For the ⅜ pitch, the figures are shown to be 12 on tongue and 9 on blade, 9 being ⅜ of the span, 24 inches.
The same rule applies to all the pitches. The ⅙ pitch is shown to rise 4 inches to the foot of run, because 4 inches is ⅙ of the span, 24 inches, the ⅓ pitch is shown to rise 8 inches to the foot of run, because 8 inches is ⅓ of the span, 24 inches; etc.
Fig. 15. Steel Square Giving Various Pitches to Foot of Run.
The roof referred to in [Figs. 16] and [17] is to rise 9 inches to the foot of run; it is therefore a ⅜-pitch roof. For all the common rafters, the figures to be used on the square will be 12 on blade to represent the run, and 9 on tongue to represent the rise to the foot of run; and for all the hips and valleys, 17 on blade to represent the run, and 9 on tongue to represent the rise of the roof to the foot of run.
Why 17 represents the run for all the hips and valleys, will be understood by examining [Fig. 19], in which 17 is shown to be the diagonal of a foot square.
In equal-pitch roofs the corners are square, and the plan of the hip or valley will always be a diagonal of a square corner as shown at 1, 2, 3, and 5 in [Fig. 14].
In [Fig. 18] are shown ⅙ pitch, ⅜ pitch and ½ pitch over a square corner. The figures to be used on the square for the hip, will be 17 for run in each case. For the ⅙ pitch, the figures to be used would be 17 inches run and 4 inches rise, to correspond with the 12 inches run and 4 inches rise of the common rafter. For the ⅜ pitch, the figures to be used for hip would be 17 inches run and 9 inches rise, to correspond with the 12 inches run and 9 inches rise of the common rafter; and for the ½ pitch, the figures to be used on the square will be 17 inches run and 12 inches rise, to correspond with the 12 inches run and 12 inches rise of the common rafter.