It is sometimes the case that the roof against which the moulding butts, has a curved surface either concave or convex, as shown by B C in Fig. 280, which surface is convex. Complete the elevation of the moulding, as D E; and in its proper position draw the section 1 9, which divide into equal spaces as shown by the small figures, from which draw horizontal lines until they intersect the curved line B C, which is struck from the center point A. At right angles to the line of the moulding erect the line 1' 9', upon which place the stretchout of the section, as shown by the figures on the stretchout line. Through the numbered points, at right angles to 1' 9', draw lines, which intersect by lines drawn at right angles to 2 I) from similarly numbered intersections on the curve B C, thus resulting in the intersections 1" to 9" in the pattern, as shown. The arcs 2" 3" and 7" 8" are simply repro ductions of the arcs 2 3 and 7 9 on B C. These arcs can be traced by any convenient method; or, if the radius A C is not too long to make it inconvenient to use, the arcs in the pattern may be obtained as follows: Using A C as radius, and 7" and 8" as centers, describe arcs intersecting each other at A'; in similar manner, using 2" and 3" as centers, and with thy same radius, describe arcs intersecting each other at N. With the same radius, and with A' and as centers, draw the arcs 8" 7" and 3" 2" respectively. Trace a line through the other various intersections as shown. Then will 1' 1" 9" 9' be the desired pattern.
In Fig. 281 is shown an elevation of an oblong or rectangular panel for which a miter-cut is desired on the line a b—known as a "panel" or "face" miter. The rule to apply in obtaining this pattern is shown in Fig. 282. A shows the part elevation of the panel; a b and c d, the miter-lines drawn at angles of 45°. In its proper position with the lines of the mould ing, draw the profile B, the curve or mould of which divide into equal spaces, as shown by the figures 1 to 7; and from the points thus obtained, par allel to 1 b, draw lines inter secting the miter-line a b as shown. From these intersections, par allel to h d, draw lines intersecting also c d. At right angles to b d draw the stretchout line 1' 7', upon which place the stretchout of the profile B. At right angles to 1' 7', and through the numbered points of division. draw lines, which intersect by lines drawn at right angles to b d from similarly numbered intersections on the miter lines a b and c d. Trace lines through the various points of inter section in the pattern as shown. Then will CD E F be the required cut for the ends of the panel.
The same miter-cuts would be employed for the long side a c in Fig. 281, it being necessary only to make D E in Fig. 282 that length when laying out the patttern on the sheet metal.
Where the miter-cut is required for a panel whose angles are other than right angles, as, for example, a triangular panel as shown in Fig.
283, then proceed as shown in Fig. 284. First draw the elevation of the triangular panel as shown by.A B C, the three sides in the case being equal. Bisect each of the angles A, B, and C, thus obtaining the miter-lines A c, B b, and C a. In line with the elevation, place in its proper position the profile E, which divide into equal spaces as shown; and from the numbered division points, parallel to A C, draw lines cutting the miter-line C a. From these intersec tions, parallel to' C B, draw lines intersecting the miter line, b B. At right angles to C B draw the stretchout line 1' 7', upon which place the stretchout of the profile E. Through the numbered points of divi sion and at right angles to 1' 7', draw lines as shown, which intersect by lines drawn at right angles to C B from intersections of similar numbers on the miter-lines a C and b B. Through the points thus obtained, trace the pattern F G H I.
It makes no difference what shape or angle the panel may have; the principles above explained are applicable to any case.
In ornamental cornice work, it often happens that tapering mould ed panels are used, a plan and elevation of which are shown in Fig. 285.
By referring to the plan, it will be seen that the four parts b a, a b', b' a', and a' b are symmetrical; therefore, in practice, it is necessary only to draw the one-quarter plan, as shown in Fig. 286, and omit the eleva tion, since the height d e (Fig. 285) is known. Thus, in Fig. 286, draw the quarter-plan of the panel, no matter what is its shape, as shown by a 1 5 6 9. Divide the curves from 1 5 and 6 9 into equa spaces, indicated respectively by 1, 2, 3, 4, and 5, and 6, 7, 8, and 9. From these points, draw lines to the apex a. As the pattern will be de veloped by triangulation, a set of triangles will be required, as shown in Fig. 287, for which proceed as follows: Draw any horizontal line, as a 1; and from a erect the perpendicular a a' equal to the height the panel is to have. Now take the lengths of the various lines in Fig. 286 from a to 1, a to 2, a to 3, etc., to a to 9, and place them on the lineal in Fig. 287, as shown by similar numbers. Then using as radii the various lengths a' 1, a' 2, a' 3, etc., to a' 9, and with any point, as a' in Fig.
288 as center, describe the various arcs shown from 1 to 9. From any point on the arc 1 draw a line to a'. Set the dividers equal to the contained in the curve 1 5 in Fig. 286; and, starting from 1 in Fig. 288 step from one arc to an othe. having similar num bers, as shown from 1 to 5. In similar manner, take the distance from 5 to 6 and the spaces in the curve 6 9 in Fig. 286, and place them on corresponding arcs in Fig. 288, step ping from one arc to the other, resulting in the points 5 to 9. Trace a line through the points thus obtained. Then will a' 1569 a'bethe quarter-pattern, which can be joined in onehalf or whole pattern as desired.