Octagon Rafters. There are two ways of framing the apex of an octagonal roof,' one of which is illustrated in Fig. 92. In this it will be seen that the rafters are framed in pairs, the first pair being cut as though they were common rafters of a rectangular roof, the run of which equals one half of the diagonal of the octagon. The following formula may be used to find the length of the first pair of rafters.

A = rise of the rafter. R = run of the rafter. X = bridge measure. H = length of the rafter.

Formula 31. H =

To find the length of this pair of rafters by the steel square, the following formula may be applied:

Formula 32. H = X of R on Bl, A on To,

The length of the second pair of rafters is the same as the first, except that they are shortened at the top end by cutting a distance equal to one half of the thickness of the first pair of rafters off of the plumb or ridge cut, in the same way as common rafters are cut to fit against a ridge.

The third and the fourth pair of rafters are fitted at the top as shown in Fig. 92. The length of these rafters may be found by using the following mathematical formula : -

Fig. 92. - Apex of an Octagonal Roof.

X= bridge measure.

H = length of the 3d and 4th pairs of hip rafters. R = run of the hip rafters. C = constant same as C in Formula 19. A = rise of the hip rafters. T = pitch line.

D = diagonal thickness of the first pair of rafters upon the line of intersection of the third and the fourth pairs.

Formula 33. H =

To find the length of the third and fourth pairs of rafters with the steel square, the following formula may be used: -

Formula 34. H = X of R on Bl., A on To. - T of D/2.

In order to find the side or cheek cuts of these rafters, measure back from the plumb cut a distance equal to one half of the thickness of the rafter, and work to the middle or the top of the plumb cut, as shown in Fig. 92. This involves the principle illustrated in Fig. 79.