To find any bevel which the joints on the face of the arch mal•es with that on the intrados.
Let p q be one of the joints tending to the centre, N. of the section of the arch ; with the radius a o describe an are, o N Cutting p q at N; draw N P parallel too A, elating A 13 draw P o parallel to 5' G, cutting a A at ri; draw Da L parallel to c A, cutting A D at L, and join L o ; then Q L sa is the bevel required. In the same manner 'nay all the remaining bevels be found.
Again, let p q r s be the section of an arch-stone; then making two bevels, one to q p s, and the other to r s p, will be all the bevels that are necessary for that stone. I laving obtained the several bevels, we shall now proceed to work the a•ch-stone, whose section is vq rs: first work the lower bed of the stone corresponding to the joint p q, then draw a line for the soffit, which work also by means of the bevel q p s; then gauge the soffit to its breadth, and work the upper bed of the stone by means of the bevel r s p ; take the soffit mould from the envelope, and draw the ends of the stone which coincide with the thees of the wall ; with the face bevels Q L :a and v L at work the flee of the stone.
Xote.—That finding the bevels for half the arch will be sufficient, by reversing them.
Plate II. shows the construction of a semi-cy Hinkle arch, which is performed by a similar process to the pre ceding.
'the other arch, standing upon D c, shows the ends of the stones in the thee of the wall ; its boundaries are two ellipses of equal height to those of the section.
To construct a cylind•o-cylindric arch, or a cylindric arch, in a cylindric wall, the axis of the aperture being at right angles to the axis of the cylindric wall. See PLATE Iii.
Let A B C D be the half plan of the wall ; B c being half of the convex curve, A n half of the concave curve, c D the middle line of the aperture tending to the centre of the con centric circles which form the plan ; and A B parallel to c being the jamb. Through c draw E F perpendicular to c n; make c E and c F half the breadth of the aperture ; from the centre, c, with the radius c E or c F, describe the semicircle E G F, which will be the section of the intrados; produce c E and e F to ri and t, making E IT and F I each equal to the breadth of the beds, and describe the semicircle II E j divide the intradossal curve, E G F, into the number of parts answer ing to the number of arch-stones, and proceed to find the envelope, as described, for the straight wall, which will give the moulds for the soffits of the stones, as before.
To find the carves of the ends of the beds 'upon the face of the arch.
Let L N represent a joint : draw L N and nt o perpendicular to n r, cutting the plan of the wall at N and o : draw N P par allel to e a, cutting m o at r : in L m take any number of points, t and y, and draw t s and y w parallel to L N, cutting the plan at s and w, and p at r and v: draw Q, t y x, perpendicu lar to L nr : make m Q, t y x, respectively equal to p o, r s, v w, and L x u Q will be the curve of the joint required, which gives the face-line of the upper bed of the lower stone, and the thee-line of the lower bed of the upper stone. In the same manner all the other face-lines of the beds are to be found. The templet must be cut in the shape of L m Q.
To form an arch-stone.
First make one of the beds ; make the soffit, form the other bed, and the fhce-lines of each bed ; then run a draught round the three face-lines, and between them work the thee of the stone in lines perpendicular to the horizon. This will be easily found by drawing a vertical line upon the section of each stone.
It is only necessary to draw the moulds for one half of the arch, as the reversing of them in their application gives the other half.
The joints of any arch whatever may be found in the same manner, provided the planes of the beds intersect a vertical plane perpendicular to the curve in the middle of the aperture.
It is obvious, on finding the face-lines of the beds, that the lowest face-line is the quickest, and part of the plan of the wall itself; the next face-line is flatter, or has less curva ture, and thus each successive face-line has less curvature as it comes nearer to the top ; and, if' there were a joint in the top, the thee-line of the beds would be quite a straight line. Indeed, the thee-lines of two or three courses might be wrought with straight edges, as the difThrence could hardly be perceived. For the tools used by masons. See TOOLS.