In the matter of roofing over unequal pitches when there is no ridge and
when all hips meet, the building being longer than it is wide, the
backing of hips and their lengths and bevels would be a very easy matter
if a drawing of the whole thing was made, but, to obtain these by the
use of the square alone, is somewhat more difficult. Let us assume the
building to be 18 feet wide and 28 feet long, and having a rise of 9
feet, then, by referring to Fig. 60, we show to one inch scale the
length, run, rise, seat, and plumb cuts for the hip and common rafters
as follows: The run of the long way of the building is 14, and 9 for the
narrow way, which we take on the blade and tongue respectively, as shown
on square No. 1, and to this apply square No. 2, as shown. AD equals the
run of the hip. AE equals the rise and ED equals the length of the hip.
The reader will notice that the letters A, B, C, D form a parallelogram,
with side and ends equal to the runs of the common rafters. Therefore,
by taking the runs on the tongue, as shown by the squares Nos. 3 and 4,
will give their lengths, seat and plumb cuts.
[Illustration: Fig. 61.]
[Illustration: Fig. 62.]
In Fig. 61 is shown the intersection of the rafters at the peak and as
the lengths of all rafters are scaled to run to a common center it is
necessary that the common rafters must cut back so as to fit in the
angle formed by the hips. The proper deduction for this is shown in Fig.
62 by placing two squares on the back of the rafter, with the heel or
corner of the squares resting on the center line. The distance from the
corner of the square to B measured square back (at right angles) from
the plumb bevel, as shown in Fig. 61, will locate the point of the long
common rafter at B in Fig. 61. Proceed in like manner for the short
common rafter, taking the distance from the corner at C, and for the
side cuts, take 14 on the tongue and the length of the short common
rafter CE on the blade—the blade will give the cut at AC in Fig. 61. The
reader will observe that this angle is the same as that for the side cut
of the jack. Proceed in like manner for the long common rafter side,
using 9 on the tongue and BE on the blade. These same figures will give
the side cuts of the hip, provided hip has been previously backed.
Taking the last for example the reader will observe that 9 on the tongue
and BE on the blade the square would lay on the plane of the backing and
the blade giving the cut along the line BB in Fig. 61, or these cuts may
be found by measuring square back from a plumb bevel at points A and A,
Fig. 62, the distance AC and AB, which will give the proper plumb cut at
the sides and intersecting the line AA at the center. These same
distances, AC and AB, but transferred to opposite sides, set off on the
seat cut or a line parallel with it, will give the gauge points on the
side of the hip for the backing.
The lengths of the jacks may be found by dividing the length of the
common rafter by the number of the spacings for the jacks; the quotient
will be the common difference.