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72. The Cup Strainer.—This problem introduces the principles that apply when two cones intersect each other. Figure 231 is an elevation of the cup strainer. The body is a frustum of a cone whose apex is noted upon the drawing as Apex No. 1. The handle of the strainer is also a cone and miters upon the conical body as shown in Fig. 231. When two cones miter upon each other in this manner, the miter line must be developed.

Developing the Miter Line.—The elevation of the cup strainer, Fig. 231, should first be drawn according to the dimensions given. The body and handle should have their sides extended to determine the apex of each. The half-profile of the handle is then drawn and divided into equal spaces. After numbering each space, perpendicular lines are drawn to the base of the cone. From these points, extension lines are drawn to Apex No. 2. Directly above the elevation, a half plan of the handle is drawn using extension lines to locate the view properly. A quarter-profile, Fig. 230, is drawn and the spacing of the half-profile of Fig. 231 is transferred in such a way that point 1 falls on the horizontal center line. An extension line is drawn from point 2 perpendicular to the base line and thence to Apex No. 3. Perpendicular lines are now drawn from the points of intersection of extension lines 2 and 3 of Fig. 231 and the slant height of the body, until they meet the horizontal center line of Fig. 230. With one point of the compass on the center of the profile of the body, Fig. 230, arcs A and B are drawn. Extension lines should now be carried back from the points of intersection of arcs A and B with line 2 until they intersect lines 2 and 3 in Fig. 231. The curved miter line is now drawn in as shown.

Developing the Pattern for Handle.—From each intersection of the miter line in Fig. 231, lines intersecting the slant height should be drawn parallel to the base of the cone. These intersections are shown by letters, c, d, e, and f, in Fig. 231. The arc of stretchout is now drawn and the spacing of the profile transferred with numbers to correspond.

From each point on the arc of stretchout, Fig. 232, lines are drawn to Apex No. 2. Arcs should now be drawn from points