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Quantities of Materials (Cont'd.)

III. Volumes from Original and Final Contours.

3. Volumes of Materials in Reservoir and Similar Construction.

Preparation of Diagram.

On examination of the diagram constructed in the manner just described it is seen that it shows the two complete sets of contours— one set being the “Original” or Surface contours, and the other the “Final” or Contours of the finished reservoir— the two sets of contours being made by the same set of parallel cutting planes and one set being drawn superimposed upon the other.

It will also be seen that by passing the cutting planes in the manner described we have divided all of the material necessary to be excavated above the Zero plane into a series of oblique continuous prismoids, the bases of the various prismoids being the respective areas enclosed by any two intersection contours, one in each set of contours having the same elevation above the datum plane, and the length of each such prismoid being the vertical distance between the cutting planes, which, in this instance, is four feet.

Thus, in the diagram the first prismoid would have for its upper base the area enclosed between the contour numbered 36 of the “Original Contours” and the contour number 36 of the “Final Contours” or the area included between the curved line marked 36 and the broken line A' B'; the lower base of the prismoid being the area included between the original contour 32 and the broken line C' D', and so on to the last prismoid whose upper base would be the area OVUT and whose lower base would be the area PSML.

Since the dotted line 00 or PS is the dividing line between the excavation and embankment portions of the Reservoir, the total volume of embankment is evidently the total volume of the prismoids into which the parallel cutting planes have divided that portion of the Reservoir below the level assumed as grade. The bases of these prismoids being formed in exactly the same manner as those above the 00 line just described, these prismoids need no further description since they differ only from the other prismoids in that they are the volumes of embankment necessary to bring the original surface up to the required surface instead of volumes of excavation.

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