Let Z X Y V in Fig. 404 be the elevation of a deck cornice, against the planceer of which a hip molding, shown in elevation by U W Y T, is required to miter. Let the angle of the roof be a right angle, as shown by the plan Q D A', Fig. 405, D N representing the plan of the angle over which the hip molding is to be placed. This angle is also shown by B A of the elevation. As the only view which will show the correct angle at which the hip molding meets the planceer is a view at right angles to the line D N, the first step in the development of the patterns will be to construct such a diagonal elevation. Assume any point, as A, in the elevation on any line representing a plain surface in the profile of -the roof, as B A. Through A draw a horizontal line indefinitely, as shown by L A C.

From B, the point in which the line A B meets the planceer, drop a vertical line, cutting the horizontal line drawn through A at the point C, all as shown by B C. Produce the line of planceer W Y, as shown by W1 Y1. Draw a duplicate of the plan, Q D A1 in Fig. 405, in such a manner that the diagonal line D N shall lie parallel to the horizontal line drawn through A, all as shown by Q1 D1 A2. At right angles to the line D1 A", at any convenient point, as A2 draw the line A2 C1, in length equal to the distance A C in elevation, and through C1 draw a line parallel to D1 A2, as shown by I N', cutting the diagonal line D' N' in the point N1. Then D1 N1 represents the diagonal plan of that part of the hip from B to A in the elevation. From N1 erect a perpendicular, N' M, which produce until it meets the line carried horizontally from the planceer in the point B1. In like maimer from D1 erect a perpendicular, which produce until it meets the horizontal line L C in the point L. Connect L and B1, as shown, which will constitute the desired oblique projection of A B.

The next step will be to construct a section of the hip molding upon a line at right angles with it, as G

Fig. 404. - The Pattern of a Hip Molding in a Mansard Roof, Mitering Against the Planceer of a Deck Cornice.

H, assumed at any convenient point. It might be supposed that in such a section the two fascias of the hip molding would be at right angles to each other, as they undoubtedly would appear in the plan Q D A1 of Fig. 405 or in a section on any horizontal line, as L M. The object of this part of the demonstration is to show exactly what that angle would be and how to obtain it. Assume any point in the diagonal plan, as E, in the side D' A1, from which erect a line perpendicular to D1 N1, as shown by E F. which produce until it meets the horizontal line L C in the point L1, and thence carry it upward parallel to L B, cutting G H in the point F1. On either side of F1 lay off a space equal to F E of the diagonal plan, as shown by F1 E1 and F1 E2. Through these points E1 and E2 draw lines to K, the intersection of the lines L B2 and G H. From

K as a center describe the curve of the roll of the required diameter. Upon the lines K E1 and K E2 set off from K a distance sufficient to make the desired width of fascia, thus completing the profile of the hip molding in the diagonal elevation.

Space one-half of this profile, as G E2, in the usual manner, through the points in which carry lines parallel to L B1 cutting the line of planceer W1 Y1, which is the miter line of the roll. The edges of the fascia will of course miter with the lower edge of the fascia at the top of the mansard, shown in profile at B E3, all as shown by the dotted lines projected from E3 At right angles to the line L B1 draw the straight line S R, upon which lay off a stretchout of the profile in the usual manner, and through the points draw measuring lines. With the T-square parallel to this stretchout line, or, what is the same, at right angles to the lines of the molding in the diagonal elevation, and, bringing it successively against the points in W1 Y1, cut corresponding measuring lines drawn through the stretchout. The measuring lines 7 and 8 are cut from the intersection of the fascia of the hip with lines projected from E3 as above explained. Then a line traced through these points, as shown in the engraving, as shown by J1 P O J, will be the pattern of the hip molding mitering against the horizontal planceer.

Fig. 405. - Plan of the Fascias anf Angle of the Mansard Shown in Fig, 404.