In Fig. 412, let D B of the section represent the wash surmounting the base molding at the foot of a mansard roof, the inclination of the roof being shown by B A. The plan of the angle of the roof B2 K B2, as specified, is that of an octagon, but so far as principle and method are concerned, it may be any angle whatever. The profile of the hip mold as given in the original drawings will most likely be drawn as fitting over an octagonal angle - that is, over the angle as given in the plan of the building. As explained in the problem preceding this, a section through the angle of the roof at right angles to the line of the hip must be obtained, to which the profile of the hip mold must be adjusted before going ahead. The difference between such a section and the angle in plan may seem trifling, but will be found to increase as the pitch of the roof decreases, and in a low hip roof will be found to be considerable. Hence the original detail of the hip mold must be accepted only so far as it gives width and depth of fascias and fillets, and diameter or radius of the roll, while the angle between the fascias must be adjusted to the true section across the hip as above stated. The method of doing this is shown in Fig. 413, and the principles involved therein are explained in the previous problem in connection with Fig. 411, and need not, therefore, be repeated here.

Fig. 413. - Diagonal Section of Hip.

Fig. 412 - The Pattern of a Hip Molding Upon an Octagon Angle. Mitering Upon an Inclined Wash at the Bottom.

The first operation will consist in obtaining the "true face" of the roof in the usual manner, viz.: Assume any point upon the section of the roof, as A, at a convenient distance above the base, as a point from which to measure hight and projection. Redraw the section of the roof immediately below the first one, placing it in a vertical position and locating thereon the point A, as shown by A1. From the points A1, B1 and D1 project lines horizontally to the left, thus obtaining all the bights in the true face. It will be necessary next to complete the plan, to do which first obtain the projection of the points in the section upon any horizontal line, as the one drawn through B, which can be done by dropping vertical lines from the points A and D, cutting it as shown at I and C. Assuming the line B2 K B2 of the plan to represent the point B of the section, set off upon any lines at right angles to the lines B2 K these projections - that is, make B2 I1 equal to B I, and B2 C1 equal to B C. Through these points draw lines parallel to B2 K, intersecting and forming the line P G, widen is the plan of the angle over which the hip mold is required to fit. From the points P, K and G, which represent upon the angle of the roof the points A, B and D of the section, drop lines vertically into the true face intersecting the horizontal lines previously drawn from A1, B1 and D1, as shown; then P1 K1 I2 will be the correct angle at which to construct the miter of the half of the hip mold belonging to this face of the roof, and K1 G1 H2 I2 will represent a corresponding elevation of the wash.

The elevation of the true face may now be completed by placing one-half the profile of the hip in correct position - that is, with its base line or fascia at right angles to the hip line P1 K1, the point R coming on the line. Through the points Y, S and T project lines parallel to the hip line. To show the intersection of the hip mold with the wash, first place a duplicate of the half profile of hip mold in the sectional view, as shown by Y1 B1 T1; then divide the curved portion of both profiles into the same number of equal spaces and number all the points correspondingly, as shown. From these points drop lines downward parallel with the lines of the respective views, those in the sectional view cutting the line of the wash B1 D1. From these points of intersection carry lines horizontally, intersecting the lines dropped from the profile Y S T. Then a line traced through these points of intersection, as shown by Y2 S2 T2, will be the miter line formed by the junction of the hip molding with the wash. At right angles to the line of the hip molding in the true face lay off a complete stretchout of the hip molding, as shown by U V. Through the points in it draw measuring lines in the usual manner. Place the T-square parallel to this stretchout, or, what is the same, at right angles to the line of the hip molding, as shown in true face, and, bringing it successively against the points in the miter line Y2 S2 T2, cut the corresponding measuring lines. Then a line traced through these points of intersection, as shown from W to Z, will be the cut to fit the bottom of the hip molding.

The normal elevation may be completed, if desired, by means of projections from the plan and the section, as shown.