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Quantities of Materials (Cont'd.)

III. Volumes from Original and Final Contours.

1. General Method of Measurement.

We have thus far in the discussion of the measurement of volumes with the Polar Planimeter assumed that the volume of material measured was simply material to be excavated or moved, and without reference to any particular design or purpose in its removal other than that the area from which the material was removed should be left as a level surface.

It is also seen that, as in the case of the measurement of the volume of material for which Fig. 1 of Plate X was used as an illustration, the volume was obtained from measurement of the Original or surface contours only.

It very frequently happens, however, that either we desire the surface of the ground after the material measured has been excavated or removed to conform to some given grade or shape, or that the excavation or removal of the material should be done in furtherance of some definite final plan; in both cases the problem then is to measure the volume of material necessary to be removed in order to bring the original surface of the ground to the definite final surface or form.

The measurement of the volumes of material to be moved under these conditions can be very much simplified and shortened by the use of a specially prepared diagram which shows not only the contours of the original surface, but also the final contours or contours of the final surface to which we wish to bring the original surface either by excavation, by embankment or filling, or by a combination of both operations; by means of such a diagram the volumes of materials involved can be measured by one operation of the Planimeter, and the highest degree of accuracy attained with a minimum expenditure of time, labor and mental effort.

To illustrate the preparation of these diagrams and the method of measurement of the volumes involved with the Planimeter, two practical and frequently occurring examples have been taken, which will not only clearly illustrate the principles and methods employed, but will serve as examples of the applications of the Planimeter to every form of problem of similar nature.

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