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.

In the front gable, Fig. 14, it is shown that the run of the common rafter is 10 feet 4 inches. To find the length of the common rafter, take 12 on blade and 9 on tongue, and step 10 times along the rafter timber; and for the fractional part of a foot (4 inches), proceed as was shown in Fig. 16 for the rafter of the main roof; but in this case measure out square to the tongue of square No. 1, 4 inches instead of 6 inches. The additional length for the fractional 4 inches run can also be found by taking 4 inches on blade and 3 inches on tongue of square, and stepping one time; this, in addition to the length obtained by stepping 10 times along the rafter timber with 12 on blade and 9 on tongue, will give the full length of the rafter for a run of 10 feet 4 inches. In the intersection of this roof with the main roof, there are shown to be two valleys of different lengths. The long one extends from the plate at n (Fig. 14) to the ridge of the main roof at m; it has therefore a run of 13 feet 6 inches. For the length, proceed as for the hips, by taking 17 on blade of the square and 9 on tongue, and stepping 13 times for the length of the 13 feet; and for the fractional 6 inches, proceed precisely as shown in Fig. 17 for the hip, by squaring out from the tongue of square No. 1, 8 1/2 inches; this, in addition to the length obtained for the 13 feet, will give the full length of the long valley n m. The length of the short valley a c, as shown, extends over the run of 10 feet 4 inches, and butts against the side of the long valley at c. By taking 17 on blade and 9 on tongue, and stepping along the rafter timber 10 times, the length for the 10 feet is found; and for the 4 inches, measure 5 5/8 inches square from the tongue of square No. 1, in the manner shown in Fig. 17, where the 8 1/2 inches is shown added for the 6 inches additional run of the main roof for the hips.

Fig. 21. Corner of Square Building, Showing Plan Lines of Plates and Hip.

Fig. 22. Corner of Square Building, Showing Plan Lines of Plates and Valley.

Fig. 23. Use of Square to Determine Heel Cut of Valley.

The length 5f is found as shown in Fig. 20, by measuring 4 inches from atom along the run of common rafter for one foot. Upon m erect a line to cut the seat of the valley at c; from c to a will be the run of the valley to correspond with 4 inches run of the common rafter, and it will measure 5 5/8 inches. How to Treat the Heel Cut of Hips and Valleys. Having found the lengths of the hips and valleys to correspond to the common rafters, it will be necessary to find also the thickness of each above the plate to correspond to the thickness the common rafter will be above the plate.

In Fig. 21 is shown a corner of a square building, showing the plates and the plan lines of a hip. The length of the hip, as already found, will cover the span from the ridge to the corner 2; but the sides of the hip intersect the plates at 3 and 3 respectively; therefore the distance from 2 to 1, as shown in this diagram, is measured backwards from a to 1 in the manner shown in Fig. 17; then a plumb line is drawn through 1 to m, parallel to the plumb cut a-17. From m to o on this line, measure the same thickness as that of the common rafter; and through o draw the heel cut to a as shown.