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Quantities of Materials (Cont'd).

II. Volumes from Original Contours.

1. General Method of Measurement.

Although perfectly general and applicable to all forms of prismoid, we have so far limited our discussion to that particular form of prismoid occurring most frequently in the work of the Railroad or Canal Engineer, since it is in this form of prismoid that by far the greater portion of the quantities to be measured are presented.

In the examples thus far given to illustrate the use of the Planimeter in the measurement of the volumes of materials, the prismoids into which the material to be measured have been divided have had vertical end sections and their length as the greatest dimension.

There is, however, a very large class of problems of constant occurrence in the Engineer's practice in which the material to be measured, instead of being divided in the form of prismoids just described, is considered as divided into a number of continuous prismoids having more or less extended horizontal areas as bases and a very short vertical height between these bases or end areas as the length. These prismoids in most instances are formed by the passing of several parallel, equidistant, horizontal planes through the material to be measured, the sections made by these planes being the base of the prismoids, and the vertical distance between them the lengths.

From this it is readily seen that the form of measurement about to be described by which the volume of the prismoids thus formed is obtained, will include all problems involving the measurement of quantities of materials in operations, such as grading over extended areas, the measurement of borrow pits, volumes of materials in dredging operations, displacement diagrams, contents of reservoirs and many other problems of similar nature.

While the principles involved in the measurement of quantities is the same for all problems included in the class we are discussing, the general method of measurement can often be modified in the case of some particular application or application to some particular problem so as to simplify it for that operation and lessen the time and labor involved in the measurement.

To illustrate this and to show the use of the Planimeter in the various special applications referred to, several of the more important and most frequently occurring problems of this class will be taken up and the use of the Polar Planimeter in each will be explained.

Very complete Tables giving the Settings, Constants and other factors for the immediate adjustment of the Planimeter for all of the various forms of measurement described, and for all scales are given among the Tables. In those cases where the same Table is used for two or more different operations, the proper Table to use is designated at the end of the section describing that operation, as well as remarks on the proper use of the Table and any other notes which may serve to make the Tables of the greatest possible service.

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