vanishing lines of these planes. 16. The intersection of the paiallel of any 0W ginal line is called the vanishing point of the orlv ginal line PER L Corollary l.—The vanishing points of all lines in the same original plane, are in the vanishing line . of that plane. 0 Corollary 9. ~—Hence any number of’ original pa- rallel lines can have only one vanishing point. Corollary 3. ~Hence original lines, which are pa— rallel to the picture, have no vanishing point, because their parallels can never cut it. Corollary 4.—T he lines which generate the vanish- ing points of two original lines, make the same angle with the eye as the originals do with each other. 7. The intersection of the original plane and the directing plane, is called the directing line of that plane. 18. The intersection of any original line with the directing plane is the directing point of that ori- ginal line. Corollary—Hence the directing points of all lines in the same original plane are in the directing line of that plane. 19. A straight line drawn from the directing point of any original line to the eye, is called the director of that original line. 20.'Il1e inte1section oi the vanishing plane and the directing plane is the parallel director, or parallel (f the eye. Corollary—Hence the intersecting line, the va- nishing line, the parallel director, and directing line, are all parallel to each other. ‘21. If a straight line be drawn from the point of sight perpendicular to the picture, the point where it meets the picture is called the centre ofth picture; and the part of the line intercepted between the point of sight and the centre of the picture, is called the distance of the picture, or principal distance. 22.. If a straight line be drawn from the point of sight perpendicular to a vanishing line, the point where it meets the vanishing line, is called the centre of that vanishing line; and the part inter- cepted between the point of sight and the centre of the vanishing line, is called the distance of that vanishing line. Corollary l.—-Hence a line drawn from the centre of the picture to the centre of a vanishing line, is perpendicular to the vanishing line. Corollary 2,—The distance of a vanishing line is the hypothenuse of a right-angled triangle, the base of which is the distance of the picture, and the perpendicular the distance between the centre 451 PER . . ”h... of the picture and the centre of its vanishing line. 23. If the distance on a vanishing line, from the vanishing point to another point, be equal to the distance of that vanishing point from the eye, the other extremity of this distance, which is not the vanishing point, is called the point of distance. 24. The point where a perpendicular drawn from the centre of the vanishing line cuts the inter' secting line, is called the centre of the intersecting line. 25. IF the original plane be the level of the earth's surface, or horizon, it is called the ground plane. 26. If the original plane be the horizon, the van nishing plane is called the horizontal plane. 27. If the picture be perpendicular to the horizon, it is called a certical picture. ‘28. \Vhen the original plane is the ground plane, the intersecting line is called the ground line. 99. When the original plane is the ground plane, a plane drawn through the eye perpendicular to the ground plane and to the picture, is called the vertical plane. 30. The intersection of a vertical plane with the vertical picture, is called the vertical line. 3]. The intersection of the vertical plane with the directing plane, is called the prime director, and by some the eye director. 32. The intersection of the vertical line with the ground plane, is called the foot of the vertical line. 33. The intersection of the vertical director with the ground plane, is called the station point, or prime directing point. 34. The distance between the station point and the foot of the vertical line, is called the station line, or line ofstation. ‘ 35. A straight line drawn between the intersecting and vanishing points, is called the indefinite repre- . sentation, or projection of that line. Axiom 1. -— The common intersection of two planes is a straight line. Axiom 2.-The common straight lines is a point. Axiom :3. if two straight lines meet in a point, or are parallel to each other, a plane may be made to pass through both of them. Axiom 4. li' a straight line meet two parallel straight lines, or two straight lines meet in a point, all the three lines are in the same plane, 3 M '72 intersection of two PER 452 PER Axiom 5. Every point in any straight line, is in whatever plane the line is in. Axiom 6. Two parallel planes cannot intersect each .. other. . Aria-m 7. One part of a straight line cannot be in ayplane, while another part is out of it. Several of these axioms are propositions in the eleventh book of Euclid’s Elements, where they .g- are demonstrated; but if the notion of'a plane 1s . understood, their' evidence will be admitted upon -. the slightest reflection, so that it would be of" little use to attempt to prove them. ,' In Plate I. Figure 2, \VXYZ is the original plane; A B N I the picture; T S W X the direct- . ing plane parallel to the picture; and S V LT the vanishing plane, or. parallel of the original plane; V L, the inte1section of the parallel oft, the original plane and the picture, is the vanishing line; I N, . the intersection of the picture and the original plane, is the intersecting line; ST, the intersec- tion of the parallel of the original plane and the directing plane, is the parallel director, and W X, the intersection of the directing plane and the original plane, is the directing litre. In Fzgures ], 3, 4, 5, 6, E 1s the place of the ey:e in Fz'guresQ and 3, the parallel of the original plane1s notrep1'2esented and in Figures 1,4, 5, and 6, the intersecting line is denoted by IN, the vanishing line by V L, if necessary in the figure, the directing line by W X, and the parallel direc- ‘ ,tor, by S T. Theorem l.-—The indefinite projection ofa straight line, not parallel to the picture, passes through its intersecting and vanishing points. This is evident, because the original litre and its radial are parallel to each-other. The eye, the intersecting point, and the vanishing point, are all 1n the same plane with the original line and its 1adial; therefore, it a line be drawn in the picture between the intersecting and vanishing points, all the three straight lines will be in the same plane; and, consequently, the indefinite re— presentation will be in .the same plane with the original straight line and the eye. Since the whole practice of perspective depends upon this theorem, the reader will take the fol— lowing illustrationz—In Plate I. Figure 1, Q R is an original straight line, R its intersecting point, '0’ its vanishing point, and R v’ a line. in the picture joining the intersecting and vanishrng points. Now since E v' and R Q are two parallel lines, it a plane be supposed to be drawn through both, it will pass through the eye at the extre— mity of the radial v E; and because the straight line Rv’ joins the two straight lines Q R and o’ E, the lines R Q and R v’ are in the same plane with the eye; consequently, R v’ is the intersec- tion of the plane of rays on the picture from the straight line Q R. Farther, ifE F, G H, IK, and L M, be parallel original lines, they will have 1) for their common vanishing point; therefore the several indefinite representations from the intersecting points F, , H, K, and M, will all terminate in '02. If an original straight line and its radial be in the same right line, the whole indefinite repre- sentation of that line will be in its vanishing point. Theorem 2.~—The projection of a line parallel to the picture, is also parallel to its original. Figure 2.—Let A B be an original line parallel to the picture, a 1) its representation, and E A B the optic plane, E being the place of the eye. Now a b is the intersection of the optic plane, that is, of the triangle EA B with the picture; and.be- cause A B is parallel to the plane of the picture, and A B, a b in the plane of the triangle E A B, a b is parallel to A B; otherwise A B would -meet the picture in the intersection a b, or a I) produced, and consequently could not be pa- 1'.allel Corollary—The projections of several lines pa- rallel to each other, and to the picture, are also parallel to each other. Thus, if A I) and B C be parallel to each other, and to the picture MN 1K; 11 d and be will be respectively parallel to A D and B C, their originals. T/zeorem 3.——The representation. of a given line parallel to the picture, is to its original as the» dis- tance of the picture is to the distance between the eye and a plane passing through the original line parallel to the picture; for let the plane Q R Z Y (Figure ‘3) be parallel to the plane, M NIK, of the picture; and let E F be drawn perpendicular to the original plane and to the picture, to meet the original plane in F, and the picture inf,- join A F and af;-then A E F will be a plane, A F the intersection of the plane of the triangle and the original plane, and of that of the plane of the triangle and the picture. Now in the similar tri- _ aHSIGSEabandEAB} Ea: EA “abiABl "\§\‘\\\ \\\\\\\ ‘ \ \\\\\\\\ :'1;z//u7/ X' /)I‘(IH’/l ‘1} -yl-(‘lll’lu'fl/L PERSPECTIVE. Zulu/(w,/’/(/:/(Jr/1n//I'I/ [CIVIL/(NAN)! X' Jflu/W‘HJ, ”;I/‘(I/(u'll‘ J‘r/‘m'l, 14715,. ‘ PLATE I. \\ \~\\\ _ \\ \\ \ t‘\ \ &\ \\\\\\ \\ £137. (7'. \\‘\ \\\\ Rk‘ \ \‘. mm ~r \_ X1. \ \,\ _\ T §§\\\\\ \ .\. ‘ V \\ \\\\\\\ \\ ~\X‘ \\ filly/rural {51/ .1/3. ZI‘II/UI‘. PER 453 PER also in the similar tri- angles Eafand E A F therefore,b com aring ‘ these equill ratiibs — } a b : A B : : af: AF' Consequently, the representation of a line paral- lel to the picture, is to its original as the distance of the picture is to the distance of the eye, and a . plane passing through the original line parallel to the picture. Corollary l.—-The angle which the representa- tions of any two original lines parallel to the pic- ture make with each other, is equal to the angle made by the original lines; because each repre- sentation is parallel to its original. Corollary Q.—The projection of any plane figure parallel to the picture is similar to its original: for let A B and A D be two contiguous original . lines, and a b and ad their representations; now, in the similar tri- angles EabandEAB} Ea: EA ::a b : A B; also, in the similar trian- glesEadand EAD}Ea:EA;:ad1AD; therefore, by comparison, a b : a (I : :A B : A D. Consequently, the sides about the equal angles are proportional. Theorem 4.~—'l'he projection of a line is a line drawn through the intersecting point parallel to its director. Because E Q, E D, and v’ E, (Figure 1) are all in the same plane; and since the directing plane is parallel to the plane of the picture, the director, E D, is parallel to the inde- finite representation, v’ R ; because “ if'two planes be cut by another plane, their common sections with it are parallels.” Book II. Prop. 16. Euclid. Corollary 1.—-—The projections of lines that have the same director, are parallel with each other. Corollary 2.— Vhen the original line is parallel to the picture, it is also parallel to its director, }Ea:EA::af:AF; and therefore in the parallel of any given plane ' passing through the original line; consequently, the vanishing line of that plane, and the projec- tion of the line, are parallel with each other. Theorem .5.—~Tlie distance between the projection of any point of a straight line, and the vanishing point of that line, is to the distance between the intersecting and the vanishing points, as the dis- tance of the vanishing point to that between the directing and the original points. That is, Figure 1, q'v’ : R '0': : E’v’ : D Q. Now because of the parallel planes which form the dia- gram, 'v'E’ D R is a parallelogram, therefore Rv’ l is equal to 'D’EI; and the triangles '9 Bo and E’ D’ Q are similar, because their sides 12’ q and E’ D’ are parallel; therefore 99' : D' E‘ or R o’ : : E a! : D’ Q. _ Corollary—Hence the distance between the re- presentation ofany point in a straight line, and the vanishing point of the line, is to the distance between the intersecting and the vanishing points, as the distance of the picture is to that be- tween the original point and the directing plane. The foregoing Theorems, with the following Co- rollaries arising from the Definitions, contain all the principles that is conceived necessary in the perspective representation of any rectilinear ob- ject. But if the reader is desirous of knowing the best methods for the representation of circu- lar objects, he must be prepared with the know— ledge of conic sections, and the harmonica] divi- sion oflines which is treated of in a subsequent part of this article. Corollary ]. Proposition.-—-If there be a straight line opposed to the eye, and not directed to it, the right lines issuing from all its points to the eye form a plane. Corollary. Definition 5,—Hence the representa- tion of any straight line, rectilinear figure, or solid, is also rectilinear. Corollary 1. . Definition 7. Hence, if the origi- nal object be a plane, and the picture parallel thereto, the representation will be a figure similar to the original. Corollary Q..