Instead of placing the platform-risers at the spring of the cylinder, a . more easy and graceful appearance may be given to the rail, and the necessity of canting either of the twists entirely obviated, by fixing the place of the above risers at a certain distance within the cylinder, as shown in Fig. 149 - the lines indicating the face of the risers cutting the cylinder at k and l, instead of at p and q, the spring of the cylinder. To ascertain the position of the risers, let a be be the pitch-board of the lower flight, and cde that of the upper flight, these being placed so that b c and cd shall form a right line. Extend a c to cut de in f; draw fg parallel to db, and of indefinite length; draw go at right angles to fg, and equal in length to the radius of the circle formed by the centre of the rail in passing around the cylinder; on 0 as centre describe the semicircle jgi; through 0 draw is parallel to db; make oh equal to the radius of the cylinder, and describe on o the face of the cylinder phq; then extend db across the cylinder, cutting it in l and k - giving the position of the face of the risers, as required. To find the face-mould for the twists is simple and obvious: it being merely a quarter of an ellipse, having o j for semi-minor axis, and sf for the semi-major axis; or, at Fig. 151, let dcibea. right angle; make c i equal to of, Fig. 149, and dc equal to sf, Fig. 149; then draw do parallel to ci, and complete the curve as before.