Let A B C in Fig. 360 be the elevation of a coping to surmount a gable, the profile of which is D E K K1 D1, which, as will be seen, shows a double wash, E F and F E1 Let M O P N be the elevation of a pipe or shaft which is required to miter over this double wash at the peak of the gable. Before any patterns can be developed it will be necessary to first obtain a correct elevation of the miter line or intersection of the shaft with the coping. To accomplish this proceed as follows: In line with the pipe or shaft construct a profile of the same, as shown by G1 Ll K1 H1, which divide into any convenient number of equal parts, and from the points thus obtained drop lines vertically through the elevation. Draw a corresponding profile, as shown by H G L K, directly over the profile of the coping, all as shown, which divide into the same number of equal parts, beginning to number at a corresponding place in the profile, and from the points in it drop lines on to the profile of the coping, cutting the washes E F and F E1, and thence carry the lines parallel to the lines of the coping, producing them until they intersect the lines dropped from the profile G1 L1 K1 H1. Through the points of intersection thus obtained trace a line, as shown from O to P, then O B1P will be the miter line in elevation.

As both halves of the shaft are alike (dividing on the line H L in one profile, and on H1 L1 in the other), it is really only necessary to use one-half of the profile, as to use both halves as in the diagram requires the additional work of carrying the points from E F E1 to the center line B B1 for one-half and then down the other side of the gable for the other side. For the pattern of the shaft proceed as follows: In line with the end M N of the shaft, and at right angles to it, lay off a stretchout of the profile G1 H1 K1 L1 as shown by R S, in the usual manner, through the points in which draw measuring lines. Commence numbering these measuring lines with the figure corresponding to the point at which the seam is desired to be, in this case 1. Place the T square at right angles to the shaft, and, bringing it against the points in the miter line OB1P cut the corresponding measuring lines. Then a line traced through these points of intersection, as shown by T U V W X, will be the miter required. In case it should be desired to miter the coping against the base of the Shaft, the pattern for it may be obtained from the same lines in the following manner: At right angles to the lines of one side of the coping, as A B, lay off a stretchout of the wash of the coping E F E1. all as shown by E2 F E3. In this stretchout line set off points corresponding to the points in E F E1, obtained by the lines previously dropped from the profile G H K L. Place the T-square at right angles to A B, and, bringing it against the points in the miter line B1, cut lines of corresponding numbers drawn through the stretchout E2 E3, all us indicated by the dotted lines. Then a line traced through these points of intersection, as shown by Z I Y, will be the pattern of the wash for the side of the gable A B required to miter against the base of the shaft.

Fig 360.   The Patterns of a Cylinder Mitering with the Peck of a Gable Coping Having a Double Wash.

Fig 360. - The Patterns of a Cylinder Mitering with the Peck of a Gable Coping Having a Double Wash.

Incase the design should call for a shaft octagonal in shape, the same general rules would apply. Less divisions, however, will be required in the profile, it, only being necessary to drop points from each of the angles of the octagon, as in the case of Problem 33, previously given.