In Fig. 343 it is required to make a joint at right angles between the smaller pipe D F G E and the larger pipe H K L I. For this purpose both a side and an end view are necessary. As the two pieces forming the J are of different sections this problem really consists of two separate operations, but as certain steps can be used in both operations the following course will be most economical.

Fig. 343. - A T-Joint between Pipes of Different Diameters,

At a convenient distance from the end of the smaller pipe in each view draw a section of it. Space these sections into any suitable number of equal parts, commencing at corresponding points in each, and setting off the same number of spaces, all as shown by A B C and A1 B1 C1. From the points in A B C draw lines downward through the body of the large pipe indefinitely. From the points in A1 B1 C1 drop point onto the profile of the large pipe, as shown by the dotted lines. For the pattern of the smaller pipe the requirements are its profile A B1 C1 and the line F1 G1, which is the outline of the surface against which it miters, and therefore its miter line. Therefore, take the stretchout of A1 B1 C and lay it off at right angles opposite the end of the pipe, as shown by V W. Draw the measuring lines, as shown. Then, with the T-square set parallel to the stretchout line, and brought successively against the points between F1 and G1 upon the profile of the large pipe, cut corresponding measuring lines, as shown. Then a line traced through these points, as shown from X to Y, will form the end of the pattern.

For the pattern of the larger pipe the stretchout is taken from the profile view F1 G1 L1 and laid off at right angles to the pipe opposite one end, as shown by N P. A corresponding line, M O, is drawn opposite the other end, and the connecting lines M N and O P are drawn, thus completing the boundary of the piece through which an opening must be cut to meet or miter with the end of the smaller pipe. According to the rule given in Chapter V (Principles Of Pattern Cutting), a profile and a miter line are necessary. The profile F1 G1 L1 has already been stated, but no line has yet been drawn in the elevation of the larger pipe which shows its connection with the smaller pipe. This can only he found by projecting lines from the points dropped upon F1 G1 through the elevation till they intersect with lines previously drawn from the profile ABC, as shown between F and G. F G then constitutes the miter line. For economy's sake, then, the spaces 1 to 4 previously obtained in the profile are duplicated upon the stretchout, as shown, to which are added as many more (4 to 10) as are necessary. As the points 1 to 4 have already been dropped upon the miter line in its development it is now only necessary to drop them parallel to the stretchout line into measuring lines of corresponding number, when a line traced through the points of intersection, as shown by R S T U, will give the pattern of the opening required.

It may be noticed that, the development of the miter line F G is not really necessary in this case, as the points are really dropped from the profile ABC right through the elevation till they intersect the measuring lines. This happens in consequence of the arm or smaller pipe being at right angles to the larger one. Different conditions are shown in Problems 57 and 58 following.

PROBLEM 57. The Joint Between Two Pipes of Different Diameters Intersecting at Other Than Right Angles.

Let ABC, Fig. 344, be the size of the smaller pipe, and Y N1 Z the size of the larger pipe, and let H L M be the angle at which they are to meet. Draw an elevation of the pipes, as shown by G KI O N M L H, placing the profile of the smaller pipe above and in line with it, as shown, also placing a profile of the larger pipe in line with its elevation, as shown. In this problem the profiles of the moldings or pipes are given, but the line representing their junction must be obtained before going ahead.

To obtain this miter line, first place a duplicate of the profile of the smaller pipe in position above the end view of the larger pipe, as shown by A1 B1 C1, the centers of both being on the same vertical line, C1 N1. Divide both profiles of the small pipe into the same number of spaces, commencing at the same point in each. From the points in ABC project lines indefinitely through the elevation of the arm, as shown. From the points in A1 B1 C1 drop lines on to the profile of the large pipe, and from the points there obtained carry lines across to the left, producing them until they intersect corresponding lines in the elevation. A line traced through these several points of intersection gives the miter line K L, from which the points in the two patterns are to be obtained. For the pattern of the small pipe proceed as follows: Opposite the end lay off a stretchout, at right angles to it, as shown by E F. Through the points in it draw the usual measuring lines, as shown. In the developing of the line K L the points have already been dropped upon the miter line. It therefore only remains to carry them into the stretchout, which is done by placing the -square at right angles with the pipe, and,bringing it successively against the points in the miter line K L, cut the corresponding measuring lines, as shown by the dotted lines. A line traced through the points thus obtained will give the pattern of the end of the arm, as indicated.

Fig. 344. - The Joint between Two Pipes of Different Diameters Intersecting at Other than Right Angles.

For the pattern of the huge pipe proceed as follows: Opposite one end. and at right angles to it, lay off a stretchout line, as shown by R S in spacing off this stretchout it is best to transfer the spaces from 4 to 4 as they exist, as by so doing measuring lines will result which will correspond with points already existing in the miter line K L, thereby saving labor, as in the case of the smaller pipe, and also avoiding confusion. The other points in the profile arc taken at convenience, simply for stretchout purposes. Draw a corresponding line, P T, opposite the other end, and connect P R and T S. In laying off the stretchout R S, that number is placed first winch represents the point at which it is desired the seam shall come. For the shape of the opening in the pattern, draw measuring lines from the points 4, 3, 2, 1,2, 3, 4, as shown, and intersect them by lines dropped from corresponding points in the miter line. Through the points thus obtained trace the line U V W X, which will represent the shape of the opening required.