—If any part of an original object touch the picture, the part which is thus in con- tact will be the representation of itself. Corollary. Definition 1Q.—Hence the intersect- ing points of all lines in any original plane, are in the intersecting line of that plane. Corollary. Definition 13.—-Hence if any number of original lines be parallel to each other, only one line can pass through the eye parallel to them all. Corollary. Drjim'tion 14.—-Hence if any number of original planes be parallel to each other, one plane only can pass through the eye, which will be parallel to them all. Corollary 1. Definition l5.~—Hence the intersec- ting and vanishing lines are parallel to each other. ('orollary 2.——Hence all original parallel lines have the same vanishing point. Corollary 3.—Hence the parallels of every two original planes have the same inclination as the originals. PER 454- M J! Corollary 4.~—The vanishing point of the common intersection of any two original planes, is the common intersection of the vanishing lines of those planes. Corollary 1. Definition 16.—The vanishing points of all original lines in the same plane, are in the vanishing line of that plane. Corollary 2.——Hence any number of original pas rallel lines can have only one vanishing point. Corollary 3.———Hence original lines parallel to the picture have no vanishing point. Corollary 4.-—The radials which generate the va- nishing points of two originals, make the same angle with the eye as the originals make with each other. Corollary. Definition 19.—-Hence the directing points of all lines in the same original plane, are in the directing line of that plane. Corollary. Definition 18.-—-Hence the intersect- ing line, the vanishing line, the parallel director, and the directing line, are all parallel to each other. Corollary 1. Definition 22.—Hence a line drawn from the centre of the picture to that ofa vanish- ing line, is perpendicular to such line. Corollary Q..——The distance of a vanishing line is the hypothenuse of a right-angled triangle, whose base is the distance of the picture, and its perpen- dicular the distance between the centre of the picture and that of the vanishing line. Description of the diagrams for illustrating the principles of perspective. in Figure 1, is shewn the method of finding the representation of a point; First, by the intersect- ing and vanishing points. Let Q be any point in the original plane; through Q draw any line, QR, meeting the intersection, IN, at R; and through E’ draw E '0’ parallel to Q R, meeting the picture in '0'; join ‘0' R, and draw the visual ray, Q E’, cutting the indefinite representation, v'R, at q, the representation of the point Q; because, from Theorem 1, the indefinite representation of a line passes through its intersecting and vanish- ing point; and since the visual ray, EQ, is in the same plane with the parallelogram R D E v’, E Q will cut R 19’ at q. Secondly, by the intersecting and directing points. Draw any line, Q D’, through the original point, cutting the intersection, I N, at R, and the direct- ing line, WX, at D’; join D’ E’, which will be the director of the original line by Definition 19; draw Ro’ parallel to D’ E’, and draw the visual P E R ray Q E’, cutting Rv’ at g; then 11 is the repre- sentation of Q, as before. For since R D E’ v' is a plane, and the points E’ and Q, as well as the indefinite representation, R o’, are in that plane, the visual ray,j0ining E’ and Q, must cut R v' at . This diagram also shews, that if LM and Q Rbe two original lines,having the same directing point, D’; and if M and R be the intersecting points, the indefinite representations, M w and Rv’, will be parallel. This appears from Corollary 1, Theorem 3. In this diagram it is also shewn, that ifEF, GH, IK, LM, be several parallellines intersecting the picture at F, H, K, M, the radial E’ 2:9 being drawn parallel to any one of them, cutting the picture in '09, their indefinite representations will terminate in v”. This is evident, since any one of the lines EF, G H, Ste. is in the same plane with E’ o“, from Axiom 4; and because the eye at E’ is in E’ 1", each of the indefinite representations will be cut by any visual ray from its original to the eye at E'. Figure 9. shews the representation of a plane figure parallel to the picture. Let the original figure be A B C D, in the plane Q R Z Y, parallel to the picture I N M K; and let E be the place of the eye, in the directing plane G H X W. Draw any director, E’ D’, through each angular point, A, B, C, D, of the figure; draw A P, BS, C T, D Q, parallel to E’ D', cutting the original plane in P, S, T, Q; draw D’ P, D’ Q, l)' S, D’ T, cutting the intersecting line in p, q, s, t; draw 1) a, s l), to, q d, parallel to E’ D': from the angu~ lar points, A, B, C, D, of the original figure, draw the visual rays [3’ A, E’ B, E' C, E' D, cutting the plane of the picture, I N M K, respectively at the points a, b, c, d, in the linesp a, s b, t 0, gr], Because A P, a p, and E’ D', are parallel to each other, they are therefore in the same plane; there- fore the straight line A 13’ will cutpa, at a; con- sequently, a is the representation of A. In the same manner it may be proved thatb is the repre- sentation of B, and so of the rest. Figure 3 shews the representation of a plane figure, by means of the directing plane, in a plane inclined at any angle, or perpendicular to the pic- ture. Let A B C D be the original figure: take any point, D’, in the directing line, W X, as adirecting point: draw the director D' E’; from the angular points A, B, C, D, draw A D’, B D', C D’, D D', cutting the intersecting line at 12, 9,3, t; draw p a, g b, s c, t (1, parallel to the director D' F ; PER 455 PER draw the visual rays A E’, B E’, C E’, I) E’, cutting the lines pa, (1 I), s c, td, at the points a, b, c, d; then a b 6 dis the representation of the figure A B CD; for pa is parallel to D' E’, and the straight line A D’ Joins these parallels; thereforep a, D’ E’, and A D’, are in the same plane; and because the angular point A, and E’ the place of the eye, are in that plane, the visual ray, A E’, is also in that plane, and will therefore cut 1) a at a. In the same manner each of the other points, I), c, d, may be proved to he the representation of each of the points B, C, D. Figure 4- shews the representation of a plane figure in a plane inclined to the picture at any angle, or perpendicular to it, by means of a directing point and the vanishing points of the sides. Let the quadrilateral A B C D be the original figure; take any directing point, D’, and draw D’ E’, the diiector: draw the radial E' 12' parallel to A D and B C, cutting VL, the vanishing line, at '0’; also draw the radial -E’ 11‘1 parallel to AB and D C, cutting VL at '02. Then, if the figure be a parallelogram, draw lines to the directing point, D’, from each of the nearest angular points, B,A, D, to cut the intersecting line, IN, at p, q, s; draw 1) b, q a, and sd, parallel to E’ D'; produce the side AB of the original figure to meet the intersection I’ N' at t; join t '0‘, cutting g a at a, and pl) at b,- then a is the representation of the point a; join av’, cutting sd in d, and draw 611’ and dc”, cutting each other at c,- then abcd is the representation of AB CD, as re- quired. For t v“, is the indefinite representation of BA, by Theorem 1, and qa is the representa- tion of the line qA, Theorem 3; and since the original lines BA and q A meet, or out each other in A, their indefinite representations will also meet each other at a; now because the vanishing point ofa line is a point in the indefinite representation, if two points in that representation be found, the whole may be drawn. Now since a is the re-' presentation of the point A, and 12’ that of another point in the side A D, a 1:“ will be the indefinite representation of AB. In the same manner, it may be shewn, that av’ is the indefinite represent- ation of A D: then, since 5 d is the representation ofs D, and the point D is both in s D and A D, therefore its representation, (1, is at d, the inter- section of sd and av’, the indefinite representa- tions of these lines: for the same reason I), is the ll [W representation of B; and, by reasoning as above, it may be shewn that c is the representation of C; therefore the whole figure, a bed, is the repre- sentation of A B C D. Upon this principle, most architectmal drawings are put in perspective, by only using the original plane, first supposing the picture, the vanishing plane, and the di1ect- ing plane, 1emoved: the plan, ABCD, of the building or edifice, 13 first d1awn, and D’is taken asa station point; the intersection I’N , is then drawn, lines are then than n fiom the several points towards D’ to cut I'N’; and supposing the picture to stand perpendicular to the original plane, as is generally the case, the directing plane, S T XVV, will also be perpendicular to the original plane; then as D' in this case is the station point, the director, D’ E’, becomes perpendicular also to the original plane, and hence the directorial indefinite representations, 3 d, (1 a, p b, will be perpendicular to the intersection I' N’. Then taking a separate piece of paper for the picture, draw two parallel lines, I’ N’ and V’ L', at a distance from each other, equal to the height of the eye. I’ N' being the intersecting line, and V’ L’ the vanishing line; then transferring all the intersections to 1’ N’ on the picture, draw lines from each point perpendi- cular to l’ N’, and they will give the directorial indefinite 1epresentations; the vanishing points being also found upon the Oliginal plane, the whole obJect may be represented more advantage.- ously in this manner than 1n any other, as the 1n- definite representations of all lines on the original plane fall in the same straight lines with the re- presentations of original lines perpendicular to the original plane from the same original points. Figure 5 shews the representation of a plane figure by means of vanishing points only, viz. by findingthe vanishing points of the sides, and producing the sides of the original figure to their intersecting points, then the intersections of the indefinite representations will form the figure a bed, which is the representation of the original figure AB C D, depending entirely upon Theorem 1. This method is, however, not so convenient as the station point, or prime directing point, as it re- quires much more space to produce all the origi- nal lines, than to draw them from each of the points of the object to the directing point, and more particularly when the plan of the obJect is very remote from the intersecting line, or when large in proportion to the distance, and on this PER 456 PER acCount, though elegant in theory, it is ‘not eligible for practice. Figure 6 is here given, in order to shew that it will be the same thing, whether the plan of the object be laid on the vanishing plane, ex- tended beyond the picture, or upon the original plane; the point E’, for the eye, and the vanish- ing line being situated in the same manner with respect to the figure a bed, that the point D’ and the intersection l’ N’ are in respect of the similar and equal figure A B C D. For let the figures a b c d, and A B C D, be placed so that the corresponding sides ab, AB, ed, CD, 8L0. shall be parallel; then suppose the lines (IA, [2 B, Ste. to bejoined, these lines, will also be parallel to each other; and because the points D' and E’ are alike situated to each of these figures, if D' E’ bejoined, D' 13' will be parallel to aA, bB, 8m. and parallel to the plane, IN' LV’. Let Do be drawn parallel to A B, meeting I' N’, or I’ N' produced at v; draw D' C' perpendicular to I’ N', cutting it in C’ ; also draw E 0' parallel to (11), meeting V'L’, or V' L’ produced at v', and draw- EC” perpendicular to V’ L’, meeting it in C”; then the intersecting points G, M, N, will have the same distances in respect of each other, and with respect to v and C’ that gm n have in respect to each other, and to the points 1/ and C3; it will therefore be the same thing whether we use the vanishing plane, or the original plane, in order to ascertain the intersec- tions, the centre and distance of the picture, and the vanishing points, so as to draw the object un- connected with the original plane, as explained in Figure 4, as each of the lines drawn in the one plane has the same extension as its correspondent line in the other, and the angle made by any two adjoining lines in the one, is equal to the angle formed by the corresponding lines of the other. The foregoing diagrams, with the accompanying explanations, shew the mode of formiu g the repre— g sentation from the original obj ect, supposing all the planes to exist in their real position ; but this is not the casein practical perspective, where the picture, the original plane, and the vanishing plane must be reduced to one plane surface in the following manner: suppose the intersection, the vanishing line, the parallel of the eye, and the directing line, to be as hinges to the four planes, viz. the plane of the picture, the directing plane, the part of the . original plane between the