calculation, whenever the arch is important, or presents any complication of form. The drawings should, in the first place, be made to a scale sufficiently large to determine the parts with accuracy, and from these, pattern drawings giving the parts in their true size may be made for the use of the mason. To make the pattern drawings, the side of a vertical wall, or a firm horizontal area may be prepared, with a thin coating of mortar, to receive a thin smooth coat of plaster of Paris. The drawing may be made on this surface in the usual manner, by describing the curve either by points from its calculated abscissas and ordinates, or, where it is formed of circular arcs, by using the ordinary instrument for describing such arcs when the centres fall within the limits of the prepared surface. In ovals the positions of the extreme radii should be accurately drawn either from calculation, or construction. To construct the intermediate normals, whenever the centres of the arcs do not fall on the surface, an arc with a chord of about one foot may be set off on each side of the point through which the normal is to be drawn, and the chord of the whole arc, thus set off, be bisected by a perpendicular. This construction will generally give a sufficiently accurate practical result for elliptical and other curves of a large size. 506. The masonry of arches may be either of dressed stone, rubble, or brick.

In wide spans, particularly for oval and other flat arches, cut stone should alone be used. The joints should be dressed with extreme accuracy. As the voussoirs have to be supported by a framing of timber, termed a centre, until the arch is completed, and as this structure is liable to yield, both from the elasticity of the materials and the number of joints in the frame, an allowance for the settling in the arch, arising from these causes, is sometimes made, in cutting the joints of the voussoirs false, that is, not according to the true position of the normal, but from the supposed position the joints will take when the arch has settled thoroughly. The object of this is to bring the surfaces of the joints into perfect contact when the arch has assumed its permanent state of equilibrium, and thus prevent the voussoirs from breaking by unequal pressures on their coursing joints. This is a problem of considerable difficulty, and it will generally be better to cut the joints true, and guard against settling and its effects by giving great stiffness to the centres, and by placing between the joints of those voussoirs, where the principal movement takes place in arches, sheets of lead suitably hammered to fit the joint and yield to any pressure.

507. The manner of laying the voussoirs demands peculiar care, particularly in those which form the heads of the arch. The positions of the inner edges of the voussoirs are determined by fixed lines, marked on the abutments, or some other immovable object, and the calculated distances of the edges from these lines. These distances can be readily set off by means of the level and plumb-line. The angle of each joint can be fixed by a quadrant of a circle, connected with a plumb-line, on which the position of each joint is marked.

508. Brick may be used alone, or in combination with cut stone, for arches of considerable size. When the thickness of a brick arch exceeds a brick and a half, the bond from the soffit outward presents some difficulties. If the bricks are laid in concentric layers, or shells, a continuous joint will be formed parallel to the surface of the soffit, which will probably yield when the arch settles, causing the shells to separate (Fig. 80). If the bricks are laid like ordinary string courses,

N

M

Fig. 80-Represents an end view, M, of a brick arch built with blocks, C, and shells, A and B.

N, represents the manner of arranging the courses of brick forming the crown of the arch.

forming continuous joints from the soffit outward, these joints, from the form of the bricks, will be very open at the back, and, from the yielding of the mortar, the arch will be liable to injury in settling from this cause. To obviate both of these defects, the arch may be built partly by the first plan and partly by the second, or as it is termed in shells and blocks. The crown, or key of the arch should be laid in a block, increasing the breadth of the block by two bricks for each course from the soffit outward. These bricks should be laid in hydraulic cement, and be well wedged with pieces of thin hard slate between the joints.

509. When a combination of brick and cut stone is used, the

ring courses of the heads, with some intermediate ring courses, the bottom string courses, the keystone course, and a few intermediate string courses, are made of cut stone (Fig. 81), the

D

Fig. 81 Repre

sents a cross section of a stone segment arch, capped with brick and beton. A, stone voussoirs. Band D, brick and beton capping. C, abutment. E, cushion stone.

intermediate spaces being filled in with brick. The brick portions of the soffit may, if necessary, be thrown within the stone portions, forming plain caissons.

510. The centres of large arches should not be struck until the whole of the mortar has set firmly. After the centres are struck, the arch is allowed to assume its permanent state of equilibrium, before any of the superstructure is laid.

