Sfiherical (domes) are of various kinds, but spheres or spherical surfaces are the bases of all; so that the courses are built in horizontal rings, and consequently the vaults can be left open. It may be said that the true dome is formed when a portion of a ring (with any desired.arch line) lying in a vertical plane is rotated about a vertical axis passing through its vertex; which, of course, presupposes a circular gronnd-plan. In these forms of the pure dome the surmounted elliptical arch is usually employed, under which circumstances there is almost without exception an opening- in the vertex, roofed and with arched side windows, technically known as a " lantern." Hanging hemispherical vaults are thrown over four-sided plans, so that the corners fall into the ground circle of the vault, there will be semicircular penetrations on the four walls, and such vaults (much used in monumental architecture) are called " hanging domes." The vault shown in Figure 15 Go/. I), taken from the Church of St. Mark at Venice, is an example. All the surface is of mosaic, richly decorated, on a gold ground. The illustration shows how in these hanging domes a cornice or horizontal band may be set over the vertex of the wall arches, so that the surface of the vault can be divided into four equal spherical triangles, and a pendent spherical segment, the " calotte." A similar division is possible if instead of a hemisphere a calotte is the basis; in which case the wall penetrations become segment arches and the whole vault requires less height. These vaults when used over oblong ground-plans (not, however, divisible in the manner given) are known as surbased spherical vaults. They are fre quently used in private buildings; and it may be remarked that here also up to spans of t6;.1 feet an arch thickness of a half-brick suffices. The other forms of domes—for instance, the oblate—may be passed over, as they are seldoin used.
Fan or Funnel may be understood by imagining- curved lines or sections of circles to be so revolved about the vertical borders of a room or around any of the pillars that they will lie tangentially at their lower ends on the axis. The different parts of the vanit thus formed arrange them selves in gently-curved vertex lines; and if the basis-length of the curved line is not equal to at least half the diagonal of the space, or part of the same, they leave above an open space which may be closed in bv a small straight vault. The funnel form is seen most plainly at the pillars and when viewed from above; the lower circles are well adapted to ornamenta tion known as " fan-tracem" Figure 16 (/5/. 1) shows the top view, and the method of bonding a section of this peculiar vault, which is much em ployed in the English Gothic style. The example given is from the Cathe dral of Peterborough, a building in the "Perpendicular " style.
Arches: Pointed Arches.—English authorities discnss arches from a historical standpoint, treating the earliest as circular. These were suc ceeded by different forms of pointed arches, classified as lancet, equilateral, depressed, and four-centred, or Tudor. The development of pointed arches commenced during the Middle Ages, and greatly increased the number, beauty, and strength of arches used for decorating churches and temples, and for other purposes.
Arches in Brickwork are classified as plain, rough-cut, or gauged. The plain or common arches are built of uncut bricks and are of the ordinary slope; and, as the bricks nearly touch at the lower points, while a consid erable space intervenes between their upper portions, it is necessary that mortar should be freely used to fill the interstices. It is deemed important that this mortar or cement should be of a better quality than that used in ordinary walling, and that the centre on which such an arch is built should not be removed until the work has thoroughly hardened. In larg-e arches moderately slow-setting mortar is considered preferable, so that when the centres are struck opportunities may be left for the voussoirs slightly to accommodate themselves to the pressure. In extensive works involving the adoption of deep arch-rings it has been found advantageous to build the arch in half-brick rings, with a few bonding or lacing courses built in at intervals.
Rough-cut or Axed Arches are constructed of bricks roughly cut to a wedge-shaped form, which permits the use of a smaller proportion of mor tar or cement than is required when the structure consists of uncut bricks. The rough-cut bricks are frequently used in small arches set in common mortar when strength is required, and over openings, such as doors and windows.
Gauged Arches are used for superior face-work. They are built of bricks carefully rubbed and gauged to accurately-shaped voussoirs. The joints are made very thin, and the bricks are frequently set in fine lime putty. The English method of manufacturing- it is to have pure lime slaked in a quantity of water and strained off while hot, the water being allowed to evaporate till the consistency of cream is attained. The Hine is then mixed with silver sand or'white marble-dust and worked into the groove with a flat jointer, so as to form a raised line, the sides of which are promptly draNyn or cut parallel by drawing the pointing knife along a straight edge, so that the knife trims both edges and scrapes off the super fluous putty, leaving a raised white line standing out on the centre of the joint.
Discharging Arches are built either over or under openings. When constructed over a wood lintel, they should always run clear of both its ends. They may be quadrants of a circle, or even flatter; and if it is con sidered desirable that they should be turned in, two or more half-bricks should be used over doors and windows and other wide openings, while over the ends of beams it is not necessary that they should be more than one half-brick. Discharging arches under openings are used to equalize the weight over the substructure or foundation. Arches of two half-bricks are deemed sufficient for ordinary purposes, but in large and heavy struc tures arches of three half-bricks or a greater number may be necessary. Abutments should be provided, whether the arches are erect or inverted.