In Pig. 545, A B C D E F represents the plan at the top of a portion of the flaring article, whose general shape is rectangular with rounded corners. G H I J K L represents the plan of the bottom of the same, showing that the flare at the ends, represented by I C or J D, is greater than that of the sides, represented by A G. The arc E D of the plan of the top is struck from O as center, while the arc J K of the bottom is struck from N. Since the top and bottom are parallel, as shown by P Q and P S of the side elevation, the corner JDEK is a portion of the envelope of the frustum of a scalene cone.

To find the apex of the cone, drop lines from 0 and N at right angles to P Q, cutting respectively the top and bottom lines in the side view, as shown at T and U, and draw TU and continue the same indefinitely in the direction of X. Also continue Q S until it intersects T U at the point X. Then X will be the apex of the cone. From X erect a line vertically, cutting the line D M of the plan at M; then M will show the position of the apex of the cone in plan. Divide the arc E D into any convenient number of equal spaces, and from the points thus obtained draw arcs from M as center, cutting O D, as shown. Prom the points in 0 Ddrop lines vertically, cutting T Q, the top line of the side, otherwise the base of the cone. From the points thus obtained in T Q draw lines toward the apex, cutting U S.

With one foot of the compasses set at X, bring the pencil point successively to the points in T Q and draw-arcs indefinitely, as shown. From any convenient point upon the arc 0, as E1, draw a line to X, forming one side of the pattern. Take between the points of the dividers a space equal to that used in stepping off the plan of cone E D, and, placing one foot at the point E1, swing the other foot around, gutting the arc 1, from which intersection step to the next arc, and so continue until all the arcs have been reached at D1, from which point draw a line to the apex X. Likewise from each of the points between E1 and D1 draw lines toward the apex indefinitely. Finally, with one foot of the compasses at X, bring the pencil point to each of the points in U S and draw arcs, cutting radial lines of corresponding number in the pattern. Lines traced through the points between the points K1 and J1 and E1 and D1 will complete the pattern of the carved corner. The pattern for the plain sides can easily be obtained after the manner described in Problem 74 and added to that of the corner as may be found practicable.

Fig. 545. - Plan, Elevation and Pattern of Rounded Corner fur an Article whose Sides and Ends Flare Unequally.

Pattern. Problems. 317