34. Plumb Cut of Octagonal and other Polygonal Hips and Valleys.—The run of an octagonal hip or valley is 12.99" for each foot of run of common rafter. For practical purposes this is considered as 13". To lay off a plumb cut for an octagonal hip or valley, take 13" on the tongue and the rise per foot of run of common rafter on the blade, [Fig. 73]; scribe on the blade.
Fig. 73. Table for Octagon Hip or Valley
In a similar manner, having determined the tangent of any polygon under consideration, the run of hip or valley per foot of run of common rafter may be figured. The result will give the number to take on the tongue when the rise per foot of run of common rafter is taken on the blade, for laying out plumb cuts.
35. Side or Cheek Cuts of Hip and Valley Rafters for Roofs of Any Number of Sides.—[Fig. 74] illustrates the principles involved and method used in determining side cuts whatsoever the pitch and number of sides involved. (1) Lay the square across the jack or hip or valley, whatever is to be framed, at any convenient place, using on the blade the tangent (with 12" as base) of the polygon being framed, and on the tongue the constant of the run of the common rafter, 12". Scribe along the tongue A-C, [Fig. 74.] (2) With the square, carry the line B-C across the edge as indicated. (3) Lay off the plumb cut for the required pitch, taking upon the blade the rise, and upon the tongue the constant of the run of the hip or valley or jack, according to the requirements for that particular member as determined by the style of roof. (4) Measure square back from this plumb cut line the distance A-B of [Fig. 74.] (5) Thru point A scribe a line D-A parallel to that of the plumb cut line and (6) square this across the edge as at D-E. (7) Adjust the bevel to pass thru E and F, [Fig. 74.] (8) Scribe a plumb cut line upon the reverse surface of the stock.
Fig. 74-a.
Fig. 74-b.
Laying off Side Cut of Jack, Hip or Valley, any Polygon]