At Fig. 161 so much of the plan of the hand-railing of the stairs of Fig. 158 is repeated as is required to show the rail from / to g, but drawn at a larger scale. To prepare for the face-moulds, perpendicular to pf draw pp',and make pp' equal to p"'p„ of Fig. 158 (taking this height now at its actual measurement); join p' and f; then fp' is the tangent of the vertical plane C, and f is a point in the cutting plane at its intersection with the bass-plane A. Now since rs, the tangent over pg, is horizontal and is in the cutting plane, therefore from f draw fa parallel with r s or pg; then fa is the line of intersection of the cutting and horizontal planes, and gives direction to the ordinates. Draw f'p"' perpendicular to fa; make p"'p" equal to pp'; join p" and f'; then the angle pp"f' is the plumb-bevil; perpendicular to p"f' draw f'f" and p"p"'; make p"p"" equal to p"',g, p"'d equal to p"'p; join d and f"; then df" and dp"" are the tangents. Make p" e equal to half the thickness of the plank; draw f" a parallel with f'p"; make f" a equal to ec; draw dc' parallel with the tangent f"d; through f", perpendicular to f" d, draw the line for the butt-joint; then f"c' is the distance required to determine the vertical line on the face of the joint at f", as shown at A. Through p"" perpendicular to the tangent p"" d, draw the line for the butt-joint; make p"" b equal to ec, then p""b is the distance required for determining the vertical line on the face of the joint at p"" as shown at B (see Art. 284). The curved lines are obtained by drawing a line against the edges of a flexible rod bent to as many points as desirable, obtained by measuring the ordinates of the plan at A and transferring them to the face-mould by the corresponding ordinates, as before explained. Fig. 161.