Equal pyramids, &c., reciprocate their bases and altitudes, i. e. the altitude of one is to that of the other, as the base of the one is to the base of the other. 8. A sphere is equal to a pyramid whose base is equal to the surface, and its height to the radius of the sphere.

PYRAMID, FRUSTUM OF A. See FRUSTUM.

PYRAMIDION.

The small flat pyramid which terminates the top of an obelisk. PYTHEUS. See ARCHITECTS, list of, 8.

Q.

QUADRA. (Ital.) A square border of frame round a basso-relievo, panel, &c. ; the term is not strictly applicable to any circular border. The term is also applied to the bands or fillets of the Ionic base on each side of the scotia; and also to the plinth or lower member of the podium.

QUADRANGLE. Any figure with four angles and four sides. This term is in architecture in England applied to the inner square or rectangular court of a building, as in the college courts of Oxford, &c.

QUADRANT. (Lat.) The quarter of a circle, or an arc of it containing ninety degrees within its enclosed angle.

QUADRATURE. (Lat.) The determination of the area of a figure in a square, or even any other rectilinear form.

QUADRELS. Artificial stones perfectly square, whence their name, much used formerly by the Italian architects. They were made of a chalky or whitish and pliable earth, and dried in the shade for at least two years.

QUADRIFORES. (Lat.) In ancient architecture folding doors whose height was divided into two parts. When they opened in one height, they were termed fores valvatæ or

valvæ.

QUADRILATERAL.

In geometry a figure whose perimeter consists of four right lines making four angles, whence it is also called a quadrangular figure. QUARREL, vulgarly called QUARRY. (Fr. Carré.) A square or lozenge-shaped piece of glass used in lead casements.

QUARRY. (Irish, Carrig.) A place whence stones or slates are procured. The principal stone quarries of England have been given in the body of the work, Book II. Chap. II. Sect. 1. to which place the reader is referred. The slates obtained from the different quarries of the country may be found from the information in Book II. Chap. II. Sect. 8. QUARRYING. The operation of extracting the produce of a quarry is one which requires much practical knowledge to render it beneficial to the owner of a quarry, but in respect of the particulars whereof this work does not require our notice.

QUARTER GRAIN. See FELT GRAIN.

QUARTER PARTITION. One consisting of quarters.

QUARTER ROUND. The same as OvOLO and ECHINUS, which see, being a moulding whose profile is the quadrant of a circle.

QUARTERING. A series of quarters, as in a partition, &c.

QUARTERFOIL. (Fr. Quatrefeuille.) A modern term denoting a form disposed in four segments of circles, and so called from its imagined resemblance to an expanded flower of four petals. It is only found in the windows, pannels, &c., of Gothic architecture. Mr. Gunn with charming simplicity, not unusual among the amateur writers on Gothic architecture, thinks that the form has no reference to any type in the vegetable kingdom, but that it was originally a representation of the Greek cross rounded towards the extremities. If the writings on the subject from the two universities of the country were all put in juxtaposition, they would perhaps afford more scope for mirth than was ever exhibited on any subject.

QUARTERS. Small vertical timber posts, rarely exceeding four by three inches, used instead of walls for the separation or boundary of apartments. They are placed, or ought to be, about twelve inches apart, and are usually lathed and plastered in the internal apartments, but if used for external purposes are commonly boarded.

QUARTZ. (Germ.) A mineral production better known by the name of rock crystal. It includes a variety of stones with which we have nothing here to do, and the only motive for mentioning it is its occurrence in the granites, wherein it is immediately recognised, from its glass-like appearance.

QUAY. (Fr.) A bank formed towards the sea or on the side of a river for free passage, or for the purpose of unloading merchandise.

QUEEN-POST. A suspending post where there are two in a trussed roof,

QUICKLIME. See Book II. Chap. II. Sect 10.

QUIRK.

A piece taken out of any regular ground-plot or floor; thus, if the ground

plan were square or oblong, and a piece were taken out of the corner, such piece is called a quirk

QUIRK MOULDING. One whose sharp and sudden return from its extreme projection to the re-entrant angle seems rather to partake of a straight line on the profile than of the curve. Of this class are a great number of the ancient Greek mouldings.

QUOINS. (Fr. Coin.) A term applied to any external angle, but more especially applied to the angular courses of stone raised from the naked of the wall at the corner of a building, and called rustic quoins. See RUSTIC QUOINS.

R.

RABBET. See REBATE.

RABIRIUS. See ARCHITECTS, list of, 44.

RACK. The case, enclosed by bars, over the manger in a stable, wherein the hay is placed for the horses.

