In Fig. 307 is shown the elevation and plan of the shaft of a finial of the design shown in Fig. 308. The -haft is octagon throughout, and if it were designed to stand upon a level surface, the method of obtaining its patterns would be the same in all respects as that described in Problem 21. As shown by the line K m K, however, its lower end is designed to fit over the ridge of a. roof or gable, to obtain the patterns of which proceed as follows:

Fig. 307. - Plan, Elevation and Patterns.

Fig. 303 - Design of Finial.

The Patterns of an Octagonal Shaft, Curved in Profile, Fitting over a Ridge.

Construct, a plan of the shaft at its largest section, as shown by A B C D E F. from the center of which draw miter lines, as shown by G E and G F. Divide the profile of the shaft J L, corresponding to

F G E of the plan, into any number of parts in the usual manner, and from these points carry lines vertically crossing the miter lines G E and G F. From the center G draw E1 M1 at right angles to E F, upon which line lay off a stretchout of the profile J L, drawing measuring lines through the points. Place the T-square parallel to the stretchout line, and, bringing it successively against the points in G E and G F, cut corresponding measuring lines, as shown, and through the points thus obtained trace lines, all as indicated in the drawing. This gives the general shape of the pattern for the sides of the shaft. By inspection of the plan and elevation together, it will be seen that to fit the shaft over the roof some of the sections composing it will require different cuts at their lower extremities. Two of the sections will be cut the same as the pattern already described. They correspond to the side marked A B and E F in the plan. Two others, indicated in the plan by C D and H I, will be cut to lit over the ridge of the roof, as shown in the elevation by n m n. The remaining four pieces, shown in plan by B C. D E, F 1 and A H. will be cut obliquely to fit against the pitch of the roof, as shown by n o in the elevation. For the sides C D and H I, shown in the center of the elevation, it, will be seen that the line drawn from 4 touches the ridge in the point m, while the line drawn from 3 corresponds to the point at which the side terminates against the pitch of the roof. Therefore, in the pattern draw a line from the center of it, on the measuring line 4, to the sides of it, on the measuring line 3, all as shown by m1 n1 and m1 n1. Then these are the lines of cut in the pattern corresponding to to a and m n of the elevation. By further inspection of the elevation, it will be seen that for the remaining four sides it is necessary to make a cut in the pattern from one side, in a point corresponding to 3 of the profile, to the other, in a point corresponding to 1 of the profile, all as shown by n o. Taking corresponding points, therefore, in the measuring lines of the pattern, draw the lines n1 o1 as shown. Then the original pattern, modified by cutting upon these lines, will constitute the pattern for the four octagon sides.