511. When the heads of the arch form a part of an exterior surface, as the faces of a wall, or the outer portions of a bridge, the voussoirs of the head ring courses are connected with the horizontal courses, as has been explained; the top surface of the voussoirs of the intermediate ring courses are usually left in a roughly dressed state to receive the courses of masonry termed the capping (see Fig. 81), which rests upon the arch between the walls of the head. Before laying the capping, the joints of the voussoirs on the back of the arch should be carefully examined, and, wherever they are found to be open from the settling of the arch, they should be filled up with soft-tempered mortar, and by driving in pieces of hard slate. The capping may be variously formed of rubble, brick, or beton. Where the arches are exposed to the filtration of rain water, as in those used for bridges and the casemates of fortifications, the capping should be of beton laid in layers, and well rammed, with the usual precautions for obtaining a solid homogeneous mass.

512. The difficulty of forming water-tight cappings of masonry has led engineers, within a few years back, to try a coating of asphalte upon the surface of beton. The surface

of the beton capping is made uniform and smooth by the trowel, or float, and the mass is allowed to become thoroughly dry before the asphalte is laid. Asphalte is usually laid on in two layers. Before applying the first, the surface of the beton should be thoroughly cleansed of dust, and receive a coating of mineral tar applied hot with a swab. This application of hot mineral tar is said to prevent the formation of air bubbles in the layers of asphalte which, when present, permit the water to percolate through the masonry. The first layer of asphalte is laid on in squares, or thin blocks, care being taken to form a perfect union between the edges of the squares by pouring the hot liquid along them in forming each new one. The surface of the first layer is made uniform, and rubbed until it becomes smooth and hard with an ordinary wooden float. In laying the second layer, the same precautions are taken as for the first, the squares breaking joints with those of the first. Fine sand is strewed over the surface of the top layer, and pressed into the asphalte before it becomes hard.

Coverings of asphalte have been used both in Europe and in our military structures for some years back with decided success. There have been failures, in some instances, arising in all probability either from using a bad material, or from some fault of workmanship.

513. In a range of arches, like those of bridges, or casemates, the capping of each arch is shaped with two inclined surfaces, like a common roof. The bottoms of these surfaces, by their junction, form gutters where the water collects, and from which it is conveyed off in conduits, formed either of iron pipes, or of vertical openings made through the masonry of the piers which communicate with horizontal covered drains. A small arch of sufficient width to admit a man to examine its interior, or a square culvert, is formed over the gutter. When the spaces between the head walls above the capping is filled in with earth, a series of drains running from the top, or ridge of the capping, and leading into the main gutter drain, should be formed of brick. They may be best made by using dry brick laid flat, and with intervals left for the drains, these being covered by other courses of dry brick with the joints in some degree open. The earth is filled in upon the upper course of bricks, which should be so laid as to form a uniform surface.

514. From observations taken on the manner in which large cylindrical arches settle, and experiments made on a small scale, it appears that in all cases of arches where the

rise is equal to or less than the half span they yield (Fig. 82) by the crown of the arch falling inward, and thrusting outward the lower portions, presenting five joints of rupture, one at the keystone, one on each side of it which limit the portions that fall inward, and one on each side near the springing lines which limit the parts thrust outward. In

pointed arches, or those in which the rise is greater than the half span, the tendency to yielding is, in some cases, different; here the lower parts may fall inward (Fig. 83), and thrust upward and outward the parts near the crown.

n

Fig. 83-Represents the manner in which pointed arches may yield.

The letters refer to same points as in Fig. 82.

The angle which a line drawn from the centre of the arch to the joint of rupture makes with a vertical line is called the angle of rupture. This term is also used when the arch is stable, or when there is no joint of rupture, in which case it refers to that point about which there is the greatest tendency to rotate. It may also be defined as including that portion of the arch near the crown which will cause the greatest thrust or horizontal pressure at the crown. This thrust tends to crush the voussoirs at the crown, and also to overturn the abutments about some outer joint. The thrust is rarely sufficient to crush ordinary stone. The most common mode of failure is by rupturing, or turning about a joint. In very thick arches rupture may take place from slipping on the joints.

515. The joints of rupture below the keystone vary in arches of different thicknesses and forms, and in the same arch with the weight it sustains.

516. The problem for finding the joints of rupture by calculation, and the consequent thickness of the abutments necessary to preserve the arch from yielding, has been solved