At right angles to C 2, draw the line J K, upon which place the stretchout of the profile in elevation as shown by similar figures on the stretchout line, through which drop lines perpendicular to J K, which intersect with lines drawn parallel to J K from similarly numbered points of intersection on the miterline 2 H. Trace a line as shown by L M, which is the miter-cut desired.

When two mouldings having different profiles are required to miter together as shown in Fig. 291, where C miters at right angles with D, two distinct operations are necessary, which are clearly shown in Figs. 292 and 293. The first operation is shown in Fig. 292, in which C represents the elevation of an ogee moulding which is to miter at right angles with a moulding of different profile as shown at D.

Divide the profile C into equal spaces, from which points draw horizontal lines intersecting the moulding D from 1' to 10'. At right angles to the line of the moulding C, draw the line A B, upon which place the stretchout of the profile C as shown by similar figures on A B. At right angles to A B, and through the points indicated by the figures, draw lines, which intersect with lines drawn parallel to A B from similarly numbered intersections in the profile D. Trace a line through the points thus obtained, as shown by E H. Then will E F G H be the pattern for C in elevation.

Fig. 292.

Fig. 293.

To obtain the pattern for D, draw the elevation of D (Fig. 293), which is to miter at right angles with a moulding whose profile is C. Proceed in precisely the same manner as explained in connection with Fig. 292. Divide the profile D in Fig. 293 into equal parts, as shown, from which draw horizontal lines cutting the profile C. At right angles to the lines of the moulding D, draw the stretchout line A B upon which place the stretchout of the profile D. At right angles to A B, and through the numbered points of division, draw lines as shown, which intersect by lines drawn parallel to A B from similarly numbered intersections in the profile C. Through these points of intersection draw F G. Then will E F G H be the desired pattern for D.

It should be understood that when the patterns in Figs. 292and 283 are formed and joined together, they will form an inside miter, as is shown in Fig. 291.

If, however, an outside miter were required, it would be necessary only to use the reverse cuts of the patterns in Figs. 292 and 293, as shown by E J

H in Fig. 292 for the mould C, and F J G in Fig. 293 for the mould D.

When joining a curved moulding with a straight moulding in either plan or elevation even though the curved or straight mouldings each have the same profile, it is necessary to establish the true miter-line before the pattern can be correctly developed, an example being given in Fig. 294, which shows an elevation of a curved moulding which is intersected by the horizontal mouldings A B. The method of obtaining this miter-line, also the pattern for the horizontal pieces, is clearly shown in Fig. 295. First draw the profile which the horizontal moulding is to have, as 1 10. Let the distance 9 B be established.

Then, with C on the center line as center, and A C as radius, describe the arc A B. From any point on the line 9 B, as a, erect the vertical line a b. Through the various divisions in the profile 1 10, draw horizontal lines intersecting the vertical line a b from 1 to 10 as shown.

From the center C, draw any radial line, as C d, cutting the arc B A at e.

Now take the various divisions on a b, and place them from e to d as shown by points 1' to 10'. Then, using C as center, with radii determined by the various points on e d, draw arcs intersecting horizontal lines of similar numbers drawn through the divisions on a b. Through these points of intersection, draw the miter-line shown. The student will note that this line is irregular.

Fig. 294.

Having obtained the miter-line, the pattern is obtained for the horizontal moulding by drawing the stretchout line E F at right angles to 9 B. On E F lay off the stretchout of the profile 1 10; and through the numbered points and at right angles to E F, draw horizontal lines, which intersect with lines drawn at right angles to 9 B from similarly numbered intersections in the miter-line determined by horizontal lines already drawn through the vertical line a b. Trace a line through the points thus obtained, as shown by H I J K, which is the desired pattern.

Fig. 295.

Fig. 296.

In Fig. 296 is shown a shaded view of a gable moulding intersecting a pilaster, the gable moulding B cutting against the vertical pilaster A, the joint-line being represented by a b c. To obtain this joint-line, without which the pattern for the gable moulding cannot be developed, an operation in projection is required. This is explained in Fig. 297, in which B C D shows the plan of the pilaster shown in elevation by E. In its proper position in plan, place the profile of the gable moulding, as shown by A, which divide into equal spaces as shown by the figures 1 to 8, through which draw horizontal lines intersecting the plan of the pilaster B C D as shown by similar figures. For convenience in projecting the various points, and to avoid a confusion of lines, number the intersections between the lines drawn from the profile A through the wash B 2, "7o", "4o", and "3o". At the desired point H in elevation, daw the lower line of the gable moulding, as H G. Take a tracing of the profile A in plan, with all of the various intersections on same, and place it in elevation as shown by A1, placing the line 1 8 at right angles to H F. Through the various intersections 1, 7o, 4o, 3o,