However, if one is good in mathematics, it is often better to find the rafter lengths by multiplying the lengths for one foot by the run. Taking the above case: 111/4 times 13% inches equals 12 feet inches, the length of the common rafter; times 13% inches equals 1 foot 6 inches, the common difference of the jacks; and times 18 inches equals 16 feet inches, the length for the corresponding hip or valley.

The cuts on the square are as follows: 12 and 6, seat and plumb cut of the common and jack rafters; 17 and 6, seat and plumb cut of the hip or valley; 12 on the tongue and 13% on the blade will give the side cut of the jack; they also give the face cut across roof boards to fit in the valley or over the hip, the blade giving the cut in the former and the tongue in the latter. The backing of the hip may also be found by taking 18 on the tongue and 8 on the blade, and the tongue will give the required angle.

For an 8-inch rise, the lines from 12 and 17 (rig. 54) would run to 8 on the blade, and their Fig. 56. Cripple Jack Rafters in Place.

lengths would consequently be changed; but the formula remains the same.

To Find the Length of Cripple Jacks. The length and cuts for a cripple jack can be found just the same as for a jack resting against a hip. The cuts of the cripple are the same at both ends, and are identical with that for the upper end of a jack resting against a hip. Where the roof is all of the same pitch, the runs of the hips and valley will rest parallel with each other, as will be seen in Fig. 56. Now, here is a point that a great many do not grasp— namely, that the run of the cripple jack is the same as the length of the plates that form the angle. Thus, in the illustration, the length of the plate on one side is 6 feet, and on the other it is 10 feet, which represent the respective runs of the jacks in question. However, it should be remembered that this measurement is from center to center of hip and valley; and it is therefore necessary to make a deduction in the run equal to the thickness of the hip or valley. Or the length of the cripple may be found for the full run; then measure square back from the plumb cut the full thickness of the hip, which will be at the proper point for the plumb cut.

Framing Plan for Hip-and-Valley Roof. Fig. 57 is the plan of a common hip-and-valley roof, detailed to show all the different rafters, with their lengths and cuts, that usually enter into its construction. We shall assume it to be 10 inches to the foot. The view taken is from a point directly above. Consequently there is nothing in the plan to show what the rise is. In other words, if there were no pitch given the roof at all, the plan would show just the same, and the side cuts for hips and jacks would all be at an angle of 45 degrees, and their lengths would be as per the scale of the plan. That is, the first jack being placed 2 feet from the corner, its length would also be 2 feet; and Fig. 57. Framing Plan for Hip-and-Valley Roof these proportions taken on the square, as 12 and 12, will give what is generally called the side cut, but in reality should more properly be called the top cut. This, the reader will observe, is the regular miter, which is simple enough. Everybody understands so far; but when a pitch is given, this simple rule is usually for gotten.

In this example, the rafter, having a rise of 10 inches, has a gain of inches in two feet; and this, added to its run, makes its length 2 feet inches. Then the proportion of 2 feet and 2 feet inches, taken on the square as 12 and inches, will give the cut. The side on which the larger number is taken, gives the cut. If the point of the jack is removed by cutting on a line parallel to the seat, it will be found that the angle of the cut is still 45 degrees, or just what the angle shows in the plan. The same rule applies for this as for the cut of the hip or valley. It also applies to the jack for an octagon, or any other corner.

In this example there is shown an octagon bay, and the side cut of the jack would be in the proportion of 1 foot and 3 feet 2 inches. The first, because that is the space that the foot of the jack is from the corner; and the latter represents the length of the jack. This jack, like all others, is simply part of a common rafter; reduced to a one-foot basis on the square, it is 5 and inches.