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of the frustum, made by the two section planes passing vertically through it, at distances from its axis at either end equal to that which the vertical lines drawn through points 1, 4, and 2, 3 in each semi-circle are from the lines a b and c d respectively. To find the sections of the cylinder by the same cutting planes, set off at the corresponding ends of the frustum in the plan No. 1 the distances that these planes are from the axial one pp' of the two solids, and through the points 1 1', 2 2', thus found, draw faint lines cutting the plan of the cylinder at e e, ff. Obtain by projection the elevation of the sections of the cylinder at these lines, and the points where they cross the corresponding sections of the frustum in elevation will be points in the lines of intersection sought. To find the two points in the cylinder's front surface, where the frustum penetrates and leaves it, draw projectors through g g in the plan No. 1, and they will give g g' in the elevation ; through these and the points of intersection of the sections already found draw the curved lines e g h, e g' h, and they will be the lines of penetration of the cylinder by the frustum of the cone. If the axis of the penetrating solid is inclined to the VP or HP, or to both, that of the cylinder still remaining as before, as shown in No. 3 (Fig. 182), the lines of intersection of the two are found as in No. 4 (Fig. 181) viz., by direct projection from the plan No. 3 of the solids in their new position, and from the elevation No. 2 ; the result being the view given in No. 4. The return lines, or those on the surface of the cylinder nearest the YP shown dotted, are found as indicated by the projectors. Taking the converse position of the two solids which frequently