In order to cover every part of the building, the dome must be large enough to include the corners, and if made sufficiently large for this it must overhang the side walls of the building, by an amount A E B on each side, if the framing is carried down to the same horizontal plane all the way around. Horizontal sec tions taken through the dome at intervals throughout its height, however, show smaller and smaller circles as they are taken nearer and nearer to the top of the dome. Some one of these sections will cut out from the dome a circle which will appear in plan as though it were inscribed in the square formed by the walls of the building. Such a circle is shown at IJKL in Fig. 256. A dome built up with this circle as a base would not cover the corners of the build ing, so that the triangular spaces like A 1 L would be kept open. These triangular spaces, or rather the coverings over them,- arc called the pendentives. Fig. 257 shows in perspective the outline of four pendentives E D H, He G, etc.
We have seen that a dome built up on the circumscribed circle as a base is too large, while a dome built up on the inscribed circle is too small and will not completely cover the building. To over come this difficulty it is customary to erect a dome on the smaller or inscribed circle, as a base, and to extend the ribs so as to fill up the corners and form a framework for the pendentives. This is shown in Fig. 258 which is a plan of the framework for a domical roof. The ribs will be of different lengths and will in tersect the inside face of the wall at different heights, be cause as they are extended outward they must also be ex tended downward. Each one will be curved if the dome is spherical, and straight if the dome is conical. The upper ends of the ribs bear against the curb A, leaving a circular open ing for a lantern or cupola.
The lower ends may be supported on a masonry wall, or may rest on curved wood plates, as shown in Fig. 259. This is an elevation of a conical dome, and shows the straight ribs A.
Fig. 260 shows an elevation of a spherical dome which has curved ribs A, as shown. Each of these ribs must be bent or shaped to the segment of a circle, in order that the edges may lie in a spherical surface.
If the design calls for a domical ceiling and the exterior may be of some other form, then only the inside edges of the ribs need be dressed to corre spond with a spherical or conical surface, in order that they may receive the lathing or furring, and the outside may be left rough so that a false roof of any desired shape may be built. If the
exterior must be of domical form, while on the interior there is a suspended or false ceiling of some kind, then only the outside edges of the ribs must lie in the conical or spherical surface, so as to receive the roof board ing, while the inside edges may be left rough or shaped to any other form. If both the exterior and interior must be domical, then both the inside and outside edges of the ribs must be dressed so as to lie in the domical surface.
Conical domes are very uncommon, but they are sometimes used. A conical dome is much easier to frame than a spherical dome because the ribs are straight. The shape of the curved plate which sup ports the lower ends of the ribs may be easily determined, since it must conform to the line of intersection between the conical or spherical surface of the dome, and the plane of the face of the wall.
Niches. Niches are of common occurrence in building work, especially in churches, halls, and other important structures. Some times they are simply recesses in the wall with straight corners and a square head, but more often they are semicircular in form, with spherical heads, in which case the framing becomes a matter of some difficulty. The fram ing of the wall for a semicircular niche is the easiest part of the work, since all the pieces may be straight, but for the framing of the head the ribs must be bent or shaped to conform to the surface of a sphere.
Fig. 261 shows in plan the way in which the vertical studding of the walls must be placed. The inside edges must lie in a cylindri cal surface, and will receive the lathing and plastering. There must be a curved sole piece for them to rest upon at the bottom and a cap at the top. The cap is shown at A B, in Fig. 262, which is an eleva tion of the cradling or framing for the niche. This figure shows how the ribs for the head of the niche must be bent. The ribs and vertical studs must be spaced not more than 12 inches apart, center to center.
The form of niches described above is the most common one for large niches intended to hold full size casts or other pieces of statuary, but smaller ones for holding busts and vases are quite common. These are often made in the form of a quarter sphere or some smaller segment of a sphere, with a flat base or floor and a spherical head, as is shown in section in Fig.
263. They arc framed with curved ribs in the same way as described above, and finished with lathing and plastering.