The principle here involved and the method of procedure are exactly the same as in Problem 56, but the whole of the profiles must be used instead of the halves, because the two axes or center lines of the pipes do not intersect.

In Fig. 347, let A B C be the size of the small pipe and F1 H1 M1 be the size of the large pipe, between which a right-angled joint is to be made, the smaller pipe being set to one side of the axis of the large pipe, as indicated in the end view. Draw an elevation, as shown by D F I L M K G E. Place a profile of the small pipe above each, as shown by ABC and A1 B1 C, both of which divide into the same number of equal parts, commencing at the same point in each. Place the T-square parallel to the small pipe, and, bringing it successively against the points in the profile A1 B1

C1 drop lines cutting the profile of the large pipe, as shown, from F1 to II'; and in like manner drop lines from the points in the profile A B C, continuing them through the elevation of the larger pipe indefinitely. For the pattern of the small pipe set off a stretchout line, V W, at right angles to and opposite the end of the pipe, and draw the measuring lines, as shown. These measuring lines are to be numbered to correspond to the spaces in the profile, but the place of beginning determines the position of the seam in the pipe. In the illustration gives the seam has been located at the shortest part of the pipe, or, in other words, at the line corresponding to the point 10 in the section. Therefore commence numbering the stretchout lines with 10. Place the T-square at right angles to the small pipe, and, bringing the blade successively against the points in the profile of the large pipe from F 1 to H1, cut the corresponding measuring lines, as shown. A line traced through the points thus obtained, as shown by X Y Z, will form the end of the required pattern.

Fig. 347. - A T-Joint between Pipes of Different Diameters, the Axis of the Smaller ripe Passing to One Side of that of the Larger.

For the pattern of the large pipe, lay off a stretchout from the profile shown in the end view, beginning the same at whatever point it is desired to locate the seam, which in the present instance will be assumed on a line corresponding to point 13 in the pro-file. After laying off the stretchout opposite one end of the pipe, as shown on O R, draw a corresponding line opposite the other, as shown by N P, and connect N O and P R, thus completing the outline of the pattern, through which an opening must be cut to miter with the end of the smaller pipe. In spacing the profile of the large pipe, the spaces in that portion against which the small pipe fits are made to correspond to the points obtained by dropping lines from the profile of the small pipe upon it, as shown by 1 to 7 inclusive. This is done in order to furnish points in the stretchout corresponding to the lines dropped from the profile A B C, as shown. No other measuring lines than those which represent the portion of the pipe which the small pipe fits against are required in the stretchout. Accordingly the lines 1 to 7 inclusive are drawn from O R, as shown, and are cut by corresponding lines dropped from ABC. A line traced through the several points of intersection gives the shape S T U, which is the opening in the large pipe. If it be necessary for any purpose to show a correct elevation of the junction between two pipes, the miter line FH G is obtained by intersecting the lines dropped from A B C with corresponding lines carried across from the same points obtained on the profile F1 H1, by dropping from A1 Bv C, explained in Problems 56, .57 and 58, and all as shown by the dotted lines.

As remarked in Problem 56, this line is not absolutely necessary, but is of great advantage in illustrating the nature and principles of the work to be done.