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been turned on its axis through 90, has brought two of its sides into view in both plan and elevation equally inclined to the planes of their projection, and therefore requiring a third line to represent 156 FIRST PRINCIPLES OF MECHANICAL AND ENGINEERING DRAWING 157 their junction. This line or edge in No. 5 will be a a ; that part of it where it passes through the prism being out of sight. From this plan No. 5, find by projection the elevation No. 6 of the solids as if they were entire. For the lines of penetration that will be visible, draw projectors from the points 1, 2, in the line b a in No. 5, to cut b' a" in No. 6 in the points 1', 2' ; then lines drawn from these last-found points to 3, 3' ; 4, 4' ; or where the upper and lower edges of the pyramid enter and leave the prism, will be the lines of penetration required. 67. Although, as stated in a previous paragraph, it is usual in practice to make the intersections of solids in the design of mechanical details symmetrical, cases may sometimes arise in which this symmetry cannot be adhered to. Through the exigencies of position of the solid penetrated, it may be impossible to bring the axes of both into one and the same plane, although at right angles to each other. To meet such a case the following problem will show the method of procedure in determining the lines of penetration. Problem 73 (Fig. 175). Given the plan of a square prism, pene- trated by a square pyramid, their axes being in different planes ; re- quired the elevation and lines of penetration of the solids. From No. 1 (Fig. 175), which is the given plan of the solids, it is seen that the axis d, a' of the pyramid passes through the prism in a