Three of the hips are shown in Fig. 14 to extend from the plate to the ridge-pole; they are marked in the figure as 1, 2, and 3 respectively, and are shown in plan to be diagonals of a square measuring 13 feet 6 inches by 13 feet 6 inches; they make an angle, therefore, of 45 degrees with the plate.

In Fig. 18 it has been shown that a hip standing at an angle of 45 degrees with the plate will have a run of 17 inches for every foot run of the common rafter. Therefore, to lay out the hips, the figures on the square will be 17 for run and 9 for rise; and by stepping 13 times along the hip rafter timber, the length of hip for 13 feet of run is obtained. The length for the additional 6 inches in the run may be found by squaring a distance of 8 1/2 inches, as shown in Fig. 17, from the tongue of the square, and moving square No. 1 along the edge of the timber, holding the blade on 17 and tongue on 9, and marking the plumb cut where the dotted line is shown.

In Fig. 18 is shown how to find the relative run length of a portion of a hip to correspond to that of a fractional part of a foot in the length of the common rafter. From 12 inches, measure along the run of the common rafter 6 inches, and drop a line to cut the diagonal line in m. From m to a, along the diagonal line, will be the relative run length of the part of hip to correspond with 6 inches run of the common rafter, and it measures 8 1/2 inches.

The same results may be obtained by the following method of figuring:

Fig. 19. Diagram Showing Relative Lengths of Run for Hips and Common Rafters in Equal-Pitch Roofs.

In Fig. 19 is shown a 12-inch square, the diagonal m being 17 inches. By drawing lines from the base a 6 to cut the diagonal line, the part of the hip to correspond to that of the common rafter will be indicated on the line 17. In this figure it is shown that a 6-inch run on a b, which represents the run of a foot of a common rafter, will have a corresponding length of 8 1/2

Fig. 20. Method of Determining Run of Valley for Additional Run in Common Rafter.

inches run on the line 17, which represents the plan line of the hip or valley in all equal-pitch roofs.