A vaulted apartment, surrounded by an elliptic wall, is generally covered with a spheroidal vault, which is either a hemispheroid, or a portion less than a hemispheroid.
A conic surface is seldom employed in vaulting ; but when the vault is to have this kind of intrados, the intrados should be the half of a cone with its axis in a horizontal position, or a whole cone with its axis in a vertical position.
All vaults which have a horizontal straight axis, are called straight vaults.
Besides what we have already denominated an arch, the concavities which two solids form at an angle, are called an arch.
If one cylinder pierce another of a greater diameter, the arch is called a cylindro-cylindric arch ; the cylindro being applied to the cylindric part which has the greater diameter, and the cylindric to that which has the less.
If a cylinder pierce a sphere of greater diameter than the cylinder, the arch is called a sphero-cylindric arch ; and, on the contrary, if a sphere pierce a cylinder of greater diameter than the sphere, the arch is denominated a cglindro-spheric arch.
If a cylinder pierce a cone, so as to make a complete perforation through the cone, two complete arches will be ffirmed, called cono-cylindric arches ; and, on the contrary, if a cone pierce a cylinder, so as to make the interior con cavity through the cylinder a complete conic surface, the arch is called a cylindro-conic arch.
It' a straight wall he pierced with a cylindric aperture quite through, two arches will be formed, called plano cglindric arches.
Every species of arches is thus denoted by two preceding words; the former ending in o, signifying the principal vault or surface cut through, and the latter in ic, signifying the kind of aperture which pierces the wall or vault.
When two cylindric vaults, or two cylindroidie vaults, or a cylindric or eylindroidic vault, pierce each other, and also their axis, so that the diameter of each hollow may be the same, when measured perpendicular to a plane passing through the axis of both surlhees, the figure so formed is called a groin ; but fir more particular information on this point see the article GROIN.
The formation of stone arches, in various cases, has always been looked upon its a most curious and useful acquisition to the operative mason, or to the or other person who is appointed to superintend the work. In order to remove the difficulties experienced in the construction of cylindric or cylindroidic arches, both in straight and circular walls, we shall here show an example of each.
First, let it be required to construct a semi-cylindroidic arch, cutting a straight wall with its axis oblique to the su•flice of the wall, but parallel to the horizon.
Plate I. Figure A.—Let ',BCD be the plan of the aper ture, A D and a c being the plan of the jambs, and A 13 and D C the plan of the sides of the wall ; produce u A and c 13 to a and ; draw the straight line icavn at right angles with A a and c F; bisect a I' at ; draw a it K perpendicular to C ; make a n equal to the height of the intrados of the arch, and describe the semi-ellipsis 0 u F, which is the section of the intrados of the arch ; make o 1, 11 K, and li E, equal to the breadth of the beds of the arch-stone, and describe the semi-ellipsis K E, which is the section of the extrados of the arch. Now, suppose the distances between the joints around the intrados of the arch to be all equal, and all the joints to tend to the centre na ; divide the semi-ellipsis into such an odd number of equal parts, that each part may be in breadth equal to what is intended for the thickness of the stones at that part ; produce E i to s, and extend the whole number of these parts from a to s; and through the points of division draw lines perpendicular to a s, or parallel to A G. Through all the points of division of the ellipsis o n F, draw lines parallel to a A to meet A a; then take the lengths of all the parts of the lines so drawn that are terminated by c F and A a, as follows, viz., make the first line on the left of a A equal to the first on the right of a A, and the pint b will be obtained ; make the second on the left of o A equal to the second on the right of o A, and the point c will be obtained ; proceed in this manner, until all the other points are obtained ; then a curve being drawn through all the points A, c, d, to r, will give the one edge of the envelope of the intrados of the arch; and by producing the perpendiculars erected upon a s to the points e, f, g, &o., and making the several distances b e, c f, d g, &c. equal to A n or n c, the points n, e, j; 9, &c. to u, will give the other edge of the en velope by tracing a curve through them ; then A b c (1, b c f e, c d g .V.e. are the soffits of the stones.