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44. The Apron for a Conical Roof Flange.—When any solid is cut by a plane that is inclined to the plane of the base, the shape or section thus formed is not the same as the profile of the base.

The Elevation.—The elevation of the roof flange used in Problem 22 can be reproduced.

The Pattern.—Any straight line, Fig. 130, may be drawn and the exact spacing of the miter line set off upon it. Perpendicular measuring lines, Fig. 130, are erected through each point and are numbered to correspond to the miter line.

Returning to the elevation, Fig. 129, an extension line is dropped from point 1, down to the horizontal center line of the half-profile. From point 2 of the miter line, the horizontal extension line is followed over to the slant height. From this point, a perpendicular to the horizontal center line of the profile is dropped, and with one point of the compass on the center of the profile, this line is extended by an arc until it strikes a radial line from point 2 of the profile at the point B.

The perpendicular distance from point B to the horizontal center line should be measured and placed on each side of the line of stretchout. Fig. 130, on measuring line number 2. In like manner, points C, D, E, and F are located and their distances placed on measuring lines 3, 4, 5, and 6 respectively. A curve traced through the points thus obtained will give the shape of the hole in the apron as well as that of the hole to be cut in the roof.

A rectangle representing the shape of the apron should be drawn, allowing a space of at least 6 in. "up the roof," and at least 3 in. on the other sides. A hem should be added to three sides to turn or direct the flow of any roof water that might leak in. A -inch single edge should be allowed around the inside of the hole, in order to double seam the body to the apron.