=63. Gravel Roofs.=—In =gravel roofing=, the cost per square depends on the number of thicknesses of tarred felt and the quantity of pitch used per square. A value of 4 cents per square foot for four thicknesses may be considered an average. ROOF MENSURATION =64.= While a knowledge of how to apply the ordinary principles of mensuration is all that is necessary to calculate any roof area, yet the modern house, with its numerous gables and irregular surfaces, introduces complications that render some further explanation of roof measurement desirable. The most common error made in figuring roofs—and one that should be carefully guarded against—is that of using the apparent length of slopes, as shown by the plan or side elevations, instead of the true length, as obtained from the end elevations. [Illustration: FIG. 6] =65.= The area of a plain gable roof, as shown in end and side elevations in Fig. 6, is found by multiplying the length _g j_ by the slope length _b d_, and further multiplying by 2, for both sides. The area of each gable is found by multiplying the width of the gable _a d_ by the altitude _c b_, and dividing by 2. [Illustration: FIG. 7] [Illustration: FIG. 8] [Illustration: FIG. 9] =66.= In Fig. 7 is shown the plan and elevation of a hip roof, having a deck _z_. The pitch of the roof being the same on each side, the line _c d_ shows the true length of the common rafter _l m_. In Fig. 8 is shown the method of developing the true lengths of the hips and the true size of one side of the roof. Let _a b c d_ represent the same lines as the corresponding ones in Fig. 7. From the line _a d_, Fig. 8, through _b_ and _c_, draw perpendiculars, as _g h_ and _e f_; lay off from _g_ and _e_ on these lines, the length of the common rafter _c d_, Fig. 7, and draw the lines _a h_ and _d f_, Fig. 8; then the figure _a h f d_ will represent the true shape and size of the side of the roof shown in the elevation in Fig. 7. The area of the triangle _d e f_ is equal to the area of the triangle _a g h_ or a similar triangle _a i h_. Hence, the portion of the roof _a h f d_ is equal in area to the rectangle _a i f e_, the length of which is half the sum of the eave and deck lengths, while its breadth is the length of a common rafter. =67.= A method of obtaining the lengths of valley rafters, applicable also to hip rafters, is shown in Fig. 9, which is the plan of a hip-and-gable roof. To ascertain the length of the valley rafter _a b_, draw the line _a c_ perpendicular to _a b_ and equal in length to the altitude of the gable; then draw the line _c b_, which will represent the true length of the valley rafter _a b_. =68.= As an example of roof mensuration, the number of square feet of surface on the roof shown in Fig. 10 will be calculated. [Illustration: FIG. 10]