In Fig. 625, let C E F D be the front elevation of a portion of a curved pediment whose center is at K, and of which E K is the center line. C A B D of the same elevation represents the face view of a bracket having vertical sides, of which E G F is the normal profile. Since the bracket sides are vertical and are necessarily at different distances from the center line, it will be easily seen that they are of different lengths or hights; that is, the side C D, being further from E K than the side A B, is longer. The patterns for the two sides will therefore be different and the face piece will be really an irregular Baring piece.

It will first be necessary to obtain the pattern or profiles of the two sides. To facilitate this operation the normal profile of the bracket EGF has been so placed that its vertical line or back coincides with the center line E K of the arch. Divide the face of this profile into any convenient number of parts, as shown by the small figures, and from these points carry lines at right angles to the back of the bracket, cutting the line E F, as shown. Thence carry lines around the arch from the center K, from which the same is struck, cutting the sides A B and C D. Conveniently near the lower side of the bracket draw any vertical line, as E1 B1, as a base line upon which to construct the true sides of the bracket. At any convenient position upon this line, above or below, as at G1 E1 F1, draw a duplicate of the normal profile, so that its back or vertical line shall coincide with E1 B1, and divide its face line into the same spaces as G F. Place the T-square at right angles to the line E1 B1, and,bringing it successively against the points in the side G D, draw lines cutting E1 B1, continuing the same indefinitely to the left, as shown. At any convenient position, as A1 B1, on the line E1 B1 transfer the spaces from A B, as shown, and from the points thus obtained draw lines indefinitely to the left also at right angles to E1 B1. Place the T-square parallel to E1 B1, and, bringing it successively to the points in the normal profile G1 F1, cut lines of corresponding number in the two sets of parallel lines just drawn. Lines traced through the points of intersection will give the required patterns of the lower and upper sides, as shown respectively by C1 M D1 and A1 N B1. Some of the lines of projection in the pattern of the upper side have been omitted to avoid confusion. At the extreme left of the engraving is shown a side view of the bracket as seen from the right, which is made up of the two sides just obtained and which have been placed in proper relation to each other, all as shown by the dotted lines projected to the left from the points A, B, C and D of the front elevation.

Fig. 625. - A Raking Bracket in a Carved Pediment, Showing the Patterns for Its Face and Sides.

Having now obtained all that is necessary, it remains to triangulate the face of the bracket preparatory to developing the pattern of the same. With this in view first connect all points of like number in the upper and lower sides of the front view by solid lines, as shown. Also connect them in the side elevation. Since points of like number in A B and C D have the same projection from the back of the bracket, it will be seen that the solid lines just drawn connecting them represent true distances across the face of the bracket. The four-sided figures produced by drawing these lines must now be subdivided into triangles by means of dotted lines drawn diagonally through each. Therefore connect each point upon the profile of the lower side of the bracket with the point next higher in number upon the upper side, as shown in the side view. To determine the true length of these lines it will be necessary to construct a diagram of triangles, as shown by S V T in the upper part of the engraving. Draw S V and S T at right angles to each other. Make S V equal to the width of the bracket measured horizontally across the face, and upon S T, measuring from S, set off the lengths of the several dotted lines in the side view, as shown by the small figures. From each of points in S T draw lines to V. Then these lines will be the real distances between points of corresponding number on the lower side of the bracket and points of the next higher number upon the upper side. The figures in S T correspond with the figures upon the lower side of the bracket, the point V representing, in the case of each line, the next higher number; thus 2 V is the distance from 2 to 3' across the face of the bracket, 3 V the distance 3 4', 4 V the distance 4 5', etc. The dotted lines in the side view representing the distances 1 2 and 7 8 cannot, of course, be shown in that view, because they lie in surfaces which appear in profile; but since these surfaces are parallel with the plane of the back of the bracket these distances for use in the pattern may be taken directly from the front view, as shown by the dotted lines 1 2' and 7 8' in that view.

To lay out the pattern of the face piece first draw any line, as C3 A3 or 1 1' of the pattern, equal in length to 1 1' of the front view. From C3 of the pattern as center, with a radius equal to 1 2' of the front view, describe a small arc, which intersect with another arc drawn from A3 as center, with a radius equal to 1' 2' of the front view, thus establishing the point 2' of the upper side of the pattern of the face. From 2' of the pattern as center, with a radius equal to 2 2' of the front view, strike a small arc, which intersect with another arc struck from 1 of the pattern as center, with a radius equal to 1 2 of the front view, thus establishing the position of the point 2 in the lower side of the pattern. From 2 of the pattern as center, with a radius equal to 2 V of the diagram of triangles, strike a small arc, which intersect with another are struck from 2' of the pattern of center, with a radius equal to 2' 3' of the side view, thus establishing the point 3' of the pattern. From 3' of the pattern as center, with a radius equal to 3 3' of the front elevation, strike a small arc, which intersect with another arc struck from 2 of the pattern as center, with a radius equal to 2 3 of the side view. So continue, using the distances across the face indicated by the dotted lines as found in the diagram of triangles in connection with the spaces in the profile A2 B2 of the side view to form the upper side A3 B3 of the pattern, and the distances across the face as measured upon the solid lines of the front view-in connection with the spaces upon the profile C2 D2 to form the lower side C3 D3 of the pattern, until the points 13 and 13' arc reached.

As the lines C A and D B of the front of the bracket must be cut to fit the curves of the moldings above and below, against which the bracket fits, the corresponding lines of the pattern can be drawn with radii respectively equal to K E and K F, as shown by the curved lines C3 A3 and B3 B3 of the pattern.