VAULTS, DOMES, or GROINS.-A vault is an interior roof, rising in a concave direction from the walls on which it rests, either in a continued arch from side to side,—in which case the section is semicircular, or a section of a circle less than a semicircle,—or else meet ing the vertex in a point, or line, as when the section is Gothic.
The concavity, or interior surface of the vault, is call ed the intrados; which, in simple vaulting, generally consists of the portion of the surface of a cylinder, cy lindroid, or sphere, never exceeding half the solid ; while the springing lines, from which the vault rises, and by which the walls are terminated, are generally straight, and parallel to the axis.
Vaults having a horizontal straight axis, are called straight vaults; and those with their axes horizontal arc termed horizontal vaults.
The exterior, or convex curve of the superior surface of an arch, is called the e.rtrados.
The vertical sections of the intradosses of vaults may be formed in t urves of an infinite variety ; but the most elegant arc circular or elliptic, and have been adopted among the Romans, by some of our ancestors of the ages, and by the nations of modern Europe. To these, therefore, we shall at present confine our observa tions.
A cylindrical, or cradle vault, consists of a plain arch; the figure of whose extrados is a portion of a cylindrical surface, terminating on the top of the walls which sup port it, in a horizontal plane parallel to the axis of the cylinder.
A cylindroidal vault consists also of a plain arch, the figure of whose extrados springs from hoc viz ital but its section perpendicular to these Imes is eVC ry where a semiellipsis, equal and similar throughout, having its base that of either axis ; otherwise, it is sometimes the segment of an ellipsis less than a semiellipsis, having an ordinate parallel to the axis for its base.
A vault, rising from a circular, elliptical, or polygo nal plan, with a concavity within and a convexity without, so that all horizontal sections of the intrados may be of similar figures, having their centres in the same vertical line, or common axis, is called a dome.
Various names are given to domes, according to the figure of their plan, as polygonal, circular, or elliptic. Circular domes may be either spherical, spheroidal, el lipsoidal, hyperbolical, parabolical, Ste. Such as rise
higher than the radius of the base arc called surmounted domes, and such as arc below this altitude arc termed diminished, or surbased domes. I f a dome be a portion of a sphere, that is, if its base be a circle, and its verti cal section through the centre of its base the segment of a circle, it is called a cupola. A spherical dome, or cu pola, may be intersected by a cylindric vaulting in any direction ; and the intersection will always be circular, provided the axis of the cylinder tend to the centre of the sphere, because every section of a sphere made by a plane is a circle, as is also every section of a right cy linder perpendicular to the axis. Suppose, therefore, the sphere to be cut by a plane forming a section equal to that of the cylinder, and the two sections applied to gether, the right line drawn from the centre of the circle, which is the section of the sphere, to the centre of such sphere, will he perpendicular to the plane of this section ; and, since the axis of the cylinder is also perpendicular to the same plane, it will he in the same right line with the remainder of the radius of the sphere. From this we deduce, that, when the axis of a cylindrical vaulting is horizontal, and tends to that of a spherical vault, their intersection must be in the circumference of a circle, whose plane will be perpendicular to the horizon ; and hence those beautiful sphero-cylindrical groins, so great ly and justly admired in our principal buildings.
Upon this principle, any building that has a polygonal base may be made to terminate a circle, and sustain a cupola, or cylindric wall; for, if the tops of the side walls of the polygon be brought to a level, and equal segments of circles, whether semicircles or less portions, be raised on the top, meeting in the lines of intersection of the sides of the polygon, and if the angular spaces between the circular-headed walls be made good to the level of the summit of the arches, so as to coincide with the circumference of a great circle of the sphere, they will terminate in a ring at the level of the summit of the arches, and be portions of the sphere, called by our workmen spandrels, and by the French pendentives. On the ring so formed, a cornice is usually laid, on which the cylindric wall or dome is raised.