Fig. 229.
In Figure 228 the axis of piece B is not in the same plane as that of D, but to one side of it to the distance between the centre lines C, D, which is most clearly seen in the top view. In this case the process is the same except in the following points: In the side view the line w, corresponding to the line w in the end view, passes within the line x before the curve of intersection begins, and in transferring the lengths of the full lines b, c, d, e, f to the end view, and marking the arcs b', c', d', e', f', they are marked from the point w (the point where the centre line of B intersects the outline of A), instead of from the point x. In all other respects the construction is the same as that in Figure 227.
Fig. 230.
In these examples the axis of B stands at a right-angle to that of A. But in Figure 229 is shown the construction where the axis of B is not at a right-angle to A. In this case there is projected from B, in the side view, an end view of B as at B', and across this end at a right-angle to the centre line of B is marked a centre line C C of B', which is divided as before by lines d, e, f, g, h, their respective lengths being transferred from W as a centre, and marked by the arcs d', e', f', which are marked on a vertical line and carried by horizontal lines, to the arc of A as at i, j, k. From these points, i, j, k, the perpendicular lines l, m, n, o, are dropped, and where these lines meet lines p, q, r, s, t, are points in the curve of intersection of B with A. It will be observed that each of the lines m, n, o, serves for two of the points in the curve; thus, m meets q and s, while n meets p and t, and o meets the outline on each side of B, in the side view, and as i, j, k are obtained from d and e, the lines g and h might have been omitted, being inserted merely for the sake of illustration.
In Figure 230 is an example in which a cylinder intersects a cone, the axes being parallel. To obtain the curve of intersection in this case, the side view is divided by any convenient number of lines, as a, b, c, etc., drawn at a right-angle to its axis A A, and from one end of these lines are let fall the perpendiculars f, g, h, i, j; from the ends of these (where they meet the centre line of A in the top view), half-circles k, l, m, n, o, are drawn to meet the circle of B in the top view, and from their points of intersection with B, lines p, q, r, s, t, are drawn, and where these meet lines a, b, c, d and e, which is at u, v, w, x, y, are points in the curve.
