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passing through both solids simultaneously. These would give tri- angles for the cone and circles for the sphere; the latter, however, being at an angle to the YP, would in elevation be projected into ellipses. Therefore in No. 1 (Fig. 189) draw in, through a' the vertex of the cone, to its base, as many lines say three a'\ a 2 a 3, as it is intended to use section planes. Next find in No. 2 the elevation of the triangular sections produced by these planes, as in previous problems. Then, so far as the sections of the sphere are concerned, all that is required is to find the points in the ellipses into which the circular sections of the sphere are projected which intersect the 186 MECHANICAL AND ENGINEERING DRAWING triangular sections of the cone, for it is through them that the lines of penetration of the sphere by the cone will pass. To determine these points, there is no necessity to draw in the elliptic projections, as they may be found very readily by the use of the paper trammel before mentioned. Having numbered the section planes, in plan and elevation, as in No. 1 and No. 2 in the figure, and noted the points 4, 5, 6, 7, where they cut the great circle of the sphere in No. 1, draw in, in No. 2 through line cs, which passes through the centre of the sphere, the lines in which the major axes of the ellipses will lie. One of these only viz., that from x in No. 1 is drawn in, in the diagram, so as to prevent confusion. Then with half the major and projected half of the minor axes of each ellipse there being one for each section taken on the trammel, manipulated as explained, all the points in the lines of intersection, except the extreme ones, are found as shown in elevation No. 2. For the plans of these lines that will be seen from above shown in No. 1- let fall