In the last article, in getting the face-moulds for a winding stairs, the two wreaths are found to be very dissimilar in length. This dissimilarity may be obviated by a judicious location of the butt-joint connecting the two wreaths, as shown in Fig.

164. Instead of locating the joint precisely at the middle of the half circle, as was done in Fig. 163, place it farther down, say at;n, which is at n in Fig. 162, two risers down from the top, or at any other point at will. Then through n in the plan draw m' s tangent to the circle at n; and perpendicular to this tangent draw;n n"' and d d"; make n n" equal to n, n of Fig. 162; from d erect d d' perpendicular to m d; make the angle d m d' equal to that of b"' j l of Fig. 162. Make d d" equal to d d'; join d" and n" and extend the line to m', a point of intersection with the base-line n n,; then n' is a point in the base-plane, as also in the cutting plane; therefore m' m is the intersecting line parallel to which all the ordinates of the plan are to be drawn, and perpendicular to which m" n', the measuring base-line, is drawn. Make n' n"" equal to n n"; connect m" and n"", and then transfer by the ordinates to the cutting plane m d and n the three points of the plan at the ends of the tangents, as before described, as also such points in the curve as may be required to mark the curve upon the face-mould, all as shown in previous examples. For the face-mould of the upper wreath, make n" n"' equal to n u" of Fig. 162. From n"' draw n"' s" parallel with m' s; extend the line d" n" to intersect n"' s" in s"; parallel with n"' n draw s" s; from s draw s r tangent to the circle at r (s n equals s r); through r, tending to the centre of the cylinder, draw the butt-joint; then r s and s n are the horizontal projections of the tangents for the upper wreath-piece, the tangent s r being level and, consequently, parallel to the intersecting line drawn through n. Perpendicular to rs draw r'f; parallel with n" s" draw ns'; make r' r" equal to s s,; join r" and p. From this line and the measuring baseline r' p, the points for the tangents are first to be obtained and then the points in the curve, all as before described. The part of the circle from r to c is on the level, as before shown, and may be worked upon the end of the long level rail, its form being just what is shown in the plan from c to r.

Fig. 164.

##### Care Required In Drawing

283. - Face-Moulds: Test of Accuracy. - The methods which have been advanced for obtaining face-moulds are based upon principles of such undoubted correctness that there can be no question as to the results, when the methods given are thoroughly followed. And yet, notwithstanding the correctness of the system and its thorough comprehension by the stair-builder, he will fail of success unless he exercises the greatest care in getting his dimensions, his perpendiculars, and his angles. The slightest deviation in a perpendicular terminated by an oblique line will result in a magnified error at the oblique line. To secure the greatest possible degree of accuracy, care must be exercised in the choice of the instruments by which the drawings are to be made: care to know that a straight-edge is what it purports to be; that a square, or right-angle, is truly a right-angle; that the compasses or dividers be well made, the joint perfect, and the ends neatly ground to a point. Then let the drawing-board be carefully planed to a true surface; and, if possible, let the drawing, full size, be made upon large, stout roll-paper rather than upon the drawing-board itself, as then the points for the face-mould may be pricked through upon the board out of which the face-mould is to be cut, and thus a correct transfer be made. For long straight lines it is better to use a fine chalk-line than the edge of a wooden straight-edge. The line is more trustworthy. Perpendiculars, especially when long, are better obtained by measurement or by calculation (Art. 503) than by a square. The pencil used should be of fine quality - rather hard, in order that its point may be kept fine. With these precautions in regard to the instruments used, and with due care in the manipulations, the face-moulds may be correctly drawn, accurate in size and form. As a test of the accuracy of the work, it will be well to observe in regard to the tangents, that the length of a tangent, as found upon the face-mould, should always equal its length as shown upon the vertical plane. For example, in Fig. 160, the tangent k" c"' on the face-mould should be equal to k' c', the tangent on the vertical plane B; and in cases like this, where the stairs are quite regular, with equal treads at the front-string, the two tangents of a face-mould are equal to each other, or k" c"' equals k" b"; and in this case, the line b" c"' should equal the rake-line b' c".

Again, as another example, in Fig. 161, d f" the tangent upon the face-mould, should be equal to fp" the tangent of the vertical plane C; while d p"", the other tangent on the face-mould, should be equal to r s, the tangent of the vertical plane D. But the more important test is in the length of the chord-line joining the ends of the two tangents; as, for example, the chord m" b"" of Fig. 163, the horizontal projection of which is the chord;;m b in plane A. Perpendicular to m b draw bg; make bg equal to b b" and join g and m; then m" b"", the chord of the face-mould, should be equal to m g. After fully testing the accuracy of the drawing for the face-mould, choose a well-seasoned thin piece of white-wood, or any other wood not liable to split, and plane it to an even thickness throughout; mark upon it the curves, joints, tangents, and slide-line, and cut the edges true to the curvelines and joints square through the board; then square over such marks as are required to draw each tangent and the slide-line also upon the reverse side of the board. This completes the face-mould.