In Fig. 3S is shown the slope of the roof projected into the hori zontal plane. By drawing a figure based on a scale of one inch to one foot, all the timbers on the slope of the roof can be measured. Bevel 2, shown in this figure, is to fit the valleys against the ridge. By drawing a line from w square to the seat of the valley to m, making w 2 equal in length to the length of the valley, as shown, and by con necting 2 and ?n, the bevel at 2 is found, which will fit the valleys against the ridge, as shown at 3 and 3 in Fig. 36.
In Fig. 39, is shown how to find the length and cuts of octagon hips intersecting a roof. In Fig. 36, half the plan of the octagon is shown to be inside of the plate, and the hips o, z, o intersect the slope of the roof. In Fig. 39, the lines below x y are the plan lines; and those above, the elevation. From z, o, o, in the plan, draw lines to x y, as shown from o to m and from z to 711; from in, and 711, draw the vation lines to the apex o", secting the line of the roof in d" and c". From d" and c", draw the lines d" v" and c" a" parallel to x y; from c", drop a line to tersect the plan line a o in c. Make a w equal in length to a"o" of the elevation, and connect w c; measure from w to n the full height of the octagon as shown from x y The length from w to c is that of the two hips shown at o o in Fig. 36, both being equal hips intersect ing the roof at an equal distance from the plate. The bevel atw is the top bevel, and the bevel at c will fit the roof.
Again, drop a line from d" to intersect the plan line a z in d.
Make a 2 equal to v" o" in the elevation, and connect 2 d. Measure from 2 to b the full height of the tower as shown from x y to the apex o" in the elevation, and connect d b.
The length 2 d represents the length of the hip z shown in Fig. 36; the bevel at 2 is that of the top; and the bevel at d, the one that will fit the foot of the hip to the intersecting roof.
When a cornice of any con siderable width runs around a roof of this kind, it affects the plates and the angle of the val leys as shown in Fig. 40. In this figure are shown the same valleys as in Fig. 36; but, owing to the width of the cornice, the foot of each has been moved the distance a b along the plate of the main roof. Why this is clone is shown in the drawing to be caused by the necessity for the valleys to intersect the corners c c of the cornice.
The plates are also affected as shown in Fig. 41, where the plate of the narrow roof is shown to be much higher than the plate of the main roof.
The bevels shown at 3, Fig. 40, are to fit the valleys against the ridge.
In Fig. 42 is shown a very simple method of finding the bevels for purlins in equal-pitch roofs. Draw the plan of the corner as shown, and a line from 711, to o; measure from o the length x y, representing the common rafter, to w; from w draw a line to m; the bevel shown at 2 will fit the top face of the purlin. Again, from o, describe an arc to cut the seat of the valley, and continue same around to S; con nect S .7n; the bevel at 3 will be the side bevel.