In Fig. 380, let F F F F represent the plan of the square portion of a shaft and A A A A that of the octagon portion. Let D P C be the elevation of the gore piece which is required to form the transition between the two shapes. The outline C D, which represents the intersection of the gore piece with the side of the shaft, may be of any contour whatever at the pleasure of the designer, the method of laying out the pattern being the same no matter what its outline. By reference to the plan it will be seen that the lines of the molding, of which C D shows only the termination, run octogonally, or in the direction of A A. Therefore, before a stretchout of the piece can be obtained a correct profile must be developed on a line at right angles to its lines - that is, on the line E F. To do this proceed as follows: Divide the line C D, as it appears in the elevation, into any convenient number of spaces, as shown by 1, 2, 3, 4, etc. From the points thus obtained drop lines down upon the side of the plan A F, which should be placed in line below the elevation.

Fig. 380. - The Pattern for a Gore Piece Forming the Transition from an Octagon to a Square.

Continue the lines from the side A F across the corner, as shown, all parallel to A A of the octagon, crossing E F, and number the lines to correspond with the numbers of the points in the elevation from which they were derived. Draw the vertical line G H at a, convenient distance from P D, and cut G H by lines drawn at right angles to it from the points in C D, as shown by the connecting dotted lines. G H then may be considered to represent the point F in the plan, or 11 of the numbers on the line E F. From G H, on each of the several lines drawn through it, lay off a distance equal to the space from E to the corresponding number in the same plan. Thus lay off from G H on line 1 a distance equal to 11 1 on E F, and on line 2 a distance equal to 11 2 of E F, and so on for each of the lines through G H. Then a line traced through these points, as shown by I H, will be the profile of the gore piece, or the shape of its section when cut by the line E F.

Prolong E F, as shown by K L, and lay off on the latter a stretchout of the profile I H, the spaces of which must be taken from point to point as they occur, so as to have points in the stretchout corresponding to the points on the miter lines A F, previously derived from C D. Through the points thus obtained draw the usual measuring lines, as shown. Place the T-square at right angles to the measuring lines, or, what is the same, parallel to E F, and, bringing it against the points in A F and F A, cut the corresponding lines drawn through the stretchout. Lines traced through these points, as shown, will constitute the pattern.