The shape of the cover considered in this problem may perhaps be more accurately described as that of an oblong pyramid with rounded corners, as shown by the plan and elevation in Fig. 533, an inspection of which will also show that the rounded corners are portions of a scalene cone, while the four pyramidal sides are simply plain triangular surfaces.

Fig. 533.   Plan and Elevation of Cover.

Fig. 533. - Plan and Elevation of Cover.

The plan shows one-half of cover, or as much as would usually be made from one piece. First divide G H of plan into any convenient number of equal parts - in this case four - and connect the points thus obtained with O, thus obtaining the base lines of a set of right angled triangles whose hypothenuses when obtained will give the true distances from the points in G H to the apex of the cover.

To construct a diagram of triangles represented by lines in plan, draw the right angle M N P in Fig.

Fig. 534.   Diagram of Triangles.

Fig. 534. - Diagram of Triangles.

534, making M N equal to the hight of cover, as shown by B D of elevation. Measuring from N, set off on N P the length of lines in plan, including J O and O F. From the -points in N P draw lines to M, as shown. The line C M gives the slant hight of cover as seen in the end elevation, and M J' the slant hight as would be seen in side elevation. The other lines give the hypothenuses of triangles, the bases of which are shown by the lines in O G H of plan.

To describe the pattern proceed as follows:

Draw the line Q U, in Fig. 535, in length equal to M J' in the diagram of triangles. Through U, at right angles to Q U, draw V T, making U T and U V each equal to J H or J K of Fig. 533, and draw Q T and Q V. Then Q V T will be the pattern of one of the sides of the pyramid, to which may be added on either side the envelope of the portion of a scalene cone shown by H O G in Fig. 533. It should be here remarked that the method above employed of obtaining the length Q T produces the same results as that employed in the diagram of triangles as shown by the hypoth-enuse M 1, which is one side of the adjacent triangle forming part of the pattern of the rounded corner. From Q of Fig. 535 as center and M 2 of the diagram of triangles as radius strike a small arc, 2', which arc is to be intersected with one struck from T of pattern and the distance H 2 of plan as radius. Proceed in this manner, using the spaces in H G of plan for the distances in T S of pattern, and the lengths of lines drawn from M to points 2 to 5 in diagram of triangles for the distances across the pattern from Q to the points in T S. With S of pattern as center, and G F of plan as radius, describe a small arc, R, which intersect with one struck from Q of pattern as center, and M C of the triangles or B C of the elevation as radius, thus establishing the point R of pattern. Draw R S, and trace a line through the points from S to T, as shown. The

Q other part of pattern, as Q V W P, can be described in the same manner, or by duplication.

Fig. 535.   Pattern of Cover.

Fig. 535. - Pattern of Cover.