Probably no part in the construction of buildings so thoroughly taxes the skill and ingenuity of the builder as the framing of roofs. Many diagrams have been published from time to time showing how to find the lengths and bevels of hips, valleys and jacks on all kinds of roofs. Yet many of the plans heretofore published have been too complicated to satisfy the wants of the inexperienced in the art of roof framing. At this time will be presented a choice of methods, beginning with the simplest form and illustrating the subject step by step, thus showing new and novel plans as they will appear in actual practice.

Fig. 57. - Obtaining Lengths and Bevels of Rafters.

Fig. 68. - Diagram Showing Cuts of Hip or Valley Rafters.

First will be introduced a plan showing how to obtain the lengths and bevels of common rafters, hips, valleys and jacks in the simplest manner, and with the fewest lines possible. Referring to Fig. 57, draw a horizontal line twice the run of the common rafter, as A B. From the center of this line at C erect a perpendicular, continuing it indefinitely. Next set off on the perpendicular the rise of the common rafter C D; connect D and B for the length of the common rafter. A bevel set in the angle at B will give the bottom cut and at D the top cut. Next set off on the perpendicular line the length of the common rafter C E, which is the same length as D B. Connect E and A for the length of the hip or valley, as the case may be. Next space the jacks on the line A C and draw perpendicular lines joining the hip or valley. The lines J J will be the lengths of the jacks, and a bevel set in the angle at F, where the jack joins the hip or valley, will give the bevel across the back of the same. The plumb cut or down bevel of a jack is always the same as that of the common rafter. There are now shown all the lines necessary to be drawn, the plan indicating everything but the cuts of the hip or valley rafter, and this, be it remembered, is always 17 for the bottom cut and the rise of the common rafter to the foot run for the top cut. As some may think a system which does not show the cuts of a hip or valley as well as its length is incomplete, we will take the same plan and by the addition of three more lines show everything that can be desired, as in Fig. 58. Draw the lines the same as in Fig. 57, then set off on the perpendicular line the run of the common rafter C F. Connect F and B for run of hip or valley. Next square up the rise from F to G and connect G and B for the length of hip or valley rafter. A bevel set in the angle at B will give the bottom cut, and at G the top cut. It will be noticed in Fig. 58 that the lines A E and G B are of the same length, and in both cases represent the hip or valley, while showing it in different positions. The line A E shows the hip or valley in position for finding the length and bevel of the jacks, while the line G B shows the hip or valley in position to find the length and bevels of the same. This plan will work on roofs of any pitch and has only to be slightly varied to meet the require ments of roofs having hips and valleys of two pitches. On half pitch roofs one less line is required, as shown in Fig. 59. The line D B in Fig. 58 comes in the same position as F B, when applied to half pitch roofs, and is therefore the length of the common rafter and at the same time represents the run of the hip rafter. As two lines cannot be drawn in the same space we drop the line D B, remembering that it is shown by F B.