To Octagon A Given Timber. (A.) Method 1. - (Fig. 59.) In the middle of To., upon the back of the square, will be found a series of dots, a-b, forming the octagon scale.

Fig. 58. - Construction of a Circle equal to the Area of Two Given Circles.

In using this scale to octagon a 6" X 6" timber for instance, a center line is drawn upon one side of the timber and a space equal to six dots of the octagon scale laid off each side of the center line, as indicated at c, d. This gives the width of one side of the octagon, and the distance from the corner may then be lined off from the edge of each side, or if preferred, from the center line.

(B.) Method 2. - (Fig. 60.) Lay BI. of the square upon the given timber, as shown in the figure, the angle of the square and the outside corner of the other end just touching the edges of the sides of the timber; with a sharp pencil make points at 7 and 17. A line drawn through these points parallel with the edge will give the corners of the octagon. This process should be repeated upon each side of the timber or lined off from the corners. A rule may be used in the same way, working from end to end.

Fig. 59. - To octagon a Given Timber.

Method 1.

Fig. 60. - To octagon a Given Timber, Method 2.

Fig. 61. - To octagon a Given Timber. Method 3.

(C.) Method 3. - (Fig. 61.) Lay a rule upon the timber, as shown in the figure, with the inside points just touching the sides, and upon a line perfectly square with the edge; mark, 7 and 17, as shown, and proceed as previously described.

(D.) Method 4. - (Fig. 62.) A very common method is to lay out the side of the timber, as shown in the figure, using the corners as centers, and one half of the length of the diagonals as radii of circles.

The following problems will be found valuable in laying out the runs of rafters for buildings which are octagonal or hexagonal in shape.