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Problem 48 (Fig. 143). Given tlie plan of a circular plate as a circle ; to find its projections in t/ie VP and HP when making a given angle with either plane. Let the circle ABCD, No. 1, be the given plan, the diametral line AB being parallel to the IL, and the similar line CD perpendicular to it. Bisect each quarter of the circle in the points 1, 2, 3, 4. As shown, the surfaces of the plate are evidently parallel to the HP. Let it now be inclined to that plane at an angle of 60, keeping the diametral line AB parallel to the HP, and the point C uppermost, or nearest to the eye. To obtain its elevation when in that position, an edge view of it looking in the direction of the arrow x must first be given, which will be a line equal in length to CD, inclined to the IL at the required angle. Draw in this line CD as in No. 2, and bisect it in the point B, which will be the end of the diametral line AB, nearest MECHANICAL AND ENGINEERING DRAWING 95 the eye in side elevation, A being the point beyond it across the circle. Through B, No. 2, draw a projector parallel to the IL, and in- tersect it in points a, b (No. 3) by projectors from A and B in No. 1. Transfer points 2 and 4 in No. 1 to 2 and 4 in No. 2, and through them draw projectors parallel to that through B ; then from 3, 4, in No. 1, intersect by projectors which will pass through 1, 2 those drawn from 2, 4, No. 2, in I', 2' 3', 4', No. 3. Through the eight points thus found, draw the closed curved-bounding line shown, and the figure or ellipse will be the front elevation of the circle No. 1 in plan when inclined at an angle of 60 to the HP, and 30 to the VP. To find the plan of the plate in this position, let fall projectors