In Fig. 133, abcd represents the inner surface of the wall enclosing the space allotted to the stairs, a e the length of the steps, and e f g h the cylinder, or face of the front-string. The line a e is given as the face of the first riser, and the point j for the limit of the last. Make e i equal to 18 inches, and upon o, with o i for radius, describe the arc i j; obtain the number of risers and of treads required to ascend to the floor at j, according to Art. 252, and divide the arc ij into the same number of equal parts as there are to be treads: through the points of division, 1, 2, 3, etc., and from the wall-string to the front-string, draw lines tending to the centre, o: then these lines will represent the face of each riser, and determine the form and width of the steps. Allow the necessary projection for the nosing beyond a e, which should be equal to the thickness of the step, and then a e l k will be the dimensions for each step. Make a pitch-board for the wall-string having a k for the tread, and the rise as previously ascertained: with this lay out on a thicknessed plank the several risers and treads, as at Fig. 128, gauging from the upper edge of the string for the line at which to set the pitch-board.

Fig. 133.

Upon the back of the string, with a 1 1/4-inch dado plane, make a succession of grooves 1 1/4 inches apart, and parallel with the lines for the risers on the face. These grooves must be cut along the whole length of the plank, and deep enough to admit of the plank's bending around the curve abcd. Then construct a drum, or cylinder, of any common kind of stuff, made to fit a curve with a radius the thickness of the string less than oa; upon this the string must be bent, and the grooves filled with strips of wood, called keys, which must be very nicely fitted and glued in. After it has dried, a board thin enough to bend around on the outside of the string must be glued on from one end to the other, and nailed with clout-nails. In doing this, be careful not to nail into any place opposite to where a riser or step is to enter on the face.

After the string has been on the drum a sufficient time for the glue to set, take it off, and cut the mortices for the steps and risers on the face at the lines previously made; which may be done by boring with a centre-bit half through the string, and nicely chiselling to the line. The drum need not be made to extend over the whole space occupied by the stairs, but merely so far as requisite to receive one piece of the wall-string at a time; for it is evident that more than one will be required. The front-string may be constructed in the same manner; taking e l instead of a k lor the tread of the pitch-board, dadoing it with a smaller dado plane, and bending it on a drum of the proper size.

261. - Winding Stairs: Shape and Position of Timbers. -

The dotted lines in Fig. 133 show the position of the timbers as regards the plan; the shape of each is obtained as follows: In Fig. 134, the line 1 a is equal to a riser, less the thickness of the floor, and the lines 2 m, 3 n, 4 o, 5 p, and 6 q are each equal to one riser. The line a 2 is equal to a m in Fig. 133, the line m to m n in that figure, etc. In drawing this figure, commence at a, and make the lines a 1 and a 2 of the length above specified, and draw them at right angles to each other; draw 2 m at right angles to a 2, and m 3 at right angles to m 2, and make 2 m and m 3 of the lengths as above specified; and so proceed to the end. Then through the points 1, 2, 3, 4, 5, and 6 trace the line 1 b; upon the points 1, 2, 3, 4, etc., with the size of the timber for radius, describe arcs as shown in the figure, and by these the lower line may be traced parallel to the upper. This will give the proper shape for the timber, a b, in Fig. 133; and that of the others may be found in a similar manner. In ordinary cases, the shape of one face of the timber will be sufficient, for a good workman can easily hew it to its proper level by that; but where great accuracy is desirable, a pattern for the other side may be found in the same manner as for the first. In many cases, the timbers beneath circular stairs are put up after the stairs are erected, and without previously giving them the required form; the workman in shaping them being guided by the form marked out by the lower edge of the risers.

Fig. 134.

262. - Winding Stairs with Flyers: Grade of Front-String. - In stairs of this kind, if the winders are confined to the quarter circle, the transition from the winders to the flyers is too abrupt for convenience, as well as in appearance. To remove this unsightly bend in the rail and string, it is usual to take in among the winders one or more of the flyers, and thus graduate the width of the winders to that of the flyers. But this is not always done so as to secure the best results. By the method now to be shown, both rail and strings will be gracefully graded. In Fig. 135, ab represents the line of the facia along the floor of the upper story, bee the face of the cylinder, and c d the face of the front-string. Make gb equal to 1/3 of the diameter of the baluster, and parallel to a b, b e c, and c d draw the centre-line of the rail, fg, g h z, and ij; make gk and gl each equal to half the width of the rail, and through k and l, parallel to the centreline, draw lines for the convex and the concave sides of the rail; tangical to the convex side of the rail, and parallel to k m, draw n o; obtain the stretch-out, q r, of the semicircle, k p m, according to Art, 524; extend a b to t, and k m to s; make c s equal to the length of the steps, and i n equal to 18 inches, and parallel to m p describe the arcs s t and u 6; from t draw t w, tending to the centre of the cylinder; from 6, and on the line 6 u x, run off the regular tread, as at 5, 4, 3, 2, 1, and v; make u x equal to half the arc u 6, and make the point of division nearest to x, as v, the limit of the parallel steps, or flyers; make r o equal to m s; from o draw o a2* at right angles to;n o, and equal to one riser; from a2 draw a2 s parallel to n o, and equal to one tread; from s, through o, draw s b2.

Then from w draw w c2 at right angles to; n o, and set up on the line w c2 the same number of risers that the floor, A, is above the first winder, B, as at 1, 2, 3, 4, 5, and 6; through 5 (on the arc 6 u) draw d2 e2, tending to the centre of the cylinder; from e2 draw e2f 2 at right angles to no, and through 5 (on the line w c2) draw g2 f2 parallel to n o; through 6 (on the line w c2) and f2 draw the line h2 b2; make 6 c2 equal to half a riser, and from c2 and 6 draw c'2 i'2 and 6j2 parallel to n o; make h2 i2 equal to h2f2; from i2 draw i2 k2 at right angles to i2 h2, and from f2 draw f2k2 at right angles to f2 h2; upon k2, with k2 f2 for radius, describe the arc f2i2; make b2 l2 equal to b2f2, and ease oft the angle at b2 by the curve f2 l2. In the figure, the curve is described from a centre, but as this might be impracticable in a full-size plan, the curve may be obtained according to Art. 521. Then from 1, 2, 3, and 4 (on the line w c2) draw lines parallel to n o, meeting the curve in m2, n2, o2, and p2; from these points draw lines at right angles to no, and meeting it in x2, r2, s2, and t2; from x2 and r2 draw lines tending to u2, and meeting the convex side of the rail in y2 and z2; make m v2 equal to r s2, and m w2 equal to rt2, from y2, z2, v2, and w2, through 4, 3, 2, and 1, draw lines meeting the line of the wall-string in a3 b3 c3 and d3; from e3, where the centre-line of the rail crosses the line of the floor, draw e3 f3 at right angles to n o, and from f3, through 6, draw f3g2 then the heavy lines f3g2, e2d2, y2 a3, z2 b3, v2c3, w2 d3, and zy will be the lines for the risers, which, being extended to the line of the front-string, b e c d, will give the dimensions of the winders and the grading of the front-string, as was required.

* In the references a2, b2, etc., a new form is introduced for the first time. During the time taken to refer to the figure, the memory of the form of these may pass from the mind, while that of the sound alone remains; they may then be mistaken for a 2, b 2, etc. This can be avoided in reading by giving them a sound corresponding to their meaning, which is a second, b second, etc.

Fig. 135.