to indicate exactly the form of the return curve of penetration. This is shown by the dotted line I, obtained by projecting over the points 4, 5,' 6, in i h, No. 3, and finding as before the corresponding sections of the back halves of the cone and cylinder, which give the points required. 75. Had the penetrating solid been but a portion of a cone say a frustum then the lines of intersection of the two may be got in two ways. If the apex of the cone is accessible, the method already explained would be the simplest and best ; but if the taper of the cone be only slight, and its apex out of reach or at an inconvenient distance, then the procedure would be as shown in Fig. 182. First, let it be assumed that the axis of the penetrating solid is parallel to the YP, and at right angles to that of the cylinder. Having UNIVERSITY 174 FIRST PRINCIPLES OF MECHANICAL AND ENGINEERING DRAWING 175 drawn in the plan and elevation of the solids as if entire, to find their lines of intersection divergent planes are assumed to cut through both, as in the last case ; but to ensure that the planes used will pass through the apex of the cone of which the frustum forms part and thus give true sections, the procedure in finding them is as follows : In No. 2 (Fig. 182), on a 6, c c?(the ends of the frustum), as diameters, describe semi-circles ; divide each into the same number of equal parts say, six and project the points of division in them over to their respective diameters (a b, c <f), and join them by faint dotted lines, as shown. Then the surfaces included within the bounding lines 1 1', 1' 4', 4' 4, 4 1, and 2 2', 2' 3', 3' 3, 3 2, will be the true sections of the front half