While the pattern here described is especially adapted to the tapering section or "taper course" of a locomotive boiler its principles are equally applicable to tanks, cans or pipes whose shapes are governed by the spaces or positions which they are to occupy. The section of the boiler at A F, Fig. 369, is round, as shown by I N L M. The lower half of the circle I M L is the profile from L F to G D, but the upper half is raked or slanted from B K to C H, retaining its semicircular character at C H. The line H G is a vertical line, as shown by S L of the sectional view, and the surface H K G being vertical is simply a flat triangular surface, exactly as shown in the elevation.

Fig. 369. - Pattern for the Flaring Section of a Locomotive Boiler.

Since the part B K H C is semicircular when cut upon any vertical line, the first step will be to obtain a section of it as it would appear if cut upon a line at right angles to B C. This section must be derived from the normal section of the level part, and may be done as follows: Assume any line, as U W, drawn at right angles to B C at any convenient position outside of the elevation, as the vertical center line of the new section. Divide one-half, the normal section, as N L, into any convenient number of spaces, as shown by the figures, and from the points thus obtained draw lines parallel to A B, cutting B K, as shown, also extending them back to the center line N M. From B K carry them parallel to B C, cutting the line C H, and extend them indefinitely, cutting also the line U W. With the dividers measure the horizontal distance of the various points in the normal profile N L from the center line N M, and transfer these distances to lines of corresponding number, measuring each time from U W. Thus make W 7 equal to O 7; the distance from U W to the point 6 equal to P 6; and so continue till all the distances have been measured. A line traced through these points will constitute a profile of the raking portion on a line at right angles to its direction, and B K and C H will be the miter lines. To develop the pattern first lay off the stretchout of the profile T U V upon any line drawn at right angles to B C, as A1 B1. As the points in U T have already been dropped upon the miter lines in the previous process it is now only necessary to place the T-square parallel to A1 B1 and, bringing it successively against the points in C H and B K, drop lines cutting the measuring lines of corresponding number. A line traced through the points of intersection, as shown by X X Y Y, will be the pattern of the raking portion B K H C. To this may be added the flat triangular piece K H G, as shown by X Y Z. From the points X and Z lines may be drawn at right angles to X Z. as shown by Z J and X Q, extending them sufficiently to complete the lower portion of this part of the boiler, shown by K E D G of the elevation.