STONE CUTTING. The object of this Article is to explain the geometrica methods of representing the more usual and elementary combinations of blocks of stone in walls and arches, by means of their projections; and from these and the data of the problem to deduce the true dimensions of the bounding surfaces and lines of each part. a Walls bounded by Plane Surfaces. In walls of cut stone the blocks are usually separated by horizontal and vertical joints; the latter being in vertical planes perpendicular to the face of the walls, and which are termed planes of right section, to distinguish them from other vertical planes of section. When the face of the wall is inclined to the horizon, its slope, or batir, is usually expressed by the ratio of the base of the slope to the perpendicular, measured in the plane of right section; or the slope is said to be so many base to so many perpendicular. In the right section A'B'C'D', (Pl. A, Fig. 1) for example, the inclination of the face A'O' to the base of the wall A'B', is measured by dividing the perpendicular C'E' from C' upon the line A'B' by the distance "A'E' between the point A' and the foot of the perpendicular. The quotient thus obtained, is evidently the natural tangent of the angle C'A'E'; and the most convenient method of representing the batir is by a fraction; the numerator expressing the number of units in the perpendicular, and the denominator the corresponding number of units in the base; thus a batir of expresses a slope of six perpendicular to one base; a batir of 2, one of three perpendicular to two base, &c. CE A'E' 6 I Prob. 1. Having given the right section of a wall, to construct the projections of its bounding lines, and the edges of the horizontal and vertical joints. Let A'B'D'C', (Pl. A, Fig. 1,) be the right section; the base A'B' and the top C'D' being horizontal; the face A'C' having a batir GE and the back B'D' vertical. C'E' A'E Draw a line AA,, to represent the foot of the face in plan. Parallel to AA, draw CC, and at a distance from it eq tal o * See Mahan's Civil Engineering, Art. 351. A'E', the distance of the point, A' from the foot of the per pendicular drawn from 'in the plane of right section; CC, will be the top line of the face in plan. Parallel to CC, an and at a distance O'D', the breadth of the wall at top, draw BB,, which will be the projection of the back. At any convenient distance from BB, draw A"A"" parallel to it, to represent the foot of the wall in elevation; "the top C"D" will be drawn parallel to A"A", and at the height B'D' of the top above the base. To draw the projections of the horizontal edges, suppose the wall divided into four equal courses by horizontal joints. As the batir of the wall is, the base of the slope of each of these equal courses will be one-sixth of its height; if lines therefore are drawn parallel to the foot AA,, and at a distance from each other equal to the height of each course, these lines will be the projections in plan of the horizontal edges, as shown on the right of the plan. As the projections of the vertical edges are contained in planes of right section, they will be drawn perpendicular to the horizontal ones, and breaking joints with them; as represented on the same portion of the plan. The horizontal edges in elevation will be drawn parallel to A"A"", and at a distance from each other equal to the height of a course. The vertical edges will be drawn perpendicular to these last, and corresponding to their projections in plan. Remark. If the projections of any horizontal line of the face, at a given height above the foot of the wall, are required, as mn and m'n', for example, it is evident that m'n' will be drawn in elevation at the given height above the foot A"A"", and that mn will be parallel to AA, in plan, and at a distance from it equal to the height of m'n'. 6 Prob. 2. Having given the batir of the faces of two walls that intersect, the foot of each being in the same horizontal plane, to draw the projections of the line of intersection of the faces. Let Aa, (Fig. 1,) be the foot of one wall in plan, and the batir of its face ; ab the foot of the other, and the batir of its face 4 I 1 It is evident that the point a will be one point of the intersection in plan. If now a horizontal line be drawn in each face at the same altitude, they will intersect and give a second point of the intersection of the faces. Assuming any altitude for the horizontal line on one face, its projection mn, in plan, will be parallel to Aa, and at of the assumed altitude from it. In like manner, the projection no of the 6 |