Chap. XXIV.
1439
the right lines, which form the upper part of the vault, are to be drawn from the arc It Oto the arc S P, and that of the lower part from the arc EV to the arc KTK. To deter-mine the position of these lines, divide RO and VP into the same number of equalparts, and draw them from one point of division to the other, and do the same on the arcsRTE and EV.
The plan, elevation, and section are more fully comprehended by the development ofthe first, second, and third stones, in isomctrical perspective ; the mould by whichthey are set out is also shown : the letters sufficiently indicate their position, as the corre-sponding parts are similarly lettered in the plan, elevation, section, voussoirs, and mouldby which they are cut. Another method practised at Montpellier shows a difference atthe head, which instead of being circular is straight.
Clement Mctezeau adopted this arch to decorate the internal face of the gate of St. An-toine, at Paris : it has a semicircle at the back, and resembles a portion of an hemi-spherical niche; the springing of the head, being from a straight lintel, is gathered oververy ingeniously to meet the curved line which bounds the recess. Divide the circle F Oand the right line I H into equal parts, observing that the latter must contain two divisionsless than the circle; the entire semicircle would contain seven, and the horizontal line five.
Fig. 2514.
Fig. 2516.
Fig. 2518.
To find the centres of the curvatures of the joints, draw the right lines hi,fn, bm; fromtheir centres raise perpendiculars, as 1, 2, and 3; where they intersect III prolonged willbe the centres required.
The curvature in this vault is represented by a quarter ellipsis, whose two semi-axes areF O and F H ; they may be drawn by means of ordinates to a quarter of a circle of whichF II will be the radius ; or by means of foci or points, which is the most simple. Havingdeveloped the arcs kti,fsn , brm, they are taken for the great axis of quarter ellipses, whichindicate its curvature, and then drawn on a flexible mould.
In cutting the stone commence with the face nf fh, hi, and in. The voussoirs inisometrical perspective show the two intermediate stones defined by the correspondingletters.
Intersecting semicircular Vaults -Where one semicircular arch intersects another, a void
or opening is formed, its figure varying with the angle of intersection, and the diameter of