[Illustration: FIG. 1]
=14.= The ordinary rules of mensuration are all that are needed to
compute the =volume= of any excavation. The work is very simple when
the area to be removed is regular; but when the outlines are very
irregular and broken, the easiest method to employ in calculating the
excavation is to divide the plan into geometrical figures that are easy
to compute, and then calculate the area of each one separately. Adding
these areas and multiplying their sum by the depth of the cellar will
give the volume of the excavation.
This method will be made clear by referring to Fig. 1, which represents
the plan of an irregular foundation. To compute the area of the
excavation, the plan is divided into the rectangles _a d c b_, _l k b
m, j i h g, g f e c_, and the polygons _n q p o, t u r s_, and _a x w
v_. By scaling on the drawing the dimensions of these figures, the area
of each may then be readily determined by calculation.
[Illustration: FIG. 2]
=15.= It is sometimes necessary to find the volume of an excavation,
the surface of which is very irregular, as in Fig. 2. In such a case,
the following method may be used: Divide the surface of the excavation
into a number of squares, or rectangles, as at _d e f c_; these
represent the ends of prisms, the other ends of which are the bottom
of the excavation, as at _a h g b_. Then calculate the volume of each
prism by ascertaining the height of the four corners above the bottom;
add these measurements together, divide the sum by 4 (the number of
corners), and multiply the result by the end area, as _a h g b_; the
product will be the volume of the prism. The sum of these partial
volumes will be an accurate estimate of the contents of the excavation.