At Fig. 160 so much of the horizontal projection of the hand-railing of stairs in Fig. 158 is repeated as extends from the joint b to that at d, but at an enlarged scale. Upon the tangent ck set up the heights as given in Fig. 158; for example, make kk' equal to k"'k" of Fig. 158, and cc' equal to c"c' of Fig. 158. Join c' and k' and extend the line to meet c k, extended, in a. Join a and b; then ab is the line of intersection of the cutting and horizontal planes; it is therefore a horizontal line, parallel to which the ordinates are to be drawn. Perpendicular to ab draw b'c"". Parallel to ab draw cc" and kk"; join b' and c"; the angle cc" b' is the plumb-bevil; perpendicular to b' c' draw b' b', k" k"', and c" c"'; make b' b" equal to b' b, and so of the other two points, k"' and c"', make them respectively equal to their horizontal projections upon the plane A. Join c"' and k"; also, k" and b"; then b"k"' and k"' c"' are the tangents. From c"' draw the line c" b" parallel to b' c"; this is the slide-line. In this example, this line passes through the point b"; the slide-line does not always pass through the ends of the two tangents; it is not required to pass through both, but it is indispensable that it be drawn parallel with the rake-line b' c". The lines for the joints at each end are drawn square to the tangent lines. Points in the curves, as many as are desirable, are now to be found by ordinates as shown in the figure, and as before explained for the points in the tangents. The curves are made by drawing a line against the side of a flexible strip bent to coincide with the points.

Fig. 160

The face-mould may be put in position by revolving the planes C and B, as explained in the last article, for the rail at the newel.

The face-mould for the rail over the plan from c to d is to be obtained in a similar manner, taking the heights from Fig. 158. For example, make dd' equal to d"d' of Fig. 15.8, and ll, equal to l"'l" of Fig. 158 (taking the heights at their actual measurement now). Join d' and l" and extend the line to meet the line dl extended in r; join r and c; then rc is the line of intersection, and parallel to which the ordinates are to be drawn. The points in the face-mould may now be obtained as in the previous cases, giving attention first to the tangent and slide-line; drawing the lines for the joints perpendicular to the tangents.

##### Face-Moulds Continued

It may be remarked here that the chord-line be is parallel with the measuring line b'b"" and that the line ok bisects the chord-line; so, also, the line ol bisects the chord-line cd. This coincidence is not accidental; it will always occur in a regular circular stairs.

Hence in cases of this kind it is not necessary to go through the preliminaries by which to obtain the intersecting line ad, but draw it at once parallel to the line ok, bisecting the chord be and passing through the point of intersection of the two tangents For the distance to slide the mould in its after-application, the lines are given at c" and d", and their use is explained in the last article, and more fully in Art. 284.