In Fig. 505 is shown the elevation of a pinnacle having eight equal gables, upon which the conical spire E F P I is to be fitted. Produce the sides F E and P I until they meet in the point D, which is the apex of the spire. Let A H1 S K M N1 T U represent the plan of the pinnacle drawn in line just below the elevation. To ascertain the length of the cone forming the spire at its longest points, where it terminates in the valleys between the gables, it will be necessary to construct a section on the line A B representing one of the valleys in plan, which can be done as follows: From the points D, F and H in the elevation project lines horizontally to the left, which intersect with any vertical line, as D1 B1, representing the center line of spire in the section. Upon the line drawn from H set off from B1 a distance equal to A B of the plan and draw A1 F1. From D1 draw a line parallel to D F cutting A1 F1 in R1; then D1 R1 will be the length or slant hight of the cone at its longest points, and a line from R1 projected back into the elevation will locate the base of the cone in that view, as shown at R.

From B as a center, with a radius equal to R2 R1, describe a circle in the plan, which will represent the base or plan of the cone. Divide an eighth of this circle into any number of equal parts, as shown by 1, 2, 3, 4 and 5, which spaces are to be used in measuring off the arc circumscribing the pattern. Draw any line, as D R in Fig. 506, upon which set off the several points in the line D R, as shown by the letters, and from D as center describe arcs indefinitely from each point, as shown. On the arc drawn from R step off spaces corresponding to one-eighth of the plan, as shown by 1, 2, 3, 4 and 5. Draw the line D 5, as shown, cutting the are from F, as indicated by f. By inspection of the elevation it will be seen that the arc F represents the line of the top of the gables, and that the arc R represents the line of points in the base of the cone to fit down between the gables. Therefore from F to the middle point 3 draw F g, and from f draw fg. Then D f g F will be one-eighth of the re-quired pattern. Set the dividers to 1 3 on the arc R and step off a sufficient number of additional spaces to complete the pattern, as shown by 3, 5, 3, 5, etc., to W. Draw W D. Also from the points 3 draw the lines fg and gf, thus completing the pattern.

Fig. 505. - Elevation and Plan of Conical Spire Mitering upon Eight Gables.

In case the work is of large dimensions it will be advisable to miter the cone from F to g, g to f, etc., in the manner shown in the preceding problem, but in case the work is small it will be sufficiently accurate to make the lines fg straight, as shown.

Fig. 506. - Pattern of Spire Shown in Fig. 505.