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of the plane surface on which the nut is supposed to rest to be one of 30 to the horizontal, draw in a line making with the IL such an angle. Transfer to this line the view of the nut given in No. 2, and obtain by projection its plan in this inclined position, as shown in No. 4. Then to find its elevation when swung through a horizontal angle say of 45 draw in its axial line in the HP making that angle with the IL, and transfer to it the plan of the nut found in No. 4, giving the view of it shown in No. 5. From this plan, and the elevation No. 3, find by projection the view given in No. 6, and the requirements of the given problem will be fulfilled. An infinite variety of problems might be given in this very interest- ing part of our subject, but as they would only involve in their solution the correct application of principles which have been fully explained, we pass on to the elucidation of projection as applied to the " penetration " and " intersection " of solids, a knowledge of which is of the first import- ance to the would-be draughtsman. CHAPTER XVII THE PENETRATION AND INTERSECTION OF SOLIDS 61. UP to the present stage in our subject, all the objects chosen as examples to illustrate the application of the principles of projection have consisted of simple solids, with either plane or curved surfaces or both -and have each been treated independently. They have not, of course, included all the elementary forms which, in combination, give shape to machine and engine details ; but they have been such as will enable the student to delineate correctly any subsidiary solid generally derived from one of the primary ones which may enter into the con- struction of a complete mechanical structure.