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CHAPTER VII.

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Quantities of Materials (Cont'd).

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II. Volumes from Original Contours.

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4. Displacement Diagrams.

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Method of Measurement.

The successive displacement areas being numbered
in the manner already described, the volume of
displacement to any given depth in Cu. Yds. of water displaced is evidently
found by Eq. 20, or
V = (L × D² × 2) ÷ (3 × 27) (Sum
Even A's + 2 Sum Odd A's – ½ Sum Extreme A's) ... (23)
where L is the unit vertical distance between the displacement surfaces
and D is the lineal scale of the plotted diagram.
The volume of water displaced being thus found the corresponding volume
of loaded material, is found by introducing the proper coefficient for
the given material.

This coefficient is the reciprocal of the specific gravity of the material,
and is found by trial for any given material by loading the ganged scow
with a measured volume of the given material.

As the conditions are the same,
Table
9 will give the Settings and other factors for all problems or operations
of this class when the units of measurement are the same. As the vertical
distances between the displacement surfaces are usually taken as less than
1 ft., which is the distance adopted for the calculation of the Table,
the final volume of displacement must be multiplied in any given case by
the rates or per cent which the particular interval in any given case bears
to one foot, the Tabular interval.