This section is from the book "The New Metal Worker Pattern Book", by George Watson Kittredge. Also available from Amazon: The new metal worker pattern book.

Let D F G H M I K E in Fig. 327 be the elevation of two pipes of the same size meeting at right angles and forming a T, of which A B C D and A1 B1 C1 D1 are profiles drawn in line with either piece. As the two profiles are alike, and as the end of one piece (D E F K) comes against the side of the other piece (G I M H), both halves of D E F K, B A D and B C

Fig. 327. - A T-Joint between Pipes of the Same Diameter.

D, will miter with one-half, B1 C1 D1, of the piece G I M H. By projecting the points B and B1 from the profiles through their respective elevations the point L is found, which being connected with the points F and K gives the miter lines. Space the profile A B C D into any number of equal parts and lay off the stretchout N O at right angles to the pipe of which ABC

D is the profile, as shown. through the points in which draw the usual measuring lines. Set the T-square at right angles to this pipe, and, bringing the blade against the several points on the miter lines, cut the corresponding measuring lines drawn through the stretchout, as indicated by the dotted lines. Then N F U V W O will be the pattern for the upper piece. As both halves of this piece (dividing now upon the line A C) will be alike only one-half of the profile (A B C) has been divided, but the stretchout is made complete. For the pattern of the other piece, divide its profile into any convenient number of equal parts and lay off the stretchout on the line R T, drawn at right angles to the pipe. Placing the T-square parallel with the pipe drop points upon the miter lines from that portion of the profile (B1 C1 D1) which comes in line with them; then place the blade of the T-square at right angles to the pipe, and, bringing it against the several points in the miter lines, cut the corresponding measuring lines, as shown by the dotted lines. A line, X Y Q Z, traced through these points will bound the opening to be cut in the pattern for the lower pipe. From the points 1 in the stretchout draw the lines R P and T S, in length equal to the. length of the pipe. Connect P S. Then P R T S will be the required pattern. The seam in the pipe may be located as shown in the engraving, or at some other point, at pleasure.

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