Let A C B, in Fig. 400, be the section of a portion of a mansard roof, the elevation of which is shown to the left, and let P E be any bed molding whose profile does not correspond to or member with the molding used to cover the hips, a section of the hip molding being shown at Z Y C.

The solution of this problem will be accomplished by means of a "true face" of the roof, rather than by means of a diagonal elevation as in the problem immediately preceding this. Therefore, supposing the section A C B to give the correct pitch of the roof, the first step will be to obtain the true face, or elevation of the roof as it would appear if tipped or swung into a vertical position, for the purpose of getting the correct angle at A1 B1 F1.

To do this reproduce the section of mansard and bed molding as a whole at a convenient point below, but so turned as to bring the faces of the roof into a vertical position, maintaining the same distance between the points A and B as shown by A2 and B2. Project lines horizontally to the left from this section for the true face, marking the lines from the points A2 and B1 From A of the original section carry a line across intersecting the line A1 B' at the point A'. Next drop line from A1 and B1 vertically intersecting lines of corresponding letter, as shown by the dotted lines. Then A3' B3 F1 will be the correct angle upon which to construct the corner piece and develop the miter line between the hip molding and the bed molding of the deck cornice.

The next step will be to obtain a correct section of the hip molding upon a line at right angles to the line of the hip. To do this it is necessary to first construct a diagonal section through the hip. At any convenient place lay off a plan of the angle of the roof, as shown by D1 F D2 in Fig. 407, and through this angle draw a plan of the hip, as shown by F K. From D1 erect a line perpendicular to F D1, as D1 C2, in length equal to D C of the section. Through C2, parallel to D1 F, draw C2 K, producing it until it cuts the line representing the plan of the hip. From the points F and K in the lines representing the plan of the hip erect perpendiculars, as shown by F L and K C3. Draw L C2 parallel to F K, as shown at the base line of a diagonal section. From C3 erect a perpendicular, C3 E', in length equal to C E of the original section. Connect E1 L. Then L C3 E1 will be a diagonal section of a portion of the roof, and L E1 will be the length of the hip through that portion. At right angles to L E1 draw M H1, upon which to construct a correct section of the hip molding. Take any point, as G in the line F D', at convenience, and from it erect a perpendicular to F K, cutting FK in the point H, and produce it also until it cuts the base line of the diagonal section L C3, as shown, and from this point carry it parallel to the line L E1, representing the pitch of the hip, until it crosses the line M H1, cutting it in the point II'. Since D' F D2 represents the angle in plan over which the hip molding is to lit. and since H G is the measurement across that angle, if the distance H G be set off from H1 either way in the diagonal section, points will be obtained by which the angle contained between the facias of the hip molding may be determined Therefore from II' on either side set off the distance H G of the plan, as shown by G' and G2 Through these points draw lines representing the fascias of the hip molding, as shown by O G1 and O G2. Add the fillets and draw the roll according to given dimensions, all as shown.

Fig. 406. - The Pollem of a Hip Molding Upon it Right Angle in a Mansard Roof, Miltring Agnii,sl a Bed Molding.

In the true face, Fig, 406, draw a half section of the hip molding as derived from Pig. 407, as shown. M2 H1 corresponds to M H1 of the diagonal section.

Fig. 407. - Method of Obtaining Correct Cross. Section of Hip in Fig. 406.

Space this profile into any convenient number of parts in the usual manner, and through the points draw lines parallel to the lines of the hip molding indefinitely.

Place a corresponding portion of the profile of the hip molding in the vertical section, as shown, in which M' IT also corresponds to H1 M in the diagonal section. Divide this section into the same number of equal parts, and through the points draw lines upward until they intersect with the profile of the bed molding, as shown between P2 and B2. From the points in P2 B2 carry lines horizontally, intersecting the lines drawn from the profile in the true face. Then a line traced through these points of intersection will be the miter line between the hip molding and the bed molding, as seen near B3 hi elevation.

For the pattern proceed as follows: At right angles to the line of the hip molding, as shown in the true face, lay off a-stretchout of the hip molding, as shown by S R, through the points in which draw the usual measuring lines. Place the T-square at right angles to the lines of the hip molding, and, bringing it successively against the several points in the miter line, as shown in elevation, cut corresponding measuring lines, which will give the pattern for the roll and fillets, as shown from U to V. In like manner place the T-square against the point X in the true face, which is the point of junction between the flange of the hip molding and the apron of the bed molding corresponding to points 9 and 10 of the profile, and cut the corresponding measuring lines. The pattern is then completed by drawing a line from W to V and T to U.