The solution of all problems concerning mansard roofs, and especially those in which the roof surface is curved, calls for much good judgment on the part of the pattern cutter, for the reason that the original designs that come into his hands are seldom drawn mathematically correct. The upper part of a mansard dome, such as is shown in Fig. 278, as it curves away from the eye, becomes so much flattened in appearance that, if drawn correctly, it might, to any but an expert draftsman, create a false impression of the design intended; hence the original drawing must often be taken for what it means rather than for what it says.

The engraving represents an elevation of a curved hip molding occurring in a roof, of which E D is the vertical bight and M2 K3 is a section. The first step to be described is the method of obtaining the pattern of the fascias of the hip molding. For this purpose is shown in the drawing such a representation of it as would appear if the two fascias formed a close joint upon the angle of the roof, supposing that the hip molding or the bead is to be added afterward on the outside over this joint. The part to be dealt with may be considered the same as though it were the section of a molding, instead of a section of a roof, and the operations performed are identical with those employed in cutting a square miter. Space the profile H K into any convenient number of parts, introducing lines in the upper part in connection with the ornamental corner piece, shown by L D, at such intervals as will make it possible to take measurements required to describe the shape of it in the pattern. From this profile, by means of the points just indicated, lay off a stretchout, as shown by H1 K1, and through the points draw the usual measuring lines. Bring the T-square against the several points in H K, and cut the corresponding lines drawn through the stretchout just described. Then a line traced through these points, as shown by H2 K2, will be the outside line of the fascia. For the inside line take the given width of the fascia and set it off from this line at intervals, measuring at right angles to it, as indicated by A1 B1, and not along the measuring lines of the stretchout, as would be indicated by A1 C. Then a line traced through these points, as shown from M1 to L1, will be the inside line of the fascia strip. The points in the ornamental corner piece from L1 to D1 are to be obtained from the elevation, in case a correct elevation is furnished the pattern cutter, by measurement along the lines drawn horizontally through the several points in L D, which are. transferred to the measuring lines of corresponding number in the stretchout already referred to. Or the shape from L1 to D1 may be described arbitrarily upon the pattern at this stage of the operation, according to the finish required upon the roof. The latter method is the preferable one. The method of constructing the elevation, by working back from the outline thus established, is clearly indicated by the dotted lines in the engraving. From the several points in the profile H K horizontal lines are drawn, as shown, and from the intersections of the inside line of the pattern of the fascia piece with the various measuring lines, as above described, lines are dropped, cutting these horizontal lines of corresponding numbers. Then a line traced through these points, shown from M to L, will be the inside line of the fascia piece in elevation. To cut the flange strip bounding the fascia and corner piece, commonly called the sink strip, an elevation of which is shown in the section from M2 to D2, the following method will be the simplest, and at the same time sufficiently accurate for all purposes: Draw the line G F approximately parallel to the upper part of the section M2 D2, making it indefinite in length, which cut by lines drawn from the several points in M2 D2, at right angles to it, as shown. From F G, upon the several lines drawn at right angles to it, set off spaces equal to the distance upon lines of corresponding number from D E to the line M L of the elevation. Then a line traced through these points, as indicated by M2 L2, will constitute a profile of this flange strip. In like manner set off in continuation of it, the lengths measured from points in the ornamental corner piece to D E, all as shown by L2 D2 F. From this profile lay off a stretchout parallel to G F, as shown by M4 D4, through the points in which draw measuring lines in the usual manner. Place the T-square parallel to the stretchout line, and, bringing it successively against points in both the inner and the outer lines of the elevation of the flange strip, as shown from M2 D2, cut the measuring lines of corresponding number. Then lines traced through these points of intersection, as shown from M5 to D6, will be the pattern of the flange strip bounding the edge of the fascia.