by a brick arch above it. Additional means of strengthening the plate-bande are sometimes used by forming a broken joint between the blocks, or by a projection made on the face of one block to fit into a corresponding indent in the adjacent one, or by connecting the blocks with iron bolts.

When, from any cause, the supports cannot be made sufliciently strong to resist the lateral pressure of the plate-bande, the extreme blocks must be united by an iron bar, termed a tie, suitably arranged to keep the blocks from yielding.

493. Arches. The arch is a combination of wedge-shaped blocks, termed arch stones, or voussoirs, truncated towards the angle of the wedges by a curved surface which is usually normal to the surfaces of the joints between the blocks. This inferior surface of the arch is termed the soffit. The upper, or outer surface of the arch is termed the back (Fig. 73).

Fig. 73-Represents an elevation M of the head of a right cylindrical arch,
and a section N through the crown of the arch A, with an elevation B of
the soffit and the face C of the abutment.

ab, span of the arch.

494. The extreme blocks of the arch rest against lateral supports, termed abutments, which sustain both the vertical pressure arising from the weight of the arch stones, and the weight of whatever lies upon them; also the lateral pressure caused by the action of the arch.

495. In a range, or series of arches placed side by side, the extreme supports are termed the abutments, the intermediate supports which sustain the intermediate arches and the halves of the two extreme ones are termed piers. When the size of the arches is the same, and their springing lines are

in the same horizontal plane, the piers receive no other pressure but that arising from the weight of the arches.

496. Arches are classified, from the form of the soffit, into cylindrical, conical, conoidal, warped, annular, groined, cloistered, and domes. They are also termed right, oblique, or askew, and rampant, from their direction with respect to a vertical, or horizontal plane.

497. Cylindrical, groined and cloistered arches are formed by the intersections of two or more cylindrical arches. The span of the arches may be different, but the rise is the same in each. The axes of the cylinders will be in the same plane, and they may intersect under any angle.

The groined arch (Fig. 74) is formed by removing those

M

ba

Fig. 74-Represents the plan of the soffit and the right sections M and N of the cylinders forming a groined arch.

aa, pillars supporting the arch.

bc, groins of the soffit

om, mn, edges of coursing joints.

A, key-stone of the two arches formed of one block.

B, B, groin stones of one block below the key-stone forming a part of each arch.

portions of each cylinder which lie under the other and between their common curves of intersection; thus forming a projecting, or salient edge on the soffit along these curves.

The cloistered arch (Fig. 75) is formed by removing those portions of each cylinder which are above the other and exterior to their common intersection, forming thus re-entering angles along the same lines.

498. The planes of the joints in both of these arches are placed in the same manner as in the simple cylindrical arch. The inner edges of the corresponding course of voussoirs in each arch are placed in the same plane parallel to that of the axes of the cylinders. The portions of the soffit in each cylinder, corresponding to each course of voussoirs, which form either the groin in the one case, or the re-entering angle in the other, are cut from a single stone, to present no joint along the common intersection of the arches, and to give them a firmer bond.

499. When the spans at the two ends of an arch are un equal, but the rise is the same, then the soffit of the arch is made of a conoidal surface. The curves of right section at the two ends may be of any figure, but are usually taken from some variety of the elliptical, or oval curves. The soffit is formed by moving a line upon the two curves, and parallel to the plane containing their spans

The conoidal arch belongs to the class with warped soffits. A variety of warped surfaces may be used for soffits according to circumstances; the joints and the bond depending on the generation of the surface.

500. In arranging the joints in conoidal arches, the heading joints are contained in planes perpendicular to the axis of the arch. The coursing joints are also formed of plane surfaces, so arranged that the portion of the joint corresponding to each block is formed by a plane normal to the conoid at the middle point of the lower edge of the block. In this way the joints of the string course will not be formed of continuous surfaces. To make them so, it would be necessary to give them the form of warped surfaces, which present more difficulty in their mechanical execution, and not sufficient advantages over the method just explained to compensate for having them continuous.

501. The annular arch is formed by revolving the plane of a semi-circle, or semi-oval, or other curve, about a line drawn

without the figure and parallel to the rise of the arch (Fig. 76). One series of joints in this arch will be formed by conical surfaces passing through the inner edges of the stones which correspond to the string courses; and the other series will be planes passed through the axis about which the semi-circle is revolved. This last series should break joints with each other.

502. The soffit of a dome is usually formed by revolving the quadrant of one of the usual curves of cylindrical arches around the rise of the curve; or else by revolving the semicurve about the line of the span, and taking the half of the surface thus generated for the soffit of the dome. In the first of these cases the horizontal section of the dome at the springing line will be a circle; in the second the entire curve of the semi-curve by which the soffit is generated. The plan of domes may also be of regular polygonal figures, in which case the soffit will be a polygonal-cloistered arch formed of equal sections of cylinders (Fig. 77). The joints and the bond are determined in the same manner as in other arches.

503. The voussoirs which form the ring course of the heads, in ordinary cylindrical arches, are usually terminated by plane surfaces at top and on the sides, for the purpose of connecting them with the horizontal courses of the head which

lie above and on each side of the arch (Figs. 78 and 79). This connection may be arranged in a variety of ways. The two points to be kept in view are, to form a good bond between the voussoirs and horizontal courses, and to give a pleasing

Fig. 78-Represents a manner of connecting the voussoirs and horizontal courses in an oval arch.

o, o, are examples of voussoirs with elbow joints.

Fig. 79-Represents a mode of arranging the voussoirs and horizontal courses in flat segment arches.

This connection

should always give a symmetrical appearance to the halves of the structure on each side of the crown. To effect these several objects it may be necessary, in cases of oval arches, to make the breadth of the voussoirs unequal, diminishing usually those near the springing lines.

504. In small arches the voussoirs near the springing line are so cut as to form a part also of the horizontal course (see Fig. 78), forming what is termed an elbow joint. This plan is objectionable, both because there is a waste of material in forming a joint of this kind, and the stone is liable to crack when the arch settles.

505. The forms and dimensions of the voussoirs should be determined both by geometrical drawings and numerical