Fig. 87 - Showing how to find the Lengths and Bevels of Jack Rafters in an Octa. gon, Hexagon or Polygon.

One of the most difficult problems in roof framing with which the mechanic has to contend - namely, that of joining a gable cornerways or diagonally to another gable - is illustrated in Fig. 89. This method is fre quently adopted in city residences to produce diversity in design. Let A B C D E F G represent the wall plate lines in the plan ; F H, the run of the common rafter on the main part ; II I, the rise, and F I the length of the common rafter. Transfer F I to F J and draw J K, which represents the main ridge. From the center of the corner gable square up the rise of the common rafter L M, and draw A M for length of common rafter on the corner gable. From C square up to N what the main common rafter rises in the part of its run represented by L C. Then L N will be the length of main common rafter up to the point where the left valley starts. Transfer L N to L O, which is the starting point of the left valley. From O set off O P, which should be the length of the dotted line L G and of the common rafter A M. Square up G R, which should be the same as L O. From R set off the rise of the common rafter on the corner gable to S, which is the same as L M.

Fig. 88. - Diagiam Illustrating the Method of obtaining the Lengths and Cuts of all the Rafters in any Regular Polygon.

Fig. 89. - Framing Gables which Join Diagonally.

From S square up the length of the common rafter to T, which is the same distance as A M. Connect T with O for the length and position of the left valley. Connect T with P for the length and position of the right valley, which runs from the ridge of the corner gable to the plate of the corner gable. Draw P G for the length and position of the right valley, which runs from the plate of the corner gable to the main plate. Space the jacks on the main ridge and draw perpendicular lines as shown. The jacks from K J to valley O T are the jacks in the main roof The jacks from O S to the valley O T are the jacks on the left side of the corner gable. The valley T P on the right side of corner gable is but little longer than the common rafter on corner gable, and runs so nearly straight with the rafters on the main roof that the jacks on this side are seldom needed in the corner gable ; but in case they are, space them between S P and draw to the valley T P, which will give the length and bevel, as shown. Draw the jacks from the valley G P to the main plate, which will give the length and cut of the same. The down bevel of the jacks will be the same as that of the common rafter.

Fig. 90. - Diagram showing Starting Point of Valley between Gables Joining Diagonally.

It is natural for one to think the valley rafter O T should start from the point C, but such is not the case, as will be plainly seen by referring to Fig. 90, which shows that the valley starts at O on the line of the main common rafter, and comes far above the point C, for C O is the same as C N in Fig. 89.