intersectingand direct- ing lines, and the vanishing plane: now as these planes are all parallelograms, and the opposite planes are equal, they will, therefore, continue parallel in all positions when moved round the four hinges, and consequently may be all made to coincide in one plane: now let it be supposed that the picture, the directing plane, and the va~ nishing plane, are moveable upon the original plane, which remains stationary, and let these planes be made to coincide with the original plane, so that the picture may cover that part of it which is between the intersecting line and the directing line, either entirely, or in part; then the part of the original plane beyond the intersecting line will be wholly uncovered. Suppose all the radials to have been previously drawn on the va- nishing plane, in order to produce the vanishing points, it is evident that these radials will be still parallel in the coincident state of the planes. The practice, with regard ‘to the use of vanishing points, may therefore be as follows: Upon any convenient part of the paper draw two parallel lines, for the intersecting and vanishing lines, then the area or space comprehended between them is the picture, the space adjacent to the intersection is the original plane, and the space adjacent to the vanishing line is the vanishing plane, so that the picture lies between the vanishing and original planes; draw the original figure in the original plane in the intended position to the intersecting line, and fix upon the eye with regard to its dis- tance from the vanishing line, and its position in regard to the station line; draw lines through the eye, parallel to the sides ofthe original figure, as radials, in order to produce the vanishing points; continue the sides of the original figure to the intersecting line, andjoin the corresponding intersecting and vanishing points ; then the space enclosed by the indefinite representation will be the representation of the original figure. For if the whole scheme were supposed to be raised into its original position, the eye would be brought into its true place, the radials would be parallel to the original sides of the object, and the inde- finite representations would be in the same plane with the radials and sides of the original object. Though the space between the intersecting and vanishing lines is called the picture, the picture is by no means limited to this space, but extends upwards, and covers the vanishing plane, so that in most cases, what is commonly called the pic- PERSPECTIVE. PMTEI. A. 17137.] . F137. 3 \ B > \ I d N V L 1 \f (1 F a N V L V a L I d . B I 3 P A 1‘ P ‘ I Fin. 5. D a V r 3? I H I /' \ ‘ V /e L I K ‘ (/, ,/ . , D // ‘ I , ‘ l ‘ ‘le A B C P . i. , , _ 1 yr”. Drawn by 1? ‘Vidwbvn. lutulon,,Hllnlch'/zal by If Without)», .fi J. Barneld, ”(n-«1mm (\hwtgflzti, [Why‘d ’1” W 0 ‘ ‘ A . F , ”Axum ~~x PER‘ 457 PER ’ .41. ture is the least part of it, except in bird’s-eye views, or where the horizon is taken very high, in consequence of the spectator being placed upon an elevated situation. In the practice of perspective, where the plan of the object is given, the principal directing point, usedin conjunction with the vanishing points of the sides, is most convenient, as has already been observed; the vanishing plane is here supposed to be removed, as all the planes in the practice of perspective delineation are supposed to coin- cide. The intersecting and vanishing lines may be drawn as before; then the principal directing or station point may be fixed in the same position to the intersecting line, that the eye is in relative- ly to the vanishing line; then the eye and the station point will be at a distance from each other, equal to the height of the picture, and in a straight line perpendicular to the intersecting line; or the distance of the eye from the vanishing line will be equal to that of the station point from the intersecting line; also the position and distance of the eye from the object will be the same as when all the planes are brought into their real position. It must be here remarked, that in the motion of these planes round the principal lines, as before observed, the parallel director and that of the vanishing line, always keep the same parallel dis- tance in all positions; but these lines vary in re- spect of the object in the original plane, because they are not in the same plane with the original plane; while the intersecting and directing lines, as also the original figure, are in the same plane, viz. in the original one. Therefore the station point, or any other directing point, may be fixed in position to the original object and intersecting line. This is the foundation. of the practice of perspective with regard to the use of the direct- ing line, and, therefore, the directing point has the same relation to the intersecting line that the eye has to the vanishing line. ' To avoid repetition in the enunciation of the following problems, the eye, the vanishing line, and intersecting line, are always given in posi- tion; the eye is denoted by E', the vanishing line by V L, and the intersecting line by I N; but as the original object may be of an indefinite number of forms, it is particularly expressed in each problem. PROBLEM I. Plate S.—-An originalline, AB, being given; to find its vanishing point. VOL. II. Figures 1 and 2.—-—Through P, the point of sight, draw P a, parallel to the original line A B, meet- ing the vanishing line, V L, in a, which is the vanishing point required; (Definition 13.) PROBLEM IL—Tofind the primary directing point and the centre of the picture. Figures 3 and 4. Through the point of sight, 1’, draw P C, perpendicular to the vanishing line, VL, meeting V L in C, which is the centre of the picture; in P C take P D, equal to the height of the picture; and D is the directing point, as required. PROBLEM III.——To find the indefinite representa- tion qf‘a straight line, A B. Plate I, Figures 1 and Q.—Produce the line A B, to meet the intersecting line [N in (1; find the vanishing point, a, of A B, by Problem I. and join a d, which is the indefinite representa- tion required. This is evident from Theorem I. since the in— definite representation of' a line passes through its intersecting and vanishing point. PROBLEM IV.——-To find the representation of a point, A, in the original plane. Figures 3 and 4.——-Find the directing point, D, as as in Problem II. from the given point, A, draw any line, Ad; find its indefinite representation, a d, by the preceding Problem; towards the di- recting point, D, draw A F, meeting the inter— secting line, IN, at f; parallel to the director, PD, draw fa, cutting a d ata; then a is the re- presentation of the original point, A. The second part of this process is evident from Theorem IV. where it is shewn, that the repre- sentation of an original line, is a line drawn through the intersecting point, parallel to its director. PROBLEM V.--The indefinite representation, ad, of a straight line, AB, being given, or already jbund; to find the representation of any original point, A. Figures 3 and 4.——Draw a straight line from A, towards the directing point, D, cutting the inter- secting line, I N, at f; parallel to the director, P D, draw fa, cutting the indefinite representa- tion, a d, in a, which is the representation of the original point, A. Because D is the directing point of the original line, A f, and fa is parallel to the director, the pointA will be seen some where in theline f‘a, bv Theorem IV. and because (1 is the intersectingr 3 N PER 458 PER’ point, and a the vanishing point, any portion of the Original line will be seen in the line a d, join- ing the intersecting and vanishing points by Theorem I. and since the point A will be seen in each of the litres, fa and a d, it will therefore be seen at the point, a, of their intersection. PROBLEM VI.~——T he representation, a, of an Ori- . ginal point, A, being given ; to find the indefinite representations of a straight line, A C, from the point, A, of the original. Figures 7 and 8. . Find the vanishing point, e, of A C, by Problem I. join ac; and a e is the indefinite representation of the line required. PROBLEM VII. Figures 3 and 4.—-—A straight line, AB, being given in the original plane, to find its indefinite representation, and the represent- ation of any point, A, of the original line. Find the indefinite representation, ad, by Pro- hlem III. and the representation, a, of the point A, by Problem V. then a is the representation of the point A, as required. PROBLEM VIII. Figures 5 and 6.——To find the definite representation of a straight line, A B. Find the directing point, D, as in Problem II. find the indefinite representation, ad, of AB, by Problem 111.; from the points A and B, draw lines towards the directing point, D, to meet the intersecting line inf and e: parallel to P D draw e l), cutting da in h, and fa, cutting da in a,- then a h is the representation required. The latter part of this Problem is evident, since fa and eh are the representations of fA and e B. Theorem IV. PROBLEM IX. Figures 7 and 8.—To find the ‘ representation of an angle, B A C. Find the indefinite representation, a b, of the original line, AB, by Problem III. the repre- sentation, a, of the point A, by Problem VII. and the representation, ac, of the original line, AC, by Problem VI. then has is the representation of the angle BA C, as required. PROBLEM X. Plate II, Figures 1 and 9..——-Tofind the representation of a triangle, ABC, in the original plane. Find the representation of the angle BAC, by Problem IX. and the representation, 1) and c, of the points B and C, by Problem V.join he; and a b c is the triangle required. PROBLEM XI. presentation of a quadrilateral, A B C D. Find the representation da 1) of the angle, D AB, Figures 3 and 4—To find the re-' a. byProblem IX. the representation, 6 and d, of the points B and D, by Problem V. and the va- nishing points of BC and D C, by Problem I. then join the points]; and d to their vanishing points, which will complete the representation. In the same manner the representation of any polygon, as Figures 5 and 6, may be found. PROBLEM XII. Plate T. Figure l.—-Given the intersecting and vanishing lines, and the place (f the e 3/e in position, the seat .r, the distance of the centre (y‘ a circle, and its radius, to find the repre. sentation of the circle. .Method 1. Figure l.——Make 933/, on the intersect— ing line, equal to the distance of the centre of the original, circle f1om its seat a, and C’ D' on the va- nishing line equal to CE ,the distance of the eyge joina‘ C’ and 3/ D’, cuttingeach other 1n e, the re- presentation of the centre of the circle , through 6 draw c d parallel to 1’ N’, the intersection; make x a and r h each equal to the radius of the circle; join C’ a, cutting c d in c, and C' 6, cutting c d in d; and c d is the representation of a diameter parallel to the picture. Then, to find the repre- sentation,fg, of any diameter drawn through e at pleasure; producefg to its vanishing point, '09; make v9 Q, on the vanishing line, equal to v2 E’, the distance of the eye from the vanishing opoint; joinQ 1, cutting fg in g, also- 0 d, and produce it toj; thenfg is the representation of a diameter of the original circle, inclined to the intersecting line. In like manner may the representations h i, kl, m u, be found; viz. by transferring the dis- tance of each of their vanishing points from the eye on the vanishing line,_and drawing two lines from each point of distance to c and d, the one cutting, and the other produced till it cut, the indefinite representation belonging to the dis— tance so transferred; then a curve drawn through all the extremities of the representative diame- ters, will be the representation of the circle required. The original circle, A, is placed in its position for the same reason as before given, Problem XII. The following are several easy methods of draw- ing the representation of a circle, and are err- ceedingly useful where accuracy is required particularly 1n the representation of large circles. The intersecting and vanishing lines, the centre and distance of the picture, the seat and distance of the centre, and the radius of the circle, are supposed to be given till otherwise announced: PLATEH. :4 PERSPECTIVE. /‘\ upon the Prz'naklw 5f the L \ ' , i ‘ Dir-(cling Plane. / , \ — / D; \\ Fig.1 Fey 2. . - Fig. 4. ) "U // / / 4' ‘ Fly. 5. 175, 9a 2 < 1 i l i 'Uf Drawn by 111.11. Nit/101m". [undamfublzlrlud by [f [Vida/Jon 3- JBar/‘I'I’IJ, Wan/our Sir-«41814. Enymva] by lewry. :. .AVA”, m. “firms... 33F; RS 1” E (‘ TEVE. ' PLATE 1'; 13; %\ , .//r/ / \ F73 1 /‘ \ /// / / \ // V M// a . C’ ‘ I L 9 “Mimi!" II'llIlIllfl‘v < i III I I | N fig-2' ' Fig.3- V C I D i {r C 71') i; "Ilmmlllflml'lmfll’m‘ .I. ”ml“fl"lllmn"Nmmmlln ...... r ‘ ‘uIIIIIIII II“ IIIIIII IIIIIiiIIIlIIIIlIIIIIII"HI “Hm ufllmflflm "mm" In I ,I IIIIIIIII III...IIIIIIIIIIIiiIm , ,z, LIIII,IIIIIIIIIIIIIIIIIIIIII IIIIIIIIIIII'II 3'!" c I I I I / I 3/ N I b x d ‘N Fig. 5. III II IIIIIIIIII‘ ‘r'r ““ W ,1! . N 171 111/ 1‘...th1 I. L . - ' . I “ I H. . " J” ’ Lam/ml;/Im/;..