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sides of the tube seen from above when the upper part cut off by the plane x y is removed. By its removal, however, a part of the in- terior of the tube is now seen when viewed from above, and this must be indicated in the plan. The part seen is the angle formed by the meeting of the two bottom inside surfaces of the tube immediately over the point lettered c, and as these are plane surfaces, their inter- section forms a line the plan of which is found by letting fall a pro- jector from c cutting the lines a" b", a 9 b', in c" c, and joining them by a straight line. With the section lining of the parts cut by the plane x y t the " sectional plan " of the " original object," or hollow tube C, is completed. The projection of the sectional plan of the object represented in end elevation by D, in Sheet 1, would give little useful practice to the student if kept in the same position as there shown, all its surfaces being either parallel or perpendicular to the HP, and therefore result- ing in a very trifling change in the plan (got by a horizontal section of it) from that previously obtained ; it is consequently shown with its principal surfaces inclined to the HP, thereby giving a more difficult, but more useful, problem in projection. With the original object in this altered position the student will at once be struck with the identity in appearance of its elevation with that of the hollow tube in the last problem, and he will perhaps be momentarily puzzled to under- stand how two apparently similar end views are the vertical projections 58 MECHANICAL AND ENGINEERING DRAWING of two such different objects. Here we have an instance showing the absolute necessity of a pre-conceived knowledge of the form of the object to be delineated, or the possession of a model of it. Having