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87. Transition between a Square Pipe and the Second Piece of an Elbow.—In order to save height the sheet metal draftsman is often compelled to design a transition between a square or a rectangular pipe and the second piece of a round pipe elbow. In other words, the transition takes the place of the first piece of the elbow.

In order to accomplish this purpose it is necessary to incline the plane of the top to that of the base of the transition. Figure 278 shows the elevation of the small end of a two-piece 45° elbow with the transition attached in its proper position. In drawing this view care must be taken to get the true miter line according to the rules laid down in Chapter III.

Directly above the small end of the elbow a half-profile is drawn and divided into eight equal parts. The divisions are numbered as shown, and extension lines carried down through the elevation until they meet the miter line. Numbers are placed on the miter line to correspond to the numbering of the half-profile.

As has already been pointed out in previous chapters, whenever a cylinder is cut by an inclined plane, the section on that cutting plane is an ellipse. In order to obtain the proper spacing on the pattern a true section on the miter line must be developed in the following manner. Line 1-9 of Fig. 279 is an extension of line 1-9 of the half-profile. Upon this line should be placed the exact spacing of the miter line, and perpendiculars erected at each point. These perpendiculars are intersected by extension lines brought over from correspondingly numbered points in the half-profile. A curved line traced through the intersections thus obtained gives a true section on line 1-9 (miter line) of the elevation.

From each intersection of the miter line of Fig. 278 extension lines are dropped vertically for an indefinite distance. The profile of the square base of the transition is next drawn in its proper position as shown by A, B, C, D of Fig. 280.

The horizontal center line, EF, locates the center of the circle which is also the profile of the round pipe. The extension lines from the miter line of Fig. 278 should divide this circle into equal