In Fig. 348, let C1 B1 A1 be the size of the smaller pipe, and D1 E1 I1 the size of the larger pipe, between which a joint is required at an angle represented by W F K, the smaller pipe to be placed to the side of the larger. Draw an elevation of the pipes joined, as shown by V D G H I K F W. As in the preceding problems, the miter line or line giving a correct elevation of the junction of the pipes must be developed before the actual work of laying out the miter patterns can be begun, therefore place a profile or section of the arm in line with it, as shown by C1 B1 A1, and opposite and in line with the end of the main pipe draw a section of it, as shown by D1 E1 I1. Directly above this section draw a second profile of the small pipe, as shown by C B A, placing the center of it in the required position relative to the center of the profile of the large pipe. Divide the two profiles of the small pipe into the same number of equal spaces, commencing at the same point in each. From the divisions in C1 B1 A1 drop lines parallel to the lines of the arm indefinitely. From the divisions in C B A drop lines until they cut the profile of the large pipe, as shown by the points in the arc D1 E1. From these points carry lines horizontally to the left, producing them until they intersect the corresponding lines from C1 B1 A1. A line traced through these points of intersection, as shown by D E F, will be the miter line between the two pipes. For the pattern of the arm proceed as follows: Lay off a stretchout at right angles to and opposite the end of the arm, as shown by R P, and through the points in it draw the usual measuring lines. Place the T-square at right angles to the arm, and, bringing it successively against the points already in the miter line, cut the corresponding measuring lines. A line traced through these points, as shown by UTS, will form the required pattern.

For the pattern of the main pipe draw a stretchout line opposite one end of it, as shown by M O, numbering the divisions in it with reference to locating the seam, which can be placed at any point desired. The spaces of the profile between D1 and K1 should be transferred to the stretchout point by point as they occur, as by so doing measuring lines will be obtained which will correspond to the points already in the miter line. Draw a line corresponding to the stretchout line opposite the other end of the pipe, as shown by L N, and connect L M and N O. Through the points in the stretchout line corresponding to the points between D1 and E1 of the profile draw measuring lines, as shown by 10, 11, 12, 18, 14, 16 and 1. Place the T-square at right angles to the main pipe, and, bringing the blade against the points in D E F successively, cut the measuring lines of corresponding number, all as shown by the dotted lines. A line traced through these points of intersection, as shown near the middle of M L N O, will give the shape of the opening to be cut in the pattern of the main pipe.

Fig. 348 - .4 Joint at other than Right Angles between Two Pipes of Different Diameters, the Axis of the Smaller Pipe being Placed to One Side of that of the Larger One.