In Fig. 440, let B F H C be the elevation of a square spire which is required to miter over four equal gables in a pinnacle, the plan of which is also square.

Produce F B and H C until they meet in A, which will he the apex of the pyramid of which the spire is a section. Draw the axis A G, and at right angles to it, from the lowest point of contact between the spire and the gable, as F, draw F G. Then F G will represent the half width of one of the sides of the pyramid at the base, and A F will represent the length of a side through its center. From any convenient point, as A1 n Fig. 441, draw A1 F1, in length equal to A F. From F1 set off, perpendicular to A1 F1, on each side a space equal to F G of the elevation, as shown by F1 G1 and F1 G2. From G1 and G2 draw lines to A1, as shown. From A1 as center, and with A1 G2 as radius, describe an arc, as shown by G2 O, in length equal to three spaces of the extent of G1 G2, as shown by G2 g, gg1 and g2 O. Draw g1 A1, g A1 and O A1. Make A1 B1 equal to A B of the elevation, and through B1 draw a perpendicular to A1 F1, as shown. Draw lines corresponding to it through the other sections of the pattern. Make A1 D1 equal to A D, and draw D1 G1 and D1 G2 Set the compasses to G2 D1, and from G2 and g as centers describe arcs intersecting at d. Draw d g and d G2, as shown. Repeat the same operation in the other sections of the pattern, thus completing the required shape.

Fig. 440. - Elevation of Spire.

Fig. 441. - Pattern.

The Pattern of a Square Spire Mitering Upon Four Gables.