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200 88. Transition between an Oval Pipe and the Second Piece of an Elbow.—Figure 284 is constructed by first drawing an elevation of the required elbow according to the directions given in Chapter III. The first piece of the elbow is then erased and the elevation of the transition added. A half-profile is then drawn adjacent to the small end of the elbow and divided into eight equal parts. These divisions are numbered as shown, and extension lines are carried through the elevation until they meet the first miter fine, where corresponding numbers are placed at each intersection.

From the intersections of the miter fine vertical extension lines are dropped. These extension lines are crossed by the horizontal center line AK as shown in Fig. 286. About this center line the plan, Fig. 286, is now drawn. The vertical extension lines divide the circumference of the circle into equal parts. One-half of the oval profile may now be equally divided, although the straight line EF may be considered as one space.

A true section on the miter line should now be developed as shown by Fig. 285, in the following manner. Extension lines are carried horizontally from points 1 and 9 of Fig. 284, and a new line 1-9 is drawn parallel to line 1-9 of Fig. 284. The exact spacings of the miter line are transferred to this line, and perpendiculars are erected at each point with numbers to correspond. Upon each of these perpendiculars and on each side of the line 1-9, a distance is laid off equal to the distance from a correspondingly numbered point in the half-profile to the center line 1-9 of the half-profile. A curved line traced through the intersections thus obtained is a true section on miter line 1-9 of Fig. 284.

Before the base lines for the triangles can be drawn in Fig. 286, the order of triangulation must be determined. In a transition of this kind the elements of the surface must alternate between the upper and lower bases in order to have sufficient data with which to develop the pattern. A standard order of triangulation is given below, together with the altitude for each triangle.

The base lines may now be drawn in Fig. 287 according to this order.