. Stereotomy : Problems in stone cutting. In four classes. I. Plane-sided structures. II. Structures containing developable surfaces. III. Structrues containing warped surfaces. IV. Structures containing double-curved surfaces. For students of engineering and architecture . ve muetc., will be equal. The point m will thus generate a helix, h,but of a more general kind than the circular helix, PL VII.,Fig. 50. 124. Also if a horizontal straight line taken as a generatrixG, move upon this new helix LP, in the same manner as inPL VII., Fig. 50, the resulting surface will still be a helicoid, H,but
. Stereotomy : Problems in stone cutting. In four classes. I. Plane-sided structures. II. Structures containing developable surfaces. III. Structrues containing warped surfaces. IV. Structures containing double-curved surfaces. For students of engineering and architecture . ve muetc., will be equal. The point m will thus generate a helix, h,but of a more general kind than the circular helix, PL VII.,Fig. 50. 124. Also if a horizontal straight line taken as a generatrixG, move upon this new helix LP, in the same manner as inPL VII., Fig. 50, the resulting surface will still be a helicoid, H,but of a more general form than the usual particular form shownin that figure. But as the plan, LP, of h is no longer a circle, while the lineG continues perpendicular to it as seen in plan, Fig. 8, the linesg, gu g2, etc., horizontal projections of successive positions of G,will not pass through any one point, as at o in PL VII., , but will intersect each other, as in Fig. 8, so that wheng, g\,g<i, gn, and thence their intersections, p, q, r, etc., STONE-CUTTING. 99 become consecutive, p, q, r, r„, will form a curve to which g, gv g2, gn will be tangent. 125. We thus reach the following important conclusions;foundation of the design of stairs of every Fig. 8. 1°. The curve pqr is the horizontal projection of a verticalcylinder, C, which replaces the vertical straight line (axis) o —012 in PI. VII., Fig. 50. 2°. The curve LP is the horizontal projection of a generalform of a helix, h, (123). 3°. The straight line g, then moves upon the helix A, andremains horizontal and tangent to the cylinder C. It thus gen-erates a general form of helicoidal surface, H; such as formsthe under surface of the stairs, and such as will contain thesimilar radial edges of all the steps. Problem XVI. Winding stairs on an irregular ground plan. I. The Projections. Let a landing at AdE, PI. VIII., , provided for a door in the wall ES, be connected with afloor three feet highe
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