Fig. 63. - Great Circle of Jack Rafters.

The great circle of jack rafters is another modification of Fig. 58 for roofs of unequal pitches. Referring to Fig. 63, let A B represent the long run c f common rafter, B E the rise and A E the length. A bevel set at E on the line A E will give the down bevel and at A the bottom bevel. B C is the short run of common rafters, B E the rise and C E the length. A bevel set at E on the line C E will give the down bevel and at C the bottom bevel. B D is the short run of the common rafter and the same as B C ; then A D is the angle and run of the hip, D F the rise, and A F the length of hip rafter. The bevel at F is the down bevel and at A the bottom bevel. A H shows the hip rafter A F dropped down in position to find the length and bevel of the jacks for the side of roof having the short run of common rafter. Space the jacks on the line A B and draw perpendicular lines joining the hip line A H for the length of jacks. A bevel set in the angle at G will give the bevel across the back. The down bevel is the same as that of the common rafter for the short run and is shown at E on the line C E. H is the apex of the triangle formed on the side of the roof having the short run of common rafter. It is evident that the apex of the triangle formed on the side of the roof having the long run of the common rafter must be at the same point, therefore H is the apex of the hip and of the common rafters from either side of the hip. Now, to find the length and bevel of jacks on the side of roof having the long run of common rafter, measure down from H to I the length of the common rafter on the long run, which is the same as A E. From I set off the short run of common rafter to J ; connect J with H, which places the hip rafter in position for finding the length and bevel of jacks on the side of roof having the long run of common rafter. Space the jacks on the line I J and draw perpendicular lines, joining the hip line J H, which gives the length of jacks. A bevel set in the angle at K will give the bevel across the back. The down bevel is the same as that of the common rafter for the long run, and is shown at E on the line A E. The circular lines show that taking H as a center the triangle H I J will swing around opposite the triangle A B H, and bring every jack opposite its mate on the hip line A H, thus proving the correctness of the method, as well as showing how to space the jacks correspondingly.

In Fig. 64 is shown another method for obtaining the lengths and cuts of rafters in hip roofs of unequal pitch. Let A B C represent the wall plate and D E F the deck plate; then A E is the run of the common rafter on the short side of the hip, E D the rise and A D the length.

Fig. 64. - Another Method of Obtaining Lengths and Cute of Rafters in Hip Roofs of Unequal Pitches.

The bevel at D is the plumb cut at the top and at A the bottom cut. From A set off the length of the common rafter to G, which should be the same length as A D. Connect B G, which places the hip rafter in position to find the length and bevel of jacks on the short side of the hip. Space the jacks on the line B A, and draw perpendicular lines joining the hip line B G for the length of the jacks on the short side of the hip. The bevel at J is the bevel across the back of the same. The plumb cut or down bevel is the same as that of the common rafter shown at D. C E is the run of the common rafter on the long side of the hip, E F being the rise and C F the length. The bevel at F is the plumb cut at the top and at C the bottom cut. From C set off the length of the common rafter to H, which should be the same length as C F. Connect B H, which places the hip rafter in position to find length and bevel of jacks on the long side of the hip. Space the jacks on the line B C and draw the same, joining the hip line B H, which will give the length of jacks on the long side of the hip. The bevel at K is the bevel across the back. The plumb cut or down bevel is the same as that of the common rafter shown at F. BE is the angle and run of the hip, E I the rise and B I the length of the hip rafter. The bevel at I is the plumb cut at the top and at B the bottom cut fitting the plate. Now, the lines B G, B H and B I show the hip rafter in three different positions for finding the length and bevels of the jacks and the hip, and are practically the same as shown in Fig. 62. Of the two plans Fig. 64 is perhaps plainer and more easily understood, yet both have the common difficulty, a confusion of cross lines, which is very bothersome to many who are trying to master the art of roof framing. To make this system of roof framing so plain that even the most inexperienced may readily master it, we will show how the first simple method, Fig. 57, may be further extended to meet the requirements of any roof, showing ail the rafters without the usual complications of cross lines. The plan never fails on roofs of any pitch, equal or unequal, and, no matter how complicated the roof may be, it will all appear easy by this method.