In Fig. 444, let BEZU be the elevation of an octagon spire, mitering down upon four gables occurring upon a square pinnacle. Continue the side lines until they intersect in the apex A. Draw the center line A H, and from the point G draw G H perpendicular to the center line, showing half the width of one of the sides at the point G. By inspection of the elevation it will be seen that one-half the sides will be notched at the bottom to fit over the gables, while the others will be pointed to reach down into the angles or valleys between the gables.
To ascertain the correct length upon the center line of one of the pointed sides it will be necessary to construct a section through one of the valleys, for instance, upon the line M1 N1 of the plan. Through the point J of the elevation draw the line J M at right angles to the center line, extending it to the left indefinitely, and from the point M set off upon this line the distance M N, equal to M1 N1 of the plan. Draw N P, and extend the side A E until it intersects this line at F. Then A F will be the correct length through the center line of one of the long sides.
Fig. 444. - Plan and Elevation of Spire.
Fig. 445. - Pattern.
The Pattern of an Octugon Spire Mitering Upon Four Gables.
To describe the pattern first draw A1 F1 in Fig. 445, equal to A F of the elevation, and set off points on it corresponding to points in A F. Thus make A1 B1 equal to A B, A1 D1 equal to A D, and A1 E1 equal to A E of the elevation, etc. Through E1 draw a perpendicular equal in length to the width of a side at the point E, or to twice G H, as shown in the elevation, placing one-half on each side from E1, all as shown by L K. From L and K draw lines to A1. From A' as center, with A1 L as radius, describe an arc, as shown by L U, indefinite in length. Set the dividers to the space L K, and step off spaces from L, as L Y, Y X, etc., until as many sides are set off as are required in the spire - in this case eight. Draw the lines A1 Y, A1 X, etc. From the point D1, which, as will be seen by D in the elevation, corresponds to the top of the gable, draw lines to the points L and K, which gives the pattern for the notch in the first section. Set the dividers to L D1 as radius, and from X and Y as centers describe arcs intersecting at W. Draw W X and W Y, and repeat this upon all the alternate sides throughout the pattern, as shown, locating the points O and P. For the pattern of the point, take a space between the points of the dividers equal to L F1, and from L and Y as centers describe small arcs intersecting at M, and draw M L and M Y. With the same radius repeat the operation upon the intermediate sides, establishing the points V, H and I, thus completing the pattern.