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Quantities of Materials (Cont'd).

II. Volumes from Original Contours.

2. Grading Over Extended Areas.

Method of Measurement.

Hence to measure the total volume of all the prismoids into which the total quantity of material to be excavated has been divided, we adjust the Planimeter to that Setting which will give a Reading of 4938.2 Vernier Units for each sq. inch of actual area traced. The areas ABC and