The system to which we shall now refer is one by which the lengths of common rafters, hips, valleys and jacks, with all their different bevels, on roofs of equal pitch, may be easily found without the aid of drawings. It is so simple that any one can understand it and find the lengths and cuts in less time than it takes to describe the operation. The system consists of a table, given below, from which the lengths and cuts of any rafter may be determined at once:

Rafter Table.

 1 2 3 4 5 6 Pitch of roofs. Common rafter, 1 foot run. Corresponding hips or valleys. Common rafter cuts. Hip and valley rafter cuts. Jack rafter cuts. Inches. Feet. Feet. Inches. Inches. Inches. 6 1.12 1.50 12 and 6 17 and 6 13 1/2 and 12 7 1.16 1.53 12 and 7 17 and 7 13 5/8 and 12 8 1.20 1.56 12 and 8 17 and 8 14 3/8 and 12 9 1.25 1.60 12 and 9 17 and 9 15 and 12 10 1.30 1.64 12 and 10 17 and 10 15 5/8 and 12 12 1.42 1.73 12 and 12 17 and 12 17 and 12 18 1.60 1.88 12 and 15 17 and 15 19 1/4 and 12 18 1.80 2.07 12 and 18 17 and 18 21 5/8 and 12

Column 1 shows the pitch of roofs in the number of inches rise to the foot run. Column 2 shows the length of common rafter to a foot run. Column 3 shows the length of a hip or valley corresponding to a foot run of the common rafter. Column 4 shows the figures to take on the square for the top and bottom cuts of the common rafter - namely, 12 for the; bottom cut, and for the top cut the number of inches the common rafter rises to the foot run. Column 5 shows what figures to take on the square for the top and bottom cuts of a corresponding hip or valley, which is always 17 for the bottom cut and the number of inches the common rafter rises to the foot run for the top cut. Column 6 shows what figures to take on the square for the top bevel of the jack rafters, which is always 12 on the tongue of a square and the length of the common rafter for a foot run on the blade. The blade gives the cut. The plumb cut or down bevel is always the same as that of the common rafter.

To avoid a complication of fractions the figures given in columns 2 and 3 are in feet and decimals. To find the length of common rafters, hips, valleys and jacks, it is only necessary to multiply the run by the figures given corresponding to the pitch.

We will now give a practical example showing how to find the lengths of rafters by means of the table.

Example. - What will be the length of rafters on a building 16 feet wide, with roof of 7 inches pitch, hipped to the center and rafters placed 16 inches from centers ?

Analysis. - The run of the common rafter is one-half the width of the building, which is 8 feet. Multiplying the run by the length of rafter for 1 foot, 7-inch pitch, column 2 of the table, and pointing off the product as in multiplication of decimals, we have the length of rafter in feet and a decimal of a foot. The decimal must be multiplied by 12 to reduce it to inches.

Operation - 1.16 x 8 = 9.28 feet. 0.28 x 12 =3.36 inches. Thus the length of the common rafter is 9 feet 3.36 inches. The 0.36 is a decimal of an inch, and if great accuracy is desired it may be called ⅜ inch. The table is made to give the length in full, so that very slight decimals may be disregarded altogether. The corresponding hip or valley may be found as follows: 1.53 x 8 = 12.24 feet. 0.24 x 12 = 2.88 inches. The decimal o 88 may be called ⅞ inch. Thus the length of the hip would be 12 feet 2⅞ inches.

If the rafters are placed 16 inches from centers the run of the first jack will be 16 inches. Taking the same figures in the table as those to find the common rafter and multiplying by 16 inches, we have as follows :

1.16 x 16 = 18.56

The decimal 0.56 may be called ½ inch. Thus the length of the first jack would be 18½ inches, the second twice that, the third three times, and so on till the required number is found. In complicated roofs the table may be used to great advantage in connection with the plan. When used in this way only one diagram showing the runs of the rafters is needed, as the lengths of all the rafters may be very quickly figured and set down on the plan and the required bevels may be taken from the table. Fig. 104 shows the plan of a roof 16 x 24 feet, with wing 12x8 feet. Roof to be 8 inches to the foot pitch and rafters placed 2 feet from centers. The lengths of rafters in this plan figured by the table are as follows :

For the common rafter, main part, 1.20 x 8 = 9.60 feet. 0.60 x 12 = 7.20 inches.

Length of common rafter is therefore 9 feet 7 inches.

For the hip rafter, main part, 1.56 x 8 = 12.48 feet. 0.48 x 12 = 5 76 inches. The length of hip rafter is therefore 12 feet 5½ inches.

For the first jack, main part, 1.20 x 2 = 2.40 feet. 0.40 x 12 = 4.80 inches.

Fig. 104. - Showing: how a Plan of a Roof can be used in Connection with Rafter Table.

The length of first jack is 2 feet 4½ inches ; the length of the second jack is 4 feet 9½ inches, and the length of the third jack is 7 feet 2½ inches.

For the hip rafter on the wing:

1.56 x 6 = 9.36 feet. 0.36 x 12 = 4.32 inches. The length of hip rafter is therefore 9 feet 4½ inches Thus we have computed the different lengths of all the rafters necessary to figure in the plan, as all rafters of the same run will be the same length, these being readily seen in the plan. As the latter shows the lengths of the principal different rafters it is unnecessary to represent all those which are of the same length, although it is a good plan in actual practice. By this method one can see at a glance just where every rafter belongs, as well as noting instantly all of the same length. It is usually necessary to figure the lengths of only a few, as will be seen by referring to the plan. The valley rafter on the left side of the wing should be the same length as the main hip; then it will reach to the main ridge, the only place of support in a self-supporting roof. The jacks which cut from hip to valley on this side will each be the same length, which is 4 feet 9½ inches, the length of the second jack, as shown in the plan. The valley on the right side of the wing will be the same length as the hip on the end of the wing. The common rafter on the wing will be the same length as the third jack on the main part. It is easy to see that the length of any rafter on roofs of equal pitch may be readily found by this method.