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Details of Roofs. Hips are the external angles by the junction of the roof and its return round the ends, where the walls are not carried up to the underside of the rake of roof to form gables.

Valleys are the converse of hips, and jack rafters are the short rafters which run between the hips or valleys and the wall-plates.

Dormers are gables on a small scale, or verti cal windows placed on the incline plane of the roof.

Fig. 157 illustrates a returned roof, with hips and a valley, showing generally the positions of the parts herein before described, as particular ized in the accompanying reference—A, valley; B, hip ; C, jack rafters ; D, ridge ; E, eaves ; F, common rafters ; G, gable ; H, dormer ; P, purlins ; W, wall plate.

Octagonal Roofs.—Fig. 158 represents an octag onal roof. I n its construction the following suggestion on laying out an octagon must be referred to.

To find the side of an octagon when the side of the square is given : Multiply the side of the square by 4.97 and divide by 12. The quotient is the side of the inscribed octagon.

To continue with an octagon roof : the length of hips is found as usual from the rise and run; the run being half the diagonal of the octagon.

Cut the first pair full length to butt against each other; the next pair are to be cut up at right angles to those, and each is to be cut shorter than the first pair by half the thickness of first pair, measured square back from the down bevel.

The third and fourth pairs are to be cut shorter than the first pair by half the diagonal of a square whose side is the thickness of the first rafters.

If the thickness of the first pair is 2 inches, then the third and fourth pairs are shortened by 1 and 5-12 inches, as 2 and 10-12 is the diagonal of a square whose side is 2 inches.

The first and second pairs have no side bevels; the side bevels of the third and fourth run back on both sides from the middle of the rafter.

Find this bevel by taking the original length of rafter on the blade of a square and its run on the tongue, when the blade shows the cut. The backing of the hips obtain by taking 5-12 of the rise on the tongue and the length of hip on blade, the latter giving the cut ; for the side of an octagon is 5-12 its square width.

Half the square width is the run of the middle jack rafter, from which and its rise we get its length. From the length deduct the same amount as from the third and fourth pairs of hips. If there are to be two jacks between the middle one and the corner, we divide the length of the side into three parts, also the rise, whence are obtained as before the distance of rafters apart, and the rise of the shortest jack. Divide half the square width of octa gon by 3 to find the run of shortest jack. Just as the square is laid on to find the length of a jack, it gives the down and lower end bevels ; while the side bevel is ob tained by taking the length of the middle jack on blade and half one side of the octagon on the tongue; the blade giving the cut.

The following illus trations and reading matter are from Mr. Woods, and are largely self-explanatory. They show the lengths and bevels of hips and jacks of an octagonal tower roof. The seat and plumb cuts are found in the usual way of taking the proportion of the run and rise on the tongue and blade, but there must be an additional or diagonal cut across the back of the jack to fit against the hip, as shown in Fig. 159, by the dotted lines at A-B. These lines are always vertical and the same distance apart regardless of the pitch given. The diagonal line from A to B across the back of the jack de termines the angle. Fig. 160 illustrates this point. If there was no pitch at all then 5 and 12 would give the cut. These figures also give the starting lines A and B which, since the rafters are of the same thickness, will remain at right angles the same distance apart. Thus, if the rafter be 2 inches thick, the lines A and B will be inches apart.

The Jack Cut may be found as follows : Take 5 on the tongue and the length of the common rafter for one-foot run on the blade, the blade giving the cut. Thus it will be seen that when the principles of roof framing are understood it is not necessary to lay out an elaborate diagram.