Ciiap. XXIV.

MASONRY.

1465

the inequalities of the diameter of the elliptic base, each upright joint requires to be elon-gated. A simple method of obtaining these elongations, for example, that of the uprightjoint whose projection is expressed by the right line 64 on the plan, is first to let fall fromthe primitive centre corresponding to this joint, the perpendicular c4, and the horizontal64; secondly, after having divided 6 4 into four equal parts, draw through these pointslines parallel to c 4, till they intersect the curve ; likewise divide the projection line 6 4, onthe plan, into four equal parts, and having raised perpendiculars through these points, setoff on each the height corresponding to that on the section, and through all these pointsdraw with a flexible rule the curve 6 c, which will be that of the joint indicated by theright line 64 ; the curves for the intrados and extrados may be found in a similar mannerfor each joint. The joints in the thickness da, eb, cf do not form surfaces of concentriccones, whose summits are in the axis of the vault, as in spheroidal vaults with a circularbase, but a doubly curved surface.

A more simple and easy method is represented by the rows of voussoirs shown on theplan by right lines drawn parallel to the lesser axis, and on the section by concentriccircles, whose diameters are the corresponding lines on the plan ; the joints of these circlesform surfaces of truncated cones, whose summit is the point where the joint prolongedwould meet the great axis; the other joints will be plane surfaces tending to the axis ; bythis arrangement we draw the voussoirs, by taking the concentric arcs to form the circulararrisses, and the joint moulds from the section, which will be the same for all the voussoirsof the same row. To form the intrados and extrados, take the convex and concave curvesfrom the section, and divide the joints into the same number of equal parts.

Conoidal Vaults , as in the interior of the Dome of the Pantheon at Paris _The curve of

its centre, as well as that of the open arches, are Catenarian. To execute this kindof vault it is sufficient to have the section and the plan, because each voussoir is cut

Fig.2G45.

Fig. 2644.

Fig . 2G46.

CONOIDAL VAULTS.