-/mz 13/ ZiNirlznlwnn x1 [fir/7772M, Mun/nur- .I‘nm,m4.;. . ”WW"! [’3’ 13-30”- PER picture, 1‘ the seat of the centre of the circle, and 1’ y, its distance. Method 2. Figure 2.—-Draw x A perpendicular to . I’ N'; make .1" E and x D each equal to xA; describe the are C x B; join A E and A D, cut- ting the are C x B at C and B; draw C F and B G perpendicular to I’ N’, cutting I’ N’ at F and G; join E C’, F C’, x C’, G C’, and DC’; also join 3/ D, cutting EC', F C’, .rC’, G C’, and D C’, TI at b, m, n, k, and d; draw b a parallel to I’l\ , cutting :rC’ in e, and D C’ at a; draw dc parallel . ' to 1' N’, cutting .rC' in g, and EC’ at c; through 71 drawfh also parallel to 1’ N, cutting E C’ atf, and DC’ar It; join ac, cutting G C’ at b, and F C' at l, and a c will also cntfh oryD’ at 72; through the points e, 6, II, k, g, l,f, m, e, draw a curve, which will be the representation of the circle required. This will easily appear, when it is considered that the tangent of 45 degrees isequal to the radius, or by inspecting Figure 4, where the part l\1 F G is equal and similar to A E D. IVIet/iod 3. Figure 3.———Make x 6 and a: a each equal to the radius of the circle; join 6 C’, 1‘ C’ and a C’; make my equal to the distance of the centre of the circle; from its seat, x,join y D’, and complete the representation, d c f e, of the cir- cumscrihing square; divide the representation, lig, of the parallel diameter, into seven equal parts, setting one-seventh from II, and the other sevenh from g, each towards the centre; draw kl and 'm n, tending to C’, cutting the diagonals in the points 15,], m, n; then through the points I, h, k, p, n, g, 172, q, draw a curve, which will be the repre- sentation required. This will readily appear by observing, in Figure ’2, that the representation of the parallel diameter, fit, is divided in the same proportion as F G, or as E A, Figure 4; now E L, K A, F H, or I G, Figure 4-, are very nearly equal to one-seventh of the diameter EA; draw M C perpendicular to to E A, cutting the semi-circumference at C; through C draw F G, parallel to E A ; and through E and A draw E F and A G, parallel to M C; join F M and G M, cutting the circle in D and B; through D and B draw L H and Kl, parallel to M C, cutting EA at L and K, and FG at H and I. Now suppose the diameter, E A, to consist of seven equal parts, then the radius, M E, or M A, .C’ denotes the centre, C’ D’ the distance of the 459 will be 3.5; that is, M D, or Me, will be 3.5... PER .- By Euclid, Book 1. Proposition 47. the square of M D, or M B, is equal to the squares of M L and L D; but M L is equal to L D, therefore the square of D M is double the square of M L; that. is, the square of M. E is double the square of M L; hence M L will be obtained arithmetically, thus: L M = (M ng; therefore E L : E M 1-! — LM -_- EM— (Hf: 3.5 —- (Eff ‘2 2 : 1.026, Stc, which is exceedingly near to unity, the error being in excess. Figure 5 is an application of Method 3, Figure 3, to planes at different altitudes, to obtain the re» presentation of a circle, when the seat of its cen- tre is given on the original plane, and the seat of the centre of the circle on the original plane is given on the intersecting line, and the distance of the seat of the centre of the circle on the original plane, from its seat on the intersection, is also given. The ellipsis below is the representa- tion of a circle below the eye. To represent a circle above the level of the eye, let .2: be the seat of the centre of the circle on the original plane, given on the intersecting line; let my be the distance of the two seats. .Draw'y o perpendicular to 1’ N’, and make y 0 equal to the distance of the centre of the circle from its seat on the original plane; draw 0 D’; then having found the representation of the circle below the eye on the original plane, as in Method 3, Figure 3, let ce be the representation of the diameter pa- rallel to the picture, and a the representation of the centre; draw a]; parallel to 3/ 0, cutting o D’ in p,- draw w 2 parallel to V' L’, the vanishing line; draw cw parallel to y 0; make p 2 equal to p to; through a) draw 5 t, tending to the centre, C’, of the picture, cutting o D’ in t; and through z draw q r, tending also to C’, cutting o D’ at r; draw r s and q t parallel to V’ L’, and s r q t will be the representation of the circumscribing square; then complete the circle as in Method 8. Met/rod 4.‘ Plate IV. Figure l.——Let A BC D be the representation of the circumscribing square, with two sides of the original parallel to the in- tersecting line, consequently the other two per- pendicular thereto; and let GH be the repre- sentation of a diameter parallel to the intersect- ing line, I that of the centre, and E F the diameter perpendicular to the intersecting line, 3 N 2 PER 460 6 Divide I H into any number of equal parts (as three) and through the points of division (1, 2,) draw the lines Fm, F n; draw HK parallel to F E, cutting A B at K; divide K H into the same number of equal parts as I H, and through the points of division draw the lines Em, E n,- then the points m and n are in the curve as well as the points E and H. In the same manner, the curve E o p G, for the representation of the other quarter, will be found; also, in describing the re- presentation, G F H, ofthe remote semicircle, pro- ceed for the representation of each quarter in the same way, only changing the points Fand, E ‘for each other, and the whole curve will be obtained. .Met/zod 5. Figure 2.——Let G E H be the repre- sentation of the nearer semicircle, in the same position as before. Divide l H into any number of equal parts (as three) also divide the line B H perspectively to represent the original of BH, divided into three equal parts; that is, since 13 C' is the indefinite representation of a line, C’, its vanishing point, B k, is a line drawn through B, and C’ d is another drawn parallel thereto, and on the contrary side of B C’. On Bk set off the distances B. l , l 2, 2 k, equal to each other; join k H, andproduce it to meet C’ d in t; draw each of the lines 1 l, 2 m, tending to the point t, cut- ting B H at Z and m; then, having drawn the lines Ep 1, E q 772, as in Method 4, draw 11) E, m g E, and the points of intersection, p and q, will be in the curve. In the same manner may the part E; r s G be obtained, and also the representation of the remote half, if necessary. Figure 3 is the representation of a segment less than a semicircle, the chord of the original seg~ ment being parallel to the intersecting line: the operation is the same as in Method 4. It is hardly possible to conceive any method more con- venient and easy than this, as the perspective representation is found geometric-ally, without any other vanishing points than the centre of the picture. . Method 6. Figure 4.—-—~Having completed the re— presentation, A B C D, of a circumscribing square, the sides of the original being parallel and per- pendicular to the picture; find the perspective centre, 1, which may be done by drawing the two diagonals. Find the representation, G H, of the diameter parallel, and that of F E of the diameter perpendicular to the picture; produce GH both ways to K and L, making G K and H L each PER equal to IH, or IG; join K E and KP, L E and LF; also join ED, F A, E C, and FE, cutting the lines drawn from C and L to the points Eand F, at a, 6,0, d, which are points in the representa- tion of the circle; therefore through all the points a, E, I), H, c, F, d, G, draw a curve which will represent the circle required. Figure 5 shews the same thing for the repre— sentation of a semicircle with its diameter paral- lel to the picture. The methods shewn by Figures 1, 2, 3, 4, and 5, are derived from the following considerations: Figure 6.—-—Let A B be any straight line, cutting another, C D, at E, and dividing it into two equal parts, E C and ED; if C F and .DG be drawn parallel to B A and F G, through A, parallel to C D; and ifC E and C F be divided into any equal number of parts, in the same ratio, from C, and lines be drawn from the points of division in C F, to the point A, and lines through the several divisions in C E from the point B, to cut the former, drawn to the point a,- the respective in- tersections of every two lines will be in the curve of an ellipsis, of which CE is an ordinate, and AE an abscissa. In the same manner, the op- posite part of the curve may be described, and also the other portion on the opposite side of the double ordinate, CD. Now, to shew the truth of this: let AB(Figure 7) be a diameter, and gfan ordinate; drawf e parallel to B A, and A e parallel to gf; dividefe andfg in the same ratio, the former in k, the latter in It, and draw It A and B It; then produce B k to meet It A at C, and C will be a point in the curve. Because the triangles B D C and ng are similar, And because the triangles A D C and A i It are si- BD:Bg::DC:gk; AD:Aioreh::DC:z'lz,orgf; milar, And by construction, e}; : eforAgzz gk : gf; Therefore by multiplica— BDxAD:ngAg::DC2:gf‘~’; tion, - A well-known property of the ellipsis. Now, in Figure l, E F is a diameter, and IG, IH, ordinates at the same point, I; and as the per- spective representation of a circle is the section of an oblique cone, it is an ellipsis; and as the method is the same as that now demonstrated, it is therefore founded in truth._ In Figure 3, PER 461 PER the same data are given. In Figure 4, FA di- vides [G into two equal parts, which have their originals also equal; and F8 divides I H into two equal parts, which have their originals also equal. Again, EK divides A G into two parts, the originals of which are equal; and E L divides B H into two parts, the originals of which are likewise equal; and since a circle can be drawn through as many points found in the same manner, this method of finding eight points in the curve is correct. The same might have been observed of Figure 2; for the parts in the double ordinates, I G and I H, are divided equally, and the parts in A G and B H perspectively into parts, the originals of which are equal. Nothing can be more expeditious, nor more con- venient for practice, than the method which this principle furnishes, when it is considered that no point can be found geometrically, but by the intersection of two straight lines. Its great ad- vantage lies in 'the regularity of the operation; in not distracting the eye with irregular'crossings. As many points may be found as required, without the least confusion, within the compass of the cir- cumscribing parallelogram, which is not the case with many other methods, derived entirely from the principles of perspective. It may be always well applied when the curve is the representation of a circle inscribing a square, the sides of which are parallel and perpendicular to the picture. 1V1et/zod 7. Figure 9.-—Let W X Y Z represent a square circumscribing the representation of the circle required ; and let A B represent a dia- meter of the original circle perpendicular to the picture, and D C be the representation of the radius parallel thereto. Bisect A B in I; through I draw It i parallel to D C ; draw Be perpendicular to It 2', cutting it in e; draw Da parallel to Be; with the distance Be, from the point C, describe an arc, cutting Iii at]; join Cf, which produce to a; through a and I draw mn; then, if the straight line a C be moved, so that the point a may slide along the line 772 n, and the pointf along hi, the extremity, C, will trace therepresentation of the circle required. For drawft parallel to D a, cutting D C in t; Then because of the similar triangles Cft and C a I) ngzftzzCla : “D5 But because Cf: B 6 ft: DugitwillbeBeszzl-i: dB and C a : I i l 'Aerain, b the similar trianoles' ' . DIBanndIDu ‘3 BezDuzleJD, Therefore by equality, I B : I D : :Iiza D; But by duplication, IB‘:ID2::Ii2:aD2; Andbydivision,I B‘:IB2-—I Dzrzliz: Iii—aD‘; But I B'L—I D‘=(B 1 +1 D) x (BI—l D) : AD X DB,andaD2=a Cz—DC‘= Iiz—DC’; therefore by substitution 31’: A D X I) B :: Iiz : D C‘, which is a known property of the ellipsis; and as the perspective representation of a circle is an ellipsis, being the section of an oblique cone, the curve described is the true representation of the original circle; for the rays proceeding to the eye form the surface of a cone, which being cut by the picture produce an ellipsis. In this manner an ellipsis (Figure 8) may be de- scribed by a continued motion, having any two conjugate diameters, hi and A B, given; ora dia- meter and ordinate, without previously finding the two axes. But as it is not very easy to make an ellipsograph move freely in every position of two conjugate diameters, from the obliquity of the intersections, it may be done upon the same principle, by find- ing points in the curve upon the straight edge of a thick piece of paper, marking the points 0,], and C (Figure 9) upon the edge; then suppose a is first placed upon any point in the line 771 n, carry the other end of the slip until the point marked ffall upon It i, then mark the extremity, C, upon the plane of description or paper, and the point so marked will be in the representation of the circle required. In the same manner, as many points may be found as will be sufficient to com- plete the curve with tolerable accuracy. But as the method of describing an ellipsis by continued motion from two axes is by much the most accurate, we must here shew the method of finding a conjugate diameter, to a diameter or ordinate given, before we can proceed with the next method. Lemma. Figure lO.