RADIAL CURVES. In geometry, those of the spiral kind whose ordinates all terminate in the centre of the including circle, and appear like so many radii of such circle.

RADIUS. In geometry, the semidiameter of a circle, or a right line drawn from the centre to the circumference.

RADIUS OF CURVATURE. The radius of the osculatory circle at any point in a curve. See OSCULATORY CIRCLE.

RAFFAELLE D'URBINO. See ARCHITECTS, list of, 185.

RAFTERS. (Quasi, Roof-trees.) The inclined timbers of a roof, whose edges are in the same plane which is parallel to the covering. The rules and regulations that affect their disposition will be found in p. 544, et seq.

RAGS and RAG SLATES. See Book II. Chap. II. Sect. 8.

RAIL. (Germ. Riegel.) A term applied in various ways, but more particularly to those pieces of timber or wood lying horizontally, whether between the panels of wainscotting or of doors, or under or over the compartments of balustrades, &c.; to pieces, in framing, that lie from post to post in fences; in short, to all pieces lying in an horizontal direction which separate one compartment from another.

RAIMOND. See ARCHITECTS, list of, 93.

RAIN-WATER PIPE. One usually placed against the exterior of a house to carry off the rainwater from the roof.

RAISING PIECE. One which lies under a beam or beams and over the posts or punchions. The term is chiefly used in respect of buildings constructed of timber framework.

RAKING. A term applied to any member whose arrisses lie inclined to the horizon. RAMP. (Fr.) In handrails, a concavity on the upper side formed over risers, or over a half or quarter pace, by a sudden rise of the steps above, which frequently occasions a knee above the ramp. The term is also applied to any concave form, as in coping, &c., where a higher is to be joined by a continued line to a lower body. RAMPANT ARCH. One whose abutments or springings are not on the same level. RANGE OF RANGING. (Fr.) A term applied to the edges of a number of bodies when standing in a given plane. Thus, if the edges of the ribs of a groin were placed in a cylindric surface, they would be said to range. It is also used in respect of a work that runs straight without breaking into angles.

RANULPH. See ARCHITECTS, list of, 91.

RARI.

RATE.

See ARCHITECTS, list of, 140.

An expression used in the Building Act (see p. 819.) to denote the particular class to which a building belongs, in order to determine the thickness of its walls and mode of building.

RAY, PRINCIPAL. spective plane. REBATE. (Fr. Rebattre.) A groove or channel cut on a piece of wood, longitudinally, to receive the edge of a body, or the ends of a number of bodies that are to be secured to it. The depth of the channel is equal to the thickness of the body; so that when the end of the latter is let into the rebate, it is in the same face with the outside of the piece.

In perspective, the perpendicular distance between the eye and the per

REBATE PLANE. One used for sinking rebates.

RECESS. (Lat. Recedo.) A cavity left in a wall, sometimes for use, as to receive a sideboard, bed, &c., or to add to the quantity of floor room, and sometimes for ornament, as when formed into a niche, &c.

RECTANGLE. In geometry, a figure whose angles are all right angles. Solids are called rectangular with respect to their position, as a cone, cylinder, &c., when perpendicular to the plane of the horizon. A parabola was anciently called a rectangular section of a cone.

RECTIFICATION. In geometry, the finding of a right line that shall be equal to a given curve, or simply finding the length of a curve.

RECTILINEAR. A figure whose boundaries are right lines.

REDE. See ARCHITECTS, list of, 143.

REDUCT. A quirk or small piece taken out of a larger to make it more uniform and regular.

REDUCTION of a figure, design, or draught, is the copying it on a smaller scale than the original, preserving the same form and proportions. For this purpose a pair of proportional compasses are generally used, by which the labour is much lessened. REFECTORY. (Lat.) A room for taking refreshments. See ABBEY.

REFLEX. The light reflected from a surface in light to one in shade.

REGLET. (Fr.) A flat narrow moulding, used chiefly to separate the parts or members of compartments or panels from each other, or to form knots, frets, and other ornaments. REGRATING. In masonry, the process of removing the outer surface of an old hewn stone, so as to give it a fresh appearance.

REGULA. (Lat.) A band below the tænia in the Doric architrave.

REGULAR. An epithet to a figure when it is equilateral and equiangular. A body is said to be regular when it is bounded by regular and equal planes, and has all its solid angles equal.

REGULAR ARCHITECTURE.

parts.

That which has its parts symmetrical or disposed in counter

REGULAR CURVES. The perimeters of conic sections, which are always curved after the same geometrical manner.

REINS OF A VAULT. The sides or walls that sustain the arch.

REJOINTING. The filling up the joints of stones in old buildings when the mortar has been dislodged by age and the action of the weather.

