The term winding is applied more particularly to a stairs having steps of parallel width compounded with those which taper in width, as in Fig. 135, and as is here shown in Fig. 162, in which fabc represents the central line of the rail around the cylinder, and the quadrant de, distant from the first quadrant 20 inches, is the tread-line, upon which from d, a point taken at pleasure, the treads are run off. Through e, perpendicular to af, draw ae (the occurrence here of one of the points of division on the tread-line perpendicularly opposite a, the spring of the circle, is only an accidental coincidence); make a a, equal to two risers; join a' and f. With the diameter ac, on b as a centre, describe the arc at g, crossing ac extended; through b draw gb'; then ab' is the stretchout, or development of the quadrant ab.

Fig. 162.

Through h draw h i, tending toward the centre of the cylinder; make b' i' equal to bi; perpendicular to fb' draw b' b" and i' i". As there are four risers from e to h, make a' a" equal to four risers, and draw a" i" parallel with fa; through i " draw a' b".; by intersecting lines, or in any convenient manner, ease off to any extent the angle fa' i". Through j, a point in this curve (chosen so as to be perpendicularly over m, a point between a and f, nearer to a), draw k l, a tangent to the curve. Perpendicularly to this tangent, through j, draw the line for a butt-joint; also through b", and perpendicularly to a' b", draw the line for the joint at the centre of the half circle. On the line aa". set up points of division for the riser heights, and through these points of division draw horizontal lines to the line b"jf.

From these points of contact drop perpendiculars to the line fa b', and transfer such of them as require it to the circle at, by drawing lines tending to g. Through these points of intersection with the central line of the rail, and through the points of division on the tread-line, draw the riser-lines me, a n, etc. At half a riser above the floor-line, on top of the upper riser draw a horizontal line, and ease off the angle as shown; the intersection of the floor-line with this curve gives the position of the top riser at the centre of the rail. This completes the plan of the steps and the elevation of the rail - requisite preliminaries for the face-moulds. The graduation of the treads from flyers to winders obviates an abrupt angle at their junction in the rail and front-string. The objection to the graduation, that it interferes with the regularity of stepping at the tread-line, is not realized in practice.