——Let A BCD represent a square circumscribing the original‘circle, and let EF be the representation of the diameter perpen- dicular to the picture, It 1* the representation of the radius parallel to the picture, and It the representa- tion of the centre. Bisect EF at 0,- through 0 draw mu parallel to A2 B, or D C ; draw F g per- pendicnlar to min, cutting m n atg; from the point 1, with the distance Fg, describe an are, cutting mn at It ,- draw k 2' parallel to F g, and'pro- PER 462 PER M it — duce lh to i; make om and o h each equal to il; then m n is the diameter conjugate to F E, This method is evident from the construction given in Method 7. Figure 9. [Wetland 8. Figure ll.—-- The representation,ABCD. of a square circumscribing a circle, having its sides parallel and perpendicular to the picture, being given; to find the representation of the circle by means of the two axes. Find G, the representation of the centre; EF that of the diameter perpendicular, and G H that t of the radius parallel to the picture. Then, by the preceding lemma, find the semi-conj ugate diameter, r I); draw E k perpendicular to A B; make Elc equal to r 1); join NC, and bisect it by a perpendicular, u 0, meeting AB at 0; from o, as a centre, with the distance, 0 r, or o k, describe the semicircle pkg, cutting A B atp and q; join lrp and kg; from k, with the distance ICE, de- scribe the arc 772 El, cutting kp at m, and kg at I; join rp and rq; produce pr to t, and q r to to; draw ms parallel to k r, cutting p r at s, and draw lu, parallel also to kr, cutting rq at u; then rs and ru are the semi-axes, as shewn by the writers on conic sections; make rte equal to r u, and r t equal to rs: and um and st will be the axes by which the curve may be described by means of an instrument at one continued movement, and the curve thus described will be the representa- tion of the circle required. .llIethod 9, Figure 12.——Supposing every thing given as in the last method, C F being the repre— sentation of a diameter perpendicular to the pic- ture, E that of the centre, AB and D C that of the sides of the square parallel to the picture, and AD and BC the other two sides perpendicular to the picture; draw F X perpendicular to AB; make F X equal to A F or F B; from X, with the radius X F, describe an arc; draw X N, X B, X 0, Sue. meeting A B at N, B, O, 8tc.; join N E, B E, O E, F E; make angles on the other side of F X equal to FXM, MXL, 8cm; produce the legs to meet A B; from the points in A B draw lines to E, and produce these lines on the other side of E; from the points M, L, K, draw M c, L I), K (1, Std. meeting A B at c, b, a; draw the lines o C’, b C’, a C’, 8L0. cutting the lines drawn to the cen- tre, E, atf, e, (1, G, and g, h, i, on the opposite side of EG; then F,f, e, (1, G, g, h, 2', are points in the curve. In the same manner, points may be found in the curve on the other side of PG; and f M thus. any number ofpoints may be obtained in the representation, at pleasure. For since E is the representation of X, the lines EN, EB, E 0, EF, Ste. are the representations of XN, XB, X 0, XF, Ste. Again, a C’, b C’, c C’, Ste. are the representations of a K, b L, c M, &c.; there- fore the points Rf, e, d, G, &c. the intersections of these lines with the former, are in the curve, for each two lines are drawn from the same com-n mon point in the circle K LM F, which may be looked upon as the original; thus the point M is represented by f, L by e, K by d, and the extre~ mity of the diameter, parallel to A B, by G. In cases of this kind, where lines radiate from a centre, in approaching the parallel diameter, they frequently run out beyond the bounds of the drawing. The following remedy is very conve- nient; letX m be a line, which ifprodnced would not meet A B within aconvenient distance; from any point, S, in A B, draw S Q parallel to a straight line supposed to join the points X and E; make S Q equal to the part of the line inter- cepted between the line A B and the point X; make SR equal to the other part, and join RQ; now let Xm meet S Q in m; draw mu parallel to Q R,cutting S R at u; make S 0 equal to S n; and draw 0 E, which will be the line corresponding to, or representing m X; and thus of any other. Method 10, Figure 13.—Let E be the represent- ation of the centre, 1) Q a diameter parallel, and F G a diameter perpendicular to the picture; bisect F G in fit; through m draw qp, parallel to D Q; find the extremities, q and p, by the pre- ceding lemma, (Figure 10); join D m, and produce it to u; make m n equal to m D; join Q m, and produce Qm, to 0; make mo equal to mQ; draw Ft parallel to A H, cutting Du at y, and make gt equal to Fy; draw Fs parallel to B 1', cutting Qo at v, and make as equal to 'v F; draw G u parallel to H A, cutting D n at 3:, and make .17 u equal to a: G; draw G r parallel IB, cutting 0 Q at to; make w r equal to to G; then will the points 0, u, r, n, t, s, be in the representation of the circle. For since m is the centre of the ellipsis, and D is a point of contact, D n will be a diameter; it will there- fore be bisected by the centre m, consequently the point 72 is in the curve. Again, because Q is a point of contact, Q 0 is a diameter, there- fore mo is equal to m Q, and the point 0 is in the curve. Again, because 1) and G are points of PIA TE [17. PERSPECTIVE. L I d L Dg~4 7 , ’ ‘ “”"W'l 1'1““ ‘:\“‘i~‘§3‘\‘x‘\m‘.‘l\fi‘xt“\““‘l in G- nmitfin‘m" w w 1 “I 0 V W i v \ “W \\ H \ \\‘ \' ‘\» N B /,’ ,1 / ,E r y / ,’/," . // K 1/ I / If I X :':' 113;. 25. < [227.14. ‘,' l] C I: w. " , 6 L’ fly. ]3. V N, 11/ [/14] lz/mw mrt/uu/Iv (hunted, mm' [um/mljhblzlv/ml by 1341711'lzu/Jun X-JBdr/i'e/d,WEI/210111“ Jb'c‘c’l,1(915. fi'nyravezi 121/ 13. 7213/10)“. drawn /I(/ I? J '1} '/I4 1/42 '71. ‘=:*' 'PER Contact, and D n is a diameter; and because G u is parallel to HA, a tangent at G, Gu is a double ordinate, it is therefore bisected by D n at x, and the point it is in the curve. By parity of reasoning, the points 7', t, and s, are in the curve of an ellipsis; wherefore all the points , q, o, u, r, n, t, s, as well as the four points of con- tact D, F, Q, Gr, are in the curve of an ellipsis: here are six additional points besides those which the circumscribing square furnishes, from the mere consideration that the centre bisects all the diameters; that if there be two tangents, and the points of contact given, and if aline pass through one of the points of contact and the centre, it will be a diameter; and if another pass from the other point of contact parallel to the tangent, at the extremity of the diameter, it will be a double ordinate; and, lastly, that all the double ordinates are bisected by the diameter. .Met/tod 1], Figure 14.——Let V’ L’ be the vanish- ; ing line, l’N’ the intersecting line, b the point where the original circle touches the intersecting line, D’ R’ the directing line, and D’ the point of station, or prime directing point. Through .D’ draw E’ D’ C’, perpendicular to R’ D’, : cutting V’ L’ at C’, the centre of the picture; make D’ E’ equal to the height of the picture, and D’ R’ equal to D’ E’; draw be perpendicular to I’ N’, and make be equal to the radius of the circle; from c, with the distance 0 6, describe an arc, dba; draw a e, ct, and df, tending to the point D’, to cut I’N' at e, t, andf; draw 0 a per- pendicular to ae, and cd perpendicular to (If; draw fl, tn, and e m, parallel to D’ E’; draw dk, tq, and a s, tending to R, to cut I’ N’ at k, g, and s; transferfk tofl, fromf to 2'; tg to t u, from t to u; and es to em from e to II, and join ill; make on equal to o u; then will 0 be the centre, and . Hz and un conjugate diameters of the ellipsis, which will be the representation of the circle. For since D’ is the directing point of the lines (1], ct, a e, these lines will have have parallel re- presentations,- join R’ E’ and k i, for suppose them to be joined; then ki will be parallel to R’ E’; therefore ki will be the representation of the line dk, and becausefl is the representa- tion offal. Their intersection, 2', will represent the point d. In like manner, it may be shewn that the point a represents t, and the point It represents a; but the lines (If and a e are tangents to the circle at the points d and a; thereforethese representa- 463 . . W ' PER tions,fl and em, are tangents to the ellipsis at 2' and h,- consequently 2'}: is a diameter; and because an is parallel tofl and em, u n is a diameter con- jugate to tie. Method 12, Figure lie—This process is almost similar to the last, except that the point D’ is taken in a line perpendicular to the intersection; this causes the conjugate diameter, tie, to be pa- rallel to the intersection, and the other, gn, to tend to the centre of the picture. This method, by means of directions, furnishes conjugate diameters at once, whereas, if vanish- ing points only are used, we have only a diameter and ordinate, or double ordinate; consequently the other diameter, which would be conjugate to the one given, must be determined by a geome- trical process. The use of the directing point is therefore much more convenient, and much more accurate in the representation of curves. The di‘ recting line is always at hand, when the perspec- tive delineation is raised from a geometrical plan, instead of a perspective one. IVIethod 13. Plate V. Figure 1 .——-Let LMJ K be a square, circum scribing the original circle B CD E F GH I; draw the diagonals JL and MK, cutting the circle at C, E, G, I; through the centre, A, draw FB parallel to MJ orLK;joinGI and EC; produce MJ, GI, FB, EC, and LK, to their intersecting points, 7; 11, Ste; find the vanishing point, '0", of the parallels of FB, and draw the in- definite representations n *0", n '02, 8Lc.; also pro- duce the diagonal, M K, to meet I’ N’ at .z‘; and find the vanishing point, v3 of the diagonal M K; draw the indefinite representation a.“ '03 of the dia- gonal, which will cut the indefinite representa- tions drawn to '02 of the parallels; find the va- nishing point 2" of the sides J K and M L; draw . lines to 1:3 from the intersection in xv’; and pro- duce these lines to cut the respective indefinite representations drawn to v? in the points which represent those of the circle; then a curve drawn through the corresponding points, b, c, d, e,j,g, It, 2', will form the representation of the circle. This evidently appears from the prOperty of the circle, and the method of finding the perspective representation of a .point in the original plane. Method 14-. Figure 2.—Let A be the centre of the original circle, and let B, C, D, E, F, G, H, he points in the circumference; let E’ be the place of the eye in respect of the vanishing line V’ L’; draw E’ C’ perpendicular to V’ L’, cutting PER 4 64 it in C’; make E’ D” equal to the height of the picture; draw the two lines D” H and D" B tan- gents to the circle; draw A H perpendicular to D” H, and A B perpendicular to D"B; let the lines H D” and BD” cut IN in t, t; from the points C, D, E, F, G, draw the lines C t, D t, Et, 8L0. tending to D”, cutting the intersecting line in the points t, t, 8Lc.; from all the points, t, t, t, Ste. draw lines parallel to the director D" E'; from the same points, B, C, D, E, F, G, H, draw the parallels Bp, Cp, Dp, 8Lc. cutting I N in p, p, p, 8tc.; find the vanishing point, 1:, of the lines Bp, Cp, Dp, Ste. and join the intersecting “points, p,p, 8Lc. to a, cutting t b, t c, t d, 8:0. at b, c, d, e,f, g, 12, which will be the corresponding “points to B, C, D, E, F, G, H, of the original circle; draw I) [2, which will be a diameter. The points of the other half will therefore be found by continuing the parallel from t, t, t, &c. on the upper sides of the diameter bit, and repeating the ordinates upwards to the points i, k, l, m, n, then acurve drawn through all the points will give the representation required, as is evident from the-directing and vanishing points. Having shewn some of the most easy methods of drawing the representation of the circle, derived from the principles of perspective and the pro- ' perties of conic sections, so far as regards the section of the cone being-an ellipsis; the represen t- ation of the parabola and hyperbola being of little use in practice, is therefore omitted, as it would lead this article to too great a length. But, in order to exhibit a more comprehensive idea of ' the nature of the circle, than has already been given, it will be requisite to shew the nature of harmonical lines, and the harmonical division of lines; for this purpose, the following lemmas, are introduced. The only authors that have treated upon this subject are Hamilton and Wood, but it is to the labours of Hamilton, in his Stereography, that we are indebted for the first introduction of harmonical divisions in to per- spective, tho-ugh the very some properties have long been understood by the writers of conic sections. “ Of the properties of lines harmonically divided. “ Having thus premised some things touching the sections of a cone in general, and given rules to know, according to the situation of the origi- nal circle with respect to the directing line, which of the conic sections will be produced by the PER 1 4 image of the circle, we should proceed to the other inquiries before proposed; but, in order thereto, it will be convenient first to lay down some propositions touching the properties of lines harmonically divided, by way of lemmas, for the easier demonstration of what shall be ad- vanced on this subject, in which we shall employ the remainder of this section. “ Definition 1. Plate W. Figure 1.