RELATION. The direct conformity to each other, and to the whole, of the parts of a building.

REMIGIUS. See ARCHITECTS, list of, 82.

RENDERING. The act of laying the first coat of plaster on brickwork.

REPLUM. (Lat.) In ancient architecture, the panel of the impages of a framed door. REREDOS. (Fr. Arriéredos.) A screen or division wall placed behind an altar, rood-loft, &c., in old churches.

RESERVOIR. (Fr.) An artificial pond, basin, or cistern for the collection and supply of

water.

RESISTANCE. That power which, acting in opposition to another, tends to destroy or diminish its effect. There are several sorts of resistance, arising from the various natures and properties of the resisting bodies, as the resistance of solids, fluids, air, &c.

The resistance of solid bodies is the force with which their quiescent parts retain their aggregation. Of it there are two kinds: first, where the resisting and the resisted parts are only contiguous and do not cohere, or, in other words, where they consist of separate bodies or masses. This is by Leibnitz called the resistance of the surface, now however called friction. Second, where the resisting and resisted parts are not only contiguous, but cohere, that is, are parts of the same continued body or mass. To these may be added the resistance that takes place between surfaces or solids when completely in contact, though not forming the same body, or the resistance they offer to separation. To form a notion of the resistance of the fibres of solid bodies, suppose a cylindrical body suspended vertically by one of its ends. Here the weight of the parts makes them tend downwards and endeavours to separate the body where it is weakest. The parts, however, resist this separation by the force with which they cohere. In this case, then, we see two opposite powers, viz. the weight of the cylinder, which has a tendency to break it, and the force of cohesion to resist fracture. If the base of the cylinder be increased, the length remaining the same, it is manifest that the resistance will increase as the base; but the weight will also increase in the same ratio. Hence, all cylinders of the same matter and length, when vertically suspended, have an equal resistance, whatever their bases. When the length of the cylinder is increased, the base and the resistance remaining the same, the additional weight weakens it, and it will have a greater tendency to break.

We thus learn what length a cylinder may be so as to break with its own weight, by finding what weight is just sufficient to break another cylinder of the same base and matter; for the required length must be such that its weight may be equal to that of the first, with the additional weight employed to produce the separation.

If the cylinder be fixed horizontally into a wall, and the rest thence suspended, the weight and resistance will act under different conditions, for if it broke by the action of its weight, the fracture would occur at the end fixed into the wall. In the fracture of the cylinder two forces have acted, and one has overcome the other; that is, the weight of the mass of the cylinder has overcome the resistance arising from the largeness of the base; and as the centres of gravity are points in which all the forces arising from the

weights of the several parts of the same bodies are supposed to be collected, we may conceive the weight of the whole cylinder applied in the centre of gravity of its mass, that is, in a point in the middle of the axis; and the resistance of the cylinder applied in the centre of gravity of its base, it being the base which resists the fracture. If the cylinder breaks with its own weight all the motion is on an immoveable extremity of the diameter of the base, which extremity is the fixed point of a lever, whose arms are the radius of the base and half the axis; hence, the two opposite forces do not only act of themselves and by their absolute, but also by the relative force derived from their distance with regard to the fixed point of the lever.

The weight required to break a body placed horizontally being always less than that required to break it when placed vertically, and being greater or less according to the ratio of the two arms of the lever, the theory is reducible to the finding what part of the absolute weight the relative weight must be, supposing the figure of the body known, which is necessary for finding the centre of gravity. But wherever the centre of gravity falls, the two arms of the lever are estimated accordingly. If the base by which the body is fixed in the wall be not circular, but, for an example, parabolical, and the vertex of the parabola be at top, the motion of the fracture will not be on an immoveable point, but on a whole immoveable line, which may be termed the axis of equilibrium, and it is with regard thereto that the distances of the centres of gravity are to be determined.

A body horizontally suspended, being such that the smallest addition of weight would break it, there is an equilibrium existing between its positive and relative weight; those two opposite powers are consequently to each other reciprocally as the arms of the lever to which they are applied. So, e converso, the resistance of a body is always equal to the greatest weight it will sustain, without breaking, in a vertical situation, that is, equal to its absolute weight. If we, therefore, substitute actual weight for the resistance, it follows that the absolute weight of a body suspended horizontally is to its relative weight, as the distance of the centre of gravity from the axis of equilibrium is to the distance of the centre of gravity of its base from the same axis. From this fundamental proposition many consequences are deducible. Thus, if the distance of the centre of gravity of the base from the axis of equilibrium be half the distance of the centre of gravity of the body, the relative weight will only be half the absolute weight.

