is a 5-inch width introduced between the straight flight and the cylinder, which provides for a better easement, or ramp, from the pitch of the straight rail into the steeper pitch of the wreath rail; besides, if the winders were all contained in the cylinder, it would make a sudden and abrupt change of inclination in the stairway, causing travelers to stumble and fall.
32. Development of Stringers. — At <I >(c)</I> and <I >(e)</I> in
Fig. 23Fig. 23. A stairway winding one-quarter turn at the top and bottom are shown the methods of developing the front stringer when each end curves around a cylinder. The plan <I >(c)</I> of the front stringer is the same as in (a). The distance <I >ab</I> in <I >(c)</I> is equal to the "layout" of the semicircular well, obtained as in (d) where <I >de</I> is the outstretched, or developed, length of the curve <I >afb</I>. The length of de may be determined as follows: Make ab equal to the diameter of the cylinder; from r, with a radius equal to one-half of ab, describe an arc afb; from a and b as centers, with a radius equal to ab, describe arcs intersecting in g. From g, through the points a and b, draw lines gd and ge; through f draw a line tangent to the arc and parallel to ab; the points where this line intersects with the lines drawn through g, will define the length of de, or the developed length of the arc <I >afb</I>. <I >A C B </I>in (e) is the front stringer, any outstretched step, as C, being obtained by projecting the line of the riser vertically from the plan, and the tread horizontally from the story rod. As the steps D, E, etc., in the cylinder, have their width marked on the plan as 3J inches, that width is therefore transferred to the development. The stringer in this case is 6£ inches, measured from the angle between the treads and risers. This width is marked out with a compass from each angle, and a pleasing curve is drawn tangent to the arcs, as shown. When a cylinder is of this diameter, or smaller, at the bottom of the flight, the curve of the hand rail presents a better appearance, and is more convenient when the rail over the regular treads is continued on its pitch into the wreath, without ramping the straight rail. In this case there would