—If a line, A B, be so divided into three parts, by the points C and D, as that the whole line, A B, may have the same proportion to either of the extreme parts, AC, as the other extreme part, D B, hath to the middle part, C D; then the line A B is said to be harmonically divided in the points A, B, C, and D. “ To divide a given line harmonically. “ Lemma 1. Figure 2.——Let A B be the given line, and C one ofits intermediate points of divi» sion, and let it be required to find a fourth point, D, between C and B, so that the given line, AB, may be thereby divided harmonically in A, C, D, and B. “ 1. From any point, E, without AB, draw E A and E B, and through the given intermediate point, C, draw G F parallel to E B, cutting EA in F; make C G equal to CF, and draw EG, which will out A B in D, the point sought. “ Demonstration—Because of the similar trianm gles, AEB,AFC, AB : AC :: EB : FC: C G ; and because of the similar triangles, B E D, DGC, BD : DC : : EB : CG; therefore AB : A C : : BD : ‘DC; and, consequently, AB is harmonically divided in A, B, C and D. “ 92. If the point sought were required to fall be- tween C and A; through C draw f g parallel to EA, cutting EB inf,- and having taken Cg equal to Cf, draw E g, which will cut A B in d, the point desired; by which A B will also be har- monically divided in A, d, C, and B. “ The demonstration of thisis the same as before. “ Lemma '2.—-If two lines, harmonically divided, being laid upon each other, agree in any three points of division, whereby one part in the one 3 must necessarily agree with a part in the other; the fourth point of each will also agree, provided the agreeing part be either an extreme part, or the middle part of both. “ Figure l.—Let AB and a b be the two given lines laid upon each other; and, first, let the points, A, B, and C, of the one, agree with the points a, b, and c, of the other, whereby the parts, PER M AC and ac, which are both extreme parts, as also the whole lines AB and ab do agree; it must be proved, that the points D and d also agree. “ Demonstration.———Because of the harmonical di- visionof AB, AB : AC : : DB : DC; and for the same reason, in the line ab, a b : a c: : db :dc. But AB = ab and AC = ac, as before; therefore DB: D C :: db : dc; and by composition DB+DC=CBzDCz2 db+dc=cbzdc. But C B is equal to c I), therefore 6 b : D C : : c b :dc; consequently D C : dc; and therefore the points D and d coincide. “ Again, let the points A, C, and D, agree with the points a, c, and d, by which means the ex- treme parts, AC and ac, and the mean parts, CD and ed, agree; it must be shewn that the points B and b also agree. “Because of the harmonical division of A B, AC : CD : : AB : DB; and for the same rea- son, in the line ab, ac : cd: : a b : db. But A C : ac and CD = ed, therefore, A B : DB : : ab : db; and,by division, AB — DB = AD :DB : :ab—db = ad:db. ButADis equal toa d, therefore ad : DB :: a d : db; conse- quently DB = db, and therefore the points B and b agree. “ After the same manner it may be shewn, that if the points C, D, and B, agree with the points 0, d, and b, the points A and a will also agree. Q. E. D. “ Definition Q. Figure 3.—-If a line, A B, be harmonically divided in A, B, C, and D, and from any point, V, without that line, there be drawn four lines, VA, V C, V D, and V B, through the points of division of AB; these four lines, pro- duced both ways from V, are called harmonical lines. “ Definition 3. Figure 4. —-And if through the same points, A, C, D, and B, four lines be drawn parallel to each other, and making any angle whatsoever with AB, those four lines are called harmonicalparallels. “ Lemma 3. Figure 4.—If four harmonical pa- rallels, A a, C c, Dd, B b, formed by a line, AB, harmonically divided in A, B, C, and D, be cut by any other line, a b, the line a b will be harmo- nically divided in its intersections with those parallels. “ Demonstration.—-If ab and AB were parallel, it is evident they would be divided in the same VOL. II. ‘ 465 PER ”- I r proportion by the harmonical parallels, seeing the corresponding parts in each would be equal; and if the lines A B and ab cross each other in any point, x, either within or without the harmo- nicals, the triangles, a: A a, a: C c, xD d, bi, will still be similar, and consequently the seg— ments, ca, ex, and, db, will have the same pro- portion to CA, Cx, x D, and D B, as .r b hath to xB, and will therefore be respectively propor- tional; and the line AB being by supposition harmonically divided in A, B, C, and D, the line a b will therefore be divided harmonically in the corresponding points, a, b, c, and d. Q. E.D. “ Lemma 4. Figure 5.——lf a line, A B, be bisected in C, and from any point, V, without that line, there be drawn three lines, V A, V C, and V B, and VF be drawn parallel to A B; then the four lines, V A, V C, V B, and V F, produced on both sides of the point V, will be harmonical lines. “ Demonstration.—Having drawn any line, BF, cutting all the four lines, VA, V C, V B, and VF, in E, D, B, and F; through D draw H L parallel to AB, which will therefore be bisected in D; A C and CB being equal by supposition. “ Now in the similar triangles, FV B, D LB, FB : DB: :FV : DL = HD, and in the simi- lar triangles FVE, EH D, F V : HD :: FE: ED; wherefore, FB : D B : : FE : ED; that is, the line PE is harmonically divided in the points F, B, E, and D (Definition 1); and consequently, the lines, V A,V C, V B, and V F, are harmonical lines (Definition 2). Q. E. D. “Lemma 5. Figure 6.—- If the angle, AVB, made by any two lines, VA and V B, be bisected by a line, V C, then if another line, V F, be drawn through V, perpendicular to V C, the four lines, VA, V C, V B, and V F, will be harmonical lines. “ Demonstration. —-Through C draw A B per- pendicular to V C; then the triangles, V CA, VCB, being every way similar and equal, the line AB will be bisected in C; but AB being perpendicular to V C, is therefore parallel to V F ; consequently the lines VA, V C, V B, and V F, are harmonical lines (Lemma 4). Q. E. D. “ Lemma 6. Figure 7.-—1f four harmonical lines, V F, V E, V D, and V B, formed by the line F B, harmonically divided in the points F, B, D, and E, be cut by any other line, fb, parallel to FB, the line f b will also be divided harmonically in the corresponding points f; b, d, and e. 3 o PER 466 PER W “ Demonstration.——Because the parts, f e, e d, d b, will be respectively proportional to the parts F E, E D, and D B. (Lemma 2.) QE. D. “ Lemma 7. Figure 7. -—If four harmonical lines, VF, VA, VC, and VB, fo1n1ed by the linefl), harmonically divided inf, b, d, and e, meet in the point V; then any line, HL, drawn parallel to any one of the ha1monicals, as V F, will cut the other three, and be bisected by them in the point D. “ Demonstration.—-First, it is plain the line H L must cut the three harmonicals VA, V C, and V B, seeing none of them are parallel to V F, to which H L is parallel by supposition. “ Through D, the middlemost point of H L, draw F B parallel to fl); then FB will be harmonically divided in the points F, E, D, and B. (Lemma 6.) “Now in the similar triangles, F V E, EH D, F V : H D : : FE : E D; and in the similar triangles FBV,DLB, FV : DL ::.FB : D B. Butbecause F B is harmonically divided, as already shewn (Lemma 6) FE : ED : : FB : DB; wherefore FV : H D : : FV : DL; and consequently H D = D L. “ Therefore H L cuts three of theharmonicals, and is bisected by them in the point D. Q. E. D. “ Corollary—If the angle made by any two of the four harmonical lines, not adjoining together, be right, the angle comprehended between the Other two will be bisected by the intermediate line. “ For if VF and VD be perpendicular, H L, drawn parallel to V F, will also be perpendicular to V D; and H L being bisected in 1) (Lemma 7) the rectangular triangles, V D H, V D L, are similar, and consequently the angles D V H, DV L, are equal; that is, the angle EVB is bisected by V D. “ Lemma 8. Figure 8.—If four harmonical lines, VA, V C, V B, and V F, meeting in V, be cut any where by a line, FB, that line will be harmoni- cally divided by them in the points F, E, D, and B. “ Demonstration—Through any of the divisions ofFB, as D, draw HL parallel to one of the harmonicals VF, so that the point D may be between H and L; then HL will be bisected in D. (Lemma 7.) “ Now in the similar triangles, FVE, EHD, FE: ED::FV:HD = DL; and in the simi- lar triangles, FVB, DLB, FB:DB::FV: DL; wherefore FE ; ED : : FB : DB; conse- quently FB IS harmonically divided 1n the points F, E, D, and B. Q E. D. “ Corollary 1. Figure 8, No. l and 2.——If in an original line any part, A B, be taken and bisected in C, the indefinite image of that line will be harmonically divided by the images of A, B, and C, and its vanishing point. “ Let I wk P represent the radial plane of an ori- ginal line, kB, in which the part AB is taken and bisected in C; then because AC and CB are equal, the lines I A, I C, I B, and Ix, which last is always parallel to A B, are harmonical lines (Lemma 4); therefore the indefinite image, Pm, which cuts all the four harmonicals (it being parallel to none of them) is harmonically divided by them in a, l), c, and .r. (Lemma 8.) “ Corollary 2. Figure 8, No.3 and 4 .—-If 1n the indefinite image of a line, any part, a b, be taken and bisected 111 c, the indefinite original of that line will be harmonically divided by the originals of a, b, and c, and its directing point: “ For a 6 being bisected in c, and I It being parallel to it, the lines Ia, Ic, I b, and I la, are harmonica] lines; therefore the indefinite original, lcP, which cuts all these four harmonicals (it being parallel to none of them) is harmonically divided by them in A, B, C, and k. “ Corollary 3. Figure 8, No. 5 and 6.~—If either of the points A, B, or C, of the original line be its directing point, the indefinite image will be bisected by the images of the two other points and its vanishing point; and, vice versa, if either of the points, a, b, or c, of the indefinite image, be its vanishing point, the indefinite original will be bisected by the originals of the two other points and its directing point. “ For in the first case, I]: is one of the harmo- nicals to which the indefinite image is parallel, and therefore cuts the other three, and is bisected by them; in the other case, I x is one of the har- monicals, to which the original line is parallel, and therefore cuts the other three, and is bisected by them. (Lemma 7.) “ Corollary 4. Figure 8, No. 7 and 8.——If an original line he harmonically divided in the points A, B, C, and D, its indefinite image will also be harmonically divided by the images of A, B, C, and D; and, vice versa, if the indefinite image of a line be harmonically divided in a, 6,0, and (1, its original will also be harmonically di= vided by the originals of a, b, c, and d. “PERSPECTIVE, 1:- .3. 113,. 2. ‘5' L 3% I? A a D 11¢ a. 1V.” 6. “ _ ii (I A . -/' . I r \ b\ d \\ \ \ [c C D ‘3 t. A ’"B (‘ Dim": 63/ I? M'rfio/Jnn. [Did/wad 611/ {ItzzUl’Il/l. PER 467 PER “For IA, IB, IC, and ID, being hatmonical lines (Definition 2) the indefiniteo image, P :1“, cutting them all four (it being parallel to none of them) is therefore harmonically divided by them in a, b, c, and (1. (Lemma 8.) In like manner, ifIa, I b, I c, and I d, be harmonical lines, the indefinite original line, k B, which cuts them all four, is harmonically divided by them in A, B, C, and D. “ Corollary 5. Figure 8. No, 3 and 4.—~lf either of the points of harmonical division of the origi— nal line be its directing point, the indefinite image of that line will be bisected by the images of the other three points; and, vice versa, (No. 1 and 9) if either of the points of harmonical division of the indefinite image be its vanishing point, the original line will be bisected by the originals of the other three points. “ This is the converse of the first and second Corol laries, and is demonstrated in the same manner. “ Corollary 6 .——If eithe1 extremity of a line bar- monically divided, be taken as the vanishing Upoint of that line, the two parts which lie fa1thest f1om that extremity will 1ep1esent equal lines. “ 'lhis plainly follows from the latter part of the last Corollary “ Lemma 9. Figure 9. ——If a line, A D, be har- monically divided in A, B, C, and D, and any two adjoining parts, A B and B C, taken togethe1, be bisected 1n m; then mB, m C, and m D, will be in continual proportion ; thatis, mB : m C 2 : m C : m D. “ Demonstration—Take Ad equal to C D; then by the supposition, AB : B C : : A D : C D; and bycomposition, AB + BC : AC : BC : : AD + CD : dD : CD; therefore, sAC : m C : BC : : édD = mD : CD; and by division, m C, ——BC=mB:mC : : mD—CD :mC : mD. Q. E. D. “ Corollary 1.—The same things being supposed as before, BC will be to B D, as B m to BA. “ For by the third step of the Lemma, alternate mC : lezz BC : CD; and by the Lemma, mC : mD : : mB : m C : mA; therefore, BC: C D : :mB :mA; consequently, by composition, BC:BC+CD=BD::mB:mB +mA= B A. “Lemma 10. Plate Y, Figure ].—If from apoint, K, without a circle, A D B E, there be drawn two tangents, K D and K E, touching the circle in D and E, and those points be joined by the chord DE; then if any line, Kb, be drawn from K, cutting the circle in a and b, and the chord of the tangents DE in c, the line Kb will be harmo- nically divided in the points K, a, c, and b. “ Demonstration—From the centre of the circle, 0, to the point 0, where K (2 cuts the circle K D OE, by which the points D and E were found, draw 00; then because of the semicircle K E0, the angle K o O is right; and therefore a o, and o b, a1e equal. “ Now because of the ciicle K DOE, Kc: CD :0 E: co; and likewise because of the circle ADBE, ac : cD :: CE : cb; wherefore, ac: K c : : co : c l). , “ But the parts ac and c b of the line K I), being bisected in o, as already shewn, the line K b is therefore harmonically divided in K, a, c, and 6. (Cor. 1. Lemma 9.) Q.E.D. “ If the line K B pass through 0, the centre of the circle, the demonstration that it is harmo- nically divided in K, A, C, and B, will be the same; the parts A C and C B of that line being bisected in O. “ Corollary.—-Hence, if a line, K b, drawn from K, through a circle, A D B E, cutting it in a and b, be harmonically divided in the points K, a,c, and b; the point c, if within the circle, will be a point in the chord of the tangents from K. “ Because, in the line K I), three points, K, a, and 6, being determined, and the part K a being taken as an extreme part, there can be no point between a and l), but one, which can divide that line harmonically (Lemma 2); and therefore it must be the point c, where it is cut by D E, the chord of the tangents from K. “ Lemma 1]. Figure 2.—-If from a point, K, with- out a circle, A D B E, a line, K B, be drawn through 0, the centre of the circle, cutting D E, the chord of the tangents, from K and C, and an- other line, L K, be drawn through K, perpendi- cularly to K B, and consequently parallel to DE; then, if from any point, L, in L K, a line, L G, be drawn through C, cutting the circle in F and G, theline LG will be harmonically divided in the points L, F, C, and G. “ Demonstration.——From K to G draw K G, cut- ting the circle in H and G, and DE, the chord of the tangents, from K, in N, and draw C H; then K G being harmonically divided in K, H, N, and G(Lem1na 10), C G, C N, C H, and C K, are harmonica] lines (Definition 2): from H draw H F 3 O 0 PER 468 - parallel to D E, one of the harmonicals, cutting the other three, C G, C K, and C H, in F, I, and H, then FH will be bisected by them in I (Lem- ma 7); but F H being perpendicular to A O, which passes through the centre of the circle, AD B E, and H being a point in the circum- ference, H F is therefore bisected by A O in I, and consequently F is a point in the circumfer- ence of the circle, as well as in the harmonica] C G. Lastly, draw K F, and because F H is bisected in I, and F H and L K are parallel, K L, K F, K I, and K H, are harmonical lines Lem- ma 4); and consequently the line, L G, which cuts these four harmonicals, is harmonically di- vided by them in the points L, F, C, and G. (Lemma 8.) Q. E. D. “ Corollary—Hence the chord of the tangents, from any point, L, in the line LK, must pass through the same point, C; and no lines in the circle, except such as pass through C, can be chords of tangents which will meet in any point of L K. “ Because from any point, L, in L K, a line may be drawn through C, which'will be harmonically divided by that point and the circle, and there- fore the chord of the tangents from L must pass through C. (Cor. Lemma 10.) “ But if the proposed chord do not. pass through C, and the tangent at either of its extremities be produced till it meet L K in any point, L, the tangent at its other extremity cannot pass through the same point L; in regard that the chord of the tangents from L must pass through C, and no more than two tangents can be drawn to a circle, which shall meet each other in one and the same point. “ Lemma 12. Figure 3.—lf from any point, K, without a circle, A D B E, a line, K B, be drawn, passing through 0, the centre of the circle, and the point C, where that line is cut by the chord of the tangents from K, be determined, and through K a line, L M, be drawn perpendicular to K B; then if any point, L, be taken in that line, and de, the chord of the tangents from that point, be produced till it cut L M in another point, M, and up0n L M, as a diameter, a semicircle, LY M, be described, that semicircle will cut K B in a point, Y, between C and O, which point Y will constantly be the same, wherever the point L is taken in the line L M. “ Demonstration.—-—Draw L O and M 0; then in the PER r triangles L K O, C N 0, de being perpendicular to L O, the angles C N O and L K O are right, and the angle N O C common to both triangles; therefore these two triangles are similar; and in the triangles C N O, C K M, the angles at N and K are right, and the vertical angles at C equal, therefore these two triangles are similar, and con- sequently the triangle L K O is similar to the tri- angle C K M, and therefore LK : KO: : KC: KM; and because of' the semicircle LY M, LK : KY : : KY: KM; therefore KC: KY : : K Y : K O. “ But the point C, in the line KB, being con- stantly the same, as well as the point 0, wherever the point L is taken in the line LM (Cor. Lemma 11); therefore the lines K0 and K C must al- ways continue the same, and consequently so will the line K Y, which is a mean proportional be- tween them; and for the same reason the point Y will always fall between C and O. (2.13. D. “ Corollary l.—It is evident, the semicircle LYM also passes through the points N and R, where L O and M 0 cut d e and 55, the chords of the tangents, from L and M ; the angles L N M and L R M, being both right. “Corollary 2.—lf LY and l\'IY be drawn, the angle L Y M will constantly be a right angle, wherever the point L is taken in LM. “ Lemma 13. Figure 4.~——The same things being supposed as before, the line K Y is equal to K E, the tangent to the circle from the point K. “ Demonstratiara—Because of the similar triangles KCE, KEO, KC:KE :: KE : KO; but K C : KY : : K Y : KO (Lemma 12); therefore KY : K E. Q.E. D. “ Corollary.—Hence, if KY be made equal to K E, and from any point, 3, in the line M L, as a centre, with the radius sY, a semicircle, L Y M, be described, cutting L M in any points L, and M; then a line, d e, drawn from M through C, and terminated by the circle in d and e, will be the chord of the tangents from L; and a line, 55, drawn from L through C, and terminated by the circle, will be the chord of the tangents from M. “ Lemma 14. Figure 5.~—-To divide a line, K O, in K, C, Y, and O, in such manner that K C, KY, and K 0 may be in continual proportion. “ 1. The whole line K O, and the point C, being given, thence to find Y. “ On K O, as a diameter, describe a semicircle, PER 469 1 “—— 0 E K ; from C erect. C E, perpendicular to K 0, cutting the semicircle in E; and having drawn K E, make K Y equal to it; and Y will be the point sought. . . ' “ For the triangles K C E, K E 0, being Slmllal‘, KC:KE:KY::KY:KO. “ 2. The whole line, K O, and the point, Y, being given, thence to find C. “ Having drawn the semicircle O E K as before, from K, as a centre, with the radius K Y, describe an arch cutting the semicircle in E, from whence EC, drawn perpendicular to OK, will cut it in C, the point desired. “ 3. The points K, C, and Y, being given, thence to find the extremity O. “ Draw C E perpendicular to K Y, and from the centre, K, with the radius KY, describe an arch cutting C E in E; and having drawn K E, draw E0 perpendicular to it, which will cut K Y in O, the point required. “ 4. The points 0, Y, and C, being given, thence to find the extremity K. i “ From any point, E, without the given line,draw E O and E C, and from Y draw Yx parallel to E 0, cutting E C in c, and a line, E .1“, parallel to O C in .1‘; and having, in Yr, taken c d, equal to cY, find a point, It, between c and (1, whereby Y .r may be harmonically divided in Y, lc, d, and 1(Lemma 1): then Ek being drawn, it will cut 0 C in K, the point sought. “ Demonstration.—Because, by the supposition, K C: K Y :: K Y : K 0; therefore, by division, KC:KY-——KC:CY :: KY:K0--KY = YO; andKC being less than KY, CY is therefore less than Y O, or its equal Ex ; where- fore also Y c, or its equal 6 d, is less than ex, and consequently E d produced, will meet 0 C in some point, D. “ Now because Y d, parallel to E O, is bisected in c, EY, Ec, Ed, and E O, are harmonical lines (Lemma 4) and the line 0 D, which is parallel to none of them, is therefore harmonically divided by them in O, Y, C, and D (Lemma 8); and be- cause Y x is harmonically divided in Y, k, d,~ and r, E Y, E h‘, Ed, and E .1“, are harmonical lines (Definition 2); wherefore Y D, which is parallel to E 1*, one of these harmonicals, is bi- sected by the other three in Y, K, and D (Lemma 7); but the whole line, 0 D, being harmonically divided in O, Y, C, and D, and its two adjoining parts, Y C and C D, taken together, being bisect- PER ed in K, as already shewn, therefore KC : KY : : K Y : KO (Lemma 9) and consequently the point K is rightly determined. Q. E. I. “ PROBLEM XIII.—An originalcircle, which doth not cut or touch the directing line, being given; therein to determine the originals if the axes, or any other conjugate diameters (f the ellipsis, formed by the image of the circle, and other lines and points in the ellipsis above described. “ Case 1. Figure 6.-—Let Z be the original plane, LM the directing line, and I K the eye’s director; and let A D B E be a circle in that plane, and 0 its centre. “ To find the originals of the conjugateaxes and their ordinates, and of the centre of the ellip- sis, and also of the tangents at the extremities of the axes. . “ Through the centre, 0, draw a diameter, a b, perpendicular to LM, cutting it in k, and find de, the chord of the tangents to the circle from It, cutting a b in C; take IcY in k a, equal to the tangent k e, and draw I Y, and bisect it by the perpendicular T 0, cutting LM in o; from o, as a centre, with the radius 0 I, or oY, draw the semicircle L I Y M, cutting L M in L and M: lastly, from M and L, through C, draw M A, L E, terminated by the circle in A, B, D, and E. “ Then A B and D E will be the originals of the conjugate axes of the ellipsis, and C the original of its centre; and all lines drawn from L, through the circle, and terminated by it, will be originals of double ordinates to the axis whose original is AB, and all lines drawn from M, terminated in like manner by the circle, will be the originals of ordinates to the axis whose original is D E, and L and M will be the directing points of those or- dinates respectively. “ Demonstration—Because AB is the chord of the tangents to the circle from L, and D E is the chord of the tangents from M (Cor. Lemma 13) therefore LE and M A are harmonically divided by the circle and the point C (Lemma 10); and L and M being directing points, the images of A B and D E are therefore bisected by the image of C (Cor. 5, Lemma 8); wherefore A B and DE are the originals of two diameters, and C the original of the centre of the ellipsis; and be— cause all lines drawn from L, cutting the circle. and the line A B, are harmonically divided by the circle and that line (Lemma 10) the images of the parts of those lines which lie within the circle; PER 470 PER are bisected by the image of A B (Cor. 5, Lemma 8) and are therefore double ordinates to the dia- meter represented by A B; and because of the directing point L, the images of all those lines being parallel to each other, and to the image of D E, (Cor. 4.) D E is therefore the original ofa dia- meter of the ellipsis, conjugate to the diameter represented by A B; and as theimages ofall lines drawn from M, and terminated by the circle, are parallel to the image ofA B, and bisected by the image of D E, they are therefore double ordinates to the diameter represented by D E. Lastly, be- cause of the semicircle LI Y M, the angle L I M is right; and I M and I L being the directors of A B and D E, their images are therefore perpen- dicular, consequently A B and D E being the ori- ginals of two conjugate diameters, which are per- pendicular to each other and to their respective L ordinates, AB and DE are the originals of the axes of the ellipsis, and M and L are the direct- ing points of their respective ordinates; and if through M and L, the tangents to the circle M D, M E, LA, LB, be drawn, their images will be tangents to the ellipsis in the extremities of the axes represented by D E and A B. Q. E. I. “ Corollary l.—-The originals, A B and D E, of the axes being found, thence to determine which of them represents the transverse axis. “ Bisect the angle L I M, made by the directors of the axes, by the line Ix, cutting L M in x; and from x, through the extremity, A, of either of the axes, AB, draw xA till it cut D E, the original of the other axis in n; then if the point It fall without the circle, AB will be the original of the transverse axis; but if 12 fall within the circle, A B will be the original of the second axis. “ For the angle L I M being bisected by Ix, the image of the triangle rzCA is an isosceles tri— angle, having its sides corresponding to C72 and CA equal; wherefore if C D be shorter than Cn, its image will be shorter than the image of Cn, and consequently shorter than that of CA; wherefore CA is the original of the longer or transverse semiaxis. On the contrary, if 11 fall within the circle, the image of CD would be greater than the image of C n or A C, and D F. would then be the original of the transverse axis. “ If, instead of drawing xA, aline, x D, were drawn, it would out A C within the circle, which Would still shew CA to be the original of the longer semiaxis. “ Corollary ‘L—The chord of the tangents to the circle from any point, L, in the line LM, is always the original of a diameter of the ellipsis, and if a line be ‘drawn through the same point L and the point C, it will be the original of a dia- meter conjugate to the other. “ For the chord of the tangents from any point, L, in the line L M, always passes through C (Cor. Lemma 11) which is the original ofthe centre of the ellipsis; and L being the directing point of the ordinates to that diameter, a line drawn through that point and the point C, must be the original of another diameter of the ellipsis, pa- rallel to the 'ordinates of the first, and conse- quently conjugate to it. “ Corollary 3.—-The diameter, a b, of the circle, which is perpendicular to the directing line, is always the original of a diameter of the ellipsis; and de, the chord of the tangents to the circle from k, where the perpendicular diameter, a b, meets the directing line, is always the original of a diameter of the ellipsis conjugate to the dia- meter represented by a b; and a b is the only dia- meter of the circle, the image of which can be a diameter of the ellipsis. “ For ab, passing always through C, is therefore the original of a diameter of the ellipsis, and de, which passes through C, is the original of another diameter; and in regard the image of d e, and of all other lines drawn in the circle parallel to ale, and terminated by the circle, are parallel to each other, and bisected by the image of ab, all such lines are the originals of double ordinates to the diameter represented by a l); wherefore the dia- meter represented by d e, which is parallel to those ordinates, is conjugate to the diameter re- presented by a 1);, and it is evident, that no other diameter of the circle, besides a b, can pass through C, and therefore that no other diameter of the circle can be the original of a diameter of the ellipsis. “ Case Q.—If the centre of the circle be in the line of station, that is, if It were the foot of the eye’s director, then a b and d e would be the origi- nals of the conjugate axes. “ Demonstration.——For a l) and d e are the origi- nals of two conjugate diameters (by Corollary 3, Case 1, of this Problem) and their images in this position of the circle being perpendicular, they are therefore the originals of the axes. Q. E.D. L fin u'n 141/1." 74'1112bvm. LPEKREKPIECTFIVWE. iK [‘13]. A9. 1y; \ 1yu&a .L._. m... . PER 471 PER “ Corollary—If J be the place of the eye, and it be required to determine which of the lines, a b or de, is the original of the transverse axis; take km on the directing line, equal to kJ, the height of the eye; and from at, through d, draw a line, which ifi't cut a b within the circle, will shew a b to be the original of the transverse axis; but if it cut a b without the circle, a b will be the original of the shorter axis. (Corollary 1, Case 1, of this Problem.) “ For here de, the original of one of the axes, being parallel to the directing line, its imaginary director is a line drawn parallel to it through J, and J]: is the director of the other axis; if then the right angle made by these two directors be bisected by aline from J, it is evident that line must cut LM in x, so that ch and kx will be equaL “ Case 3.—-If the centre of the circle be in the line of station, and the height of the eye be equal to I: Y , the image of the circle will be a circle, that is, the section of the visual cone by the picture will be subcontrary. “ It has been already shewn, that when the centre of the forming circle is in the line of station, the lines a b and de are the originals of the conjugate axes (Case 2); it must be now shewn, that at the height of the eye, It Y, the images ofa b and de are equal, and consequently that the curve pro- . duced is a circle. “ Demonstration. Figure 6.—Because of the circle ADBE, Ca: Ce: : Ce: Cb; andalsoka :ke ::lce:lcb; and because I: a is harmonically di- vided in .75, b, C, and (1 (Lemma 10) Ca : Cb : : k a : kb; consequently, Ca: ka : : Ce :ke; but, by the supposition, Ice is equal to k Y, the director of the line ka, therefore Ce : hY : : Ca : ha. . “And consequently the images of Ca and Ce are equal: but the images of Ca and Cb being equal, as also the images of Ce and C d (Cor. 5, Lemma 8) the image of a b is therefore equal to the image of d e, and consequently the curve produced by the image of the circle, is a circle. Q. E. D. “ PROBLEM XIV;—Theimage oft/rat diameter qfa circle which is perpendicular to the directing line of its plane, being given; thence to determine the axes, or any two other conjugate diameters of the ellipsis formed by the image of the circle. “ 1. To determine the axes. , “ Figure 7.—-Let E F be the vanishing line of the plane of the circle, 0 the centre of that vanishing line, and I 0 its distance; and let ab be the given image of the diameter of the circle, its vanishing point being 0, and s the image of the centre of the circle. ' “ Bisect ab in c, which will he the centre of the ellipsis, a b being one ofits diameters; then take 0 y, \in the line a b, a mean proportional between ab and 0a, (Lemma 14) and draw Iy: bisect Iy in t, by the perpendicular tv, cutting EFin v, and from v, asa centre, with the radius 1: y, or v I, de- scribe the circle I ly m, cutting E F in land m, and draw ly and my: lastly, through c draw A a parallel to ly, and Bb parallel to my; and Aa, and Bb, will be the indefinite axes sought. Demonstration. Figures 8 and 9.-——Here a b repre— sents the diameter, a b, of the circle, A D B E, in Figure 8, No. 1, and 0 represents C; and be- cause lcY, in that figure, is a mean proportional between I: a and k b, the image of Y will fall in such manner in a b, as that o y will be a mean proportional between 0 b and o a, wherefore y, found as before directed, is the representation of Y in the other figure. “ Again, the situation of L and M with respect to Y, in the original plane, is such, that lines drawn from L and M to Y, are not only perpen- dicular, but have perpendicular images; now be— cause of the circle I l ym, whose diameter is lm, the angles Mn: and lym are both right, there- fore ly and my are perpendicular, as well as their originals, and consequently represent L Y and MY in the original plane, there being no two other lines which can pass through y with these conditions, in regard that e is the only point in E F, from whence, as a centre, a circle can be de- scribed which shall pass through I and y; and because of the directing points L and M, the images of LC and M C, which pass through C, are parallel to the images of L Y and M Y, where- fore the indefinite lines, A a and B b, drawn in the picture through c, parallel to ly and my, repre- sent LC and M C in the original plane, and are therefore the indefinite axes desired. Q. E. I. “ Now to determine the length of the axes thus found: “ Through either of the extremities, b, of the given diameter, a b, draw rw parallel to EF, cut- ting A a and B b in r and w; and through b and a draw b B and a a parallel to A a, and b a and (1/3. parallel to B b, cutting Aa in p and 7r, and B b in PER 4 q and K; on 7r1‘, as a diameter, describe a semi- circle, cutting Bb in v, and make 6A and ca each equal to c v; also, on em as a diameter, de— scribe a semicircle, cutting A3. in u, and make cB and c b each equal to c u; then Aa and B b will be the determinate axes sought. “ Demonstration.——-For the original of rw being perpendicular to the original of ab, which is a diameter of the forming circle, it is therefore a tangent to the circle in the point represented by h,- rw is therefore a tangent to the ellipsis form— ed by the image of the circle in b and hp, being an ordinate to the axe A a, and r the point where . the tangent from b cuts that axe, the half of that axe is amean proportional between cp and cr; but by the construction c7:- and cp are equal, therefore cv, which is a mean proportional be- tween cr'and .e r, is also a mean proportional be- tween cp and c r, consequently cA and c a being taken each equal to cv, the axe Aa is thereby rightly found: after the same manner cq and .c I: being by construction equal, c n, which is a mean proportional between c K and c w, is also a mean proportional between cq and c w; wherefore .cB and c b being each taken equal to cu, the axe Bb is thereby truly determined. Q. E. I.” On many occasions, the representation of the square circumscribing the original circle is very frequently given; in this case, the following me- thods will be very ready, in practice, for small objects, where only few points are necessary. PROBLEM XV.-—The representation of a square circumscrib'ing an original circle, being given; to find the representation of the inscribed circle. Figure 1.—Let a b c d be the representation of «the circumscribing square, then if the vanishing line, V L, is given, let V be the vanishing point :of the sides a d and b c, and L the vanishing point of the sides do and a I); draw the diago- nals a c and hd, and let. the diagonal, a 6, meet the vanishing line, V L, in D, its vanishing point. Through a, the representation of the nearest angle, draw a m, parallel to the vanishing line VL; join Dd, and produce Dd to m -; bisect am in n, and m n in o; draw .0 p at right angles to m n; make 0 p equal to o n or o m, and make n q equal n p; make a 1' equal to m q; from the points qn and r draw lines towards the vanishing point D, of the diagonal, to cut the side ad, of the quadrilateral representing the square; from the points of divi- sion in a d, draw lines; to the vanishing point ,L, '2 PER —* cutting the diagonals in e, k, i, g, and the oppo- sides in land h; also drawfj through the repre- sentation of the centre, cutting the other two opposite sides infandj; then through the points e,f, g, h, i,j, k, l, to e, draw a curve; and efg [2 ij It 1 e will be the representation of the circle required. No. l, of this diagram shews the representation above the vanishing line, as No. 2, does below it: the same description will apply to either. l’Vhen two sides if the square are parallel, and consequently the other two perpendicular, to the picture. Figure 2.—-Let a b and c d be the representation of the parallel sides, a d and h c those of the sides perpendicular to the picture, which will conse- quently vanish in C, the centre of the picture. Bisect a b in j, and join j C, cutting c din o; thenj and 0 are opposite points of contact; draw the diagonal b d, cutting jo in q; through 9 draw mg, parallel to a 1), cutting the sides, ad and be, of the trapezoid in m and g, which are also points of contact. Produce q g to e; make g e equal to g q : join e0, as also cj, cutting each other atf; draw fn parallel to a 6, cutting oj at p. In the diameter, oj, makej r equal to op, and-j s equal to oq: through the points r, s, draw k 2' and lh parallel to a h: makep n equal to pf; rk and ri also equal to pf; makes h and sl equal to q g, or q 772; draw the ellipsis fg h ij I; l m n of, and it will be the representation re- quired. This description applies to the representation of any circle in a plane perpendicular to the picture in any position to the horizon, whether parallel, perpendicular, or inclined. No. l, is a representation of a semicircle in a ver- tical plane, upon the diameter oj: No. 3, is the representation of a whole circle in a vertical plane: Numbers 2 and 4, are the representations of circles in planes parallel to the horizon: No.2, is the representation of a circle parallel to the va- nishing plane, above the level of the eye; and No. 4, is the representation of a circle, parallel to the vanishing plane, below the level of the eye. To represent a series of arches in perspective. Plate III. B.-Supposing the breadth of the piers and'the breadth of the arches already found or given in perspective; let a h be the representation of the span of an arch; divide a h perspectively . to represent any even number of equal parts: w , n -.~ . r, 1v"~\'- u I - a» 134'1* r—ij-na‘fmr,vyu ; $.17 4 ""‘3‘7 .7. r: ' .‘H , - , .. PERSPECTIVE. PLATEHLA. fizz/awed & Drawn by I? Nd‘iwlmn. . londonJ’uéldc/Ltd 53/ 1? 2171”")er X- .ZBarr'z'elzl, [Val-«Imu- Jb'etc16’14. ~ [nymvid by ”flurry.