M. Mariotte having observed that all bodies bend before breaking, considers the fibres as so many little bent springs, never exerting their whole force till stretched to a certain point, and never breaking till entirely unbent. Hence those nearest the axis of equilibrium, which is an immoveable line, are less stretched than the more distant ones, and consequently employ a less part of their force.

The following is a synopsis of the most important results that have been drawn by different writers on the subject, both practical and theoretical : —

1. The resistance of a beam or bar to a fracture by a force acting laterally is as the solid made by a section of the beam in the place where the force is applied, into the distance of its centre of gravity from the point or line where the breach will end.

2. In square beams the lateral strengths are as the cubes of their breadths and depths.

3. In cylindric beams, the resistances of strengths are as the cubes of the diameters. 4. In rectangular beams the lateral strengths are conjointly as the breadths and squares of the depths.

5. The lateral resistances of any beams whose sections are similar figures and alike placed are as the cubes of the like dimensions of those figures.

6. The lateral strength of a beam, with its narrower face upwards, is to its strength with the broader face upwards, as the breadth of the broader face to the breadth of the

narrower.

7. The lateral strengths of prismatic beams, of the same materials, are as the areas of the sections and the distance of their centre of gravity directly, and as their lengths and weights reciprocally.

8. When the beam is fixed at both ends, the same property has place, except that in this case we must consider the beam as only half the length of the former.

9. Cylinders and square prisms have their lateral strengths proportional to the cubes of their diameters or depths directly, and their lengths and weights inversely.

10. Similar prisms and cylinders have their strength inversely proportional to their linear dimensions.

The relative resistance of wood and other bodies is shown in the following table : — Proportional Resistance.

Elm, ash

Box, yew, plum tree, oak

11

8478

The following table shows the cohesive force of a square inch of different substances from the experiments of Professor Robinson:

Oak and beech in the direction of their fibres from 8000 to 17-000

RESSAULT. (Fr.) The recess or projection of a member from or before another, so as to be out of the line or range with it.

RETAINING WALLS. Such as are built to retain a bank of earth from sliding down.

RETICULATED. Like the meshes of a net. The reticulatum opus of the ancients is described under the article MASONRY, which see.

RETUM. The continuation of a moulding, projection, &c., in an opposite direction. A side or part which falls away from the front of a straight work. RETUM BEAD, See BEAD AND DOUBLE QUIRK.

REVEALS. (Lat. Revello.) The vertical sides of an aperture between the front of the wall and the window or door frame.

REVOLUTION. In geometry, the motion of a point or line about a centre. Thus a right-angled triangle, revolving round one of its legs as an axis, generates a cone in its revolution.

RHOMBOID. (Gr.) A quadrilateral figure whose opposite sides and angles are equal. RHOMBUS. (Gr.) A quadrilateral figure, whose sides are all equal, and whose opposite angles are respectively equal, two being obtuse and two acute.

RIB. (Sax.) An arch-formed piece of timber for supporting the lath and plaster work of a vault.

RIBBING. An assemblage of ribs for a vault or coved ceiling.

RIDGE. (Sax.) The highest part of a roof. The term is more particularly applied to the piece of timber against which the upper end of the rafters pitch.

RIDGE TILE. A convex tile made for covering the ridge of a roof.

RIGA TIMBER.

RIGHT ANGLE.
RIGHT CIRCLE.

RIGHT LINE.

See p. 484.

One containing ninety degrees.

A circle drawn at right angles with the plane of projection.
A line perfectly straight.

RILIEVO (It.) or RELIEF. The projecture from its ground of any architectural ornament.
Among sculptors there are three degrees of rilievo; namely, alto rilievo, when the figure
stands quite out from its ground; mezzo rilievo, when one half of the figure projects;
and basso rilievo, when the figures are raised from the ground in a small degree.
RIPLEY. See ARCHITECTS, list of, 283.

ROD. A measure of length equal to 16 feet. A square rod is the usual measure of brickwork, and is equal to 2724 square feet.

ROD STONE OF OOLITE. A kind of limestone, found under chalk in various parts of England. See Book II. Chap. II. Sect. 4.

ROGER, ARCHBISHOP OF YORK. See ARCHITECTS, list of, 97.

ROLLS.

Pieces of wood prepared for the plumber to turn over the lead where the sheets join, so as to protect the flat roof or edge from the admission of water. The term also signifies in Gothic architecture mouldings representing bent cylinders. ROLLS OF ROLLERS. Among workmen are plain cylinders of wood, seven or eight inches diameter and three or four feet long, used for the purpose of moving large stones, beams, and other heavy weights. They are placed successively under the fore part of the masses