Let A B C in Fig 359 be the front elevation and D E F G H be the side elevation of a coping to surmount a gable, the profile of the top of which is shown at D K H in the side elevation. Also let MNOP be the elevation of a square shaft or base, as of a finial, having a curved profile, as shown, which it is required to miter down upon the top of the coping. As the matter of drawing the elevations of the shaft in correct position upon the washes of the coping is attended with some difficulty, the method of obtaining these will be briefly described first: Through the lowermost point on either side of the front elevation, as P, draw a line at the correct angle of the pitch of the coping or gable, as shown by V W, and extend the same to the right far enough to permit a section of the coping to be constructed upon it. Upon this line set off the distance X W, equal to P L (half the width of the shaft at its base), and through the point W draw a line perpendicular to V W; next through the point X draw a line, making the same angle with Y W that D K, of the given profile of the coping, does with the horizontal line D L', and extend this line to the right till it meets the line from W at K1, and to the left, making D1 K1 equal to D K. This gives one-half the profile of the wash, which is all that is necessary in obtaining the elevation. Now from the points in the profile D1 K1 project linos parallel to Y W till they meet the center line of the front elevation, and duplicate them on the other side of the center line, which will complete the front elevation of the gable. From the points in the profile D K H erect vertical lines indefinitely, which may be intersected with lines projected horizontally from the points on center line I L to complete the side elevation. Thus a line from point B intersected with line from K will give the apex of coping, and a line from point Z intersected with lines from D and H will give the points E and G, front and back of the washes at the apex.
As the shaft is exactly square, the side elevation of it, M1 N1 O1 P1, is in all respects the same as that of the front, and is drawn in line with it, as shown by the horizontal lines of projection connecting them. This having been completed, the point at which its side M1 N1 crosses the line E F (marked 4 1/2) is projected back to the front elevation, as shown, thus locating the point U; while the crossing of the side O P with the top line of coping B C (marked 4) is projected upon the center line of the side view, thus giving the point Y. This completes the elevations with the exception of the lines M U P and M1 Y P1. If the profile of the shaft O P were a straight line, either slanting or vertical, the lines U P and M1 Y would be straight lines, because they would represent the intersection of two plain surfaces; but as the profile is a curved line it will be necessary to obtain correct elevations of these two lines, as they are essential in obtaining the patterns to follow.
Fig. 359. - The Patterns for a Square Shaft, of Curved Profile Mitering Over the Peak of a Gable.
The shaft being square, the miters at its angles are plain square miters and are developed by the ordinary method, as explained in several problems in the earlier part of this chapter. The peculiarity of this problem, then, consists in obtaining the miter lines U P and M1 Y and the part of the pattern corresponding to the same, which can all be done at one operation, as follows:
Divide the profiles O P and M1 N1 into the same number of equal parts, and place the stretchout of the same upon the center lines extended, as shown at I J and I1 J,1 through which draw the usual measuring lines for subsequent use. From the points in M' N' from 4 1/2 down drop lines vertically upon the profile of coping D K, as shown by the dotted lines, and transfer the points thus obtained to the profile D1 K1, from which points draw lines parallel to V W, as shown by the dotted lines. Intersect these with lines of corresponding number (2, 3 and 4) drawn horizontally from either profile, as shown at 2', 3' and 4', thus obtaining the miter line U P. After the points 1 to 11 of the profile have been dropped into the measuring lines of corresponding number of the stretchout the points 2', 3', 4' and 4 1/2' are also dropped into the measuring lines of corresponding number, thus giving the cut U1 T at the bottom of the pattern, which can be duplicated on the other side of the center line, thus completing the pattern Q R S T U1 of the front of the shaft.
From the points 1 to 4 of the profile O P draw lines parallel to B C cutting the profile D1K1, as shown by the solid lines, and transfer the same to the profile of coping D K, and from these points erect perpendicular lines (also shown solid) indefinitely, as shown, which intersect with lines drawn horizontally from points of corresponding number in either profile, as shown at 2," 3" and 4". This will give the correct miter line M1 Y. The miters at the sides of piece M1 N1 O1 P1 are of course the same as those of the front piece, therefore after they have been obtained the points 2" and 3" are dropped into measuring lines 2 and 3 of the stretchout I1 J', which when duplicated on the other side of the center line complete the line Q1 Yl T1, which is the bottom cut of the side piece.
It has been remarked that in obtaining the intersections between U and P and M1 and Y horizontal lines may be drawn from points in either profile. The reason for this is simply that the two profiles O P and N1 M1 are identical and have been divided into the same number of equal parts. If a case should occur in which the side and face should be dissimilar it must be borne in mind that N1 M1 is the profile of the face piece and its points must be used in obtaining the intersections between U and P, while O P is the profile of the side piece, and its points must be used in obtaining the intersections between M1 and Y.