The joint-line of the face-mould will be very accurately found thus:

Produce (fig. 3) GE to w. Draw Aw parallel to MG, and wx parallel to EH, cutting GH produced in x. Draw x y parallel to Gr, and make ry equal to wA; and by this method the whole of the face-mould is found in the most accurate manner.

196. The mould for the other part may be found in a similar manner: it is, however, proper to remark, that the operation is inverted for the conveniency of finding the mould from the under side of the falling-mould, instead of from the upper side. But we shall here take the opportunity of showing a different method.

In fig. 4, draw the plan ABDFE, and let the resting points be F, B, D. Join DF, and produce DF to L. From the resting points F, B, D, draw lines parallel to each other in any convenient direction, as FI, BG, and DH; and make the lines FI, BG, DH, respectively equal BI, Ho, Fn, in fig. 2. Then, through the points IH, draw a line to meet the line FD in L; also, through the points IG draw a line to meet another drawn through the points FB, the point of meeting being K, and join LK.*

Through E, draw OP perpendicular to KL; and from F draw Fcg parallel to KL, and make cg equal to FI, and draw the line Og.

In the curve take any number of points, A, a, b, &c., and from each point draw lines parallel to KL, to meet Og in p, g, h, &c., and from each of the points thus found in the line Og, draw perpendiculars, as pk, gm, hl, &c.; then make pk equal to PA, gm equal to cF, hl equal to da, &c., by which means any number of points may be found through which the curved lines of the mould may be drawn.

The joint-line will be found most accurately by producing AF to meet OP as in t, draw tu parallel to KL, and join uk, which is the direction of the joint as required.

We have now placed it in the Joiner's power to contrast the two methods, both in point of simplicity of operation, and accuracy of determination.

TO FIND THE MOULDS FOR EXECUTING A HAND-RAIL ROUND A SEMI-CYLINDRIC WELL-HOLE, WITH FOUR WINders in one quarter, the other being flat, and FLYERS ABOVE AND BELOW.

197. To find the Falling Mould, (fig. 1, pl. LXXX.)—Draw the straight line JI, in which take any point, d, and draw dC perpendicular to JI. In dC make dt equal to the greater radius of the plan of the rail, and, through t, draw a b parallel to JI. From the centre t, with the radius td, describe the semi-circle adb. In tC make tU equal to tb, together with threefourths of tb. Join Ua and Ub. Produce Ua to meet JI in T, and Ub to meet JI in H; then TH is the rail stretched out on the plan, being an example of the method shown in art. 46, CARPENTRY. In JI make HI equal to the breadth of one of the flyers. Draw HG perpendicular to HI, and make HG equal to the height of a step, and join GĮ. Make TJ equal to the breadth of two of the flyers.

Draw JN perpendicular to JI. In JN make JK equal to the height of a step, K4 equal to the height of four steps, KL equal to the height of five steps, KM equal to the height of six steps, and KN equal to the height of seven steps. Draw 4f parallel to JI, meeting dC in f.

* The process is more neat and simple when from the point u a line u2 is drawn parallel to FB, fig. 2, and AI, BG, fig. 4, are made respectively equal to 21, and 10, for then the points L and D coincide. We shall have occasion to give other examples where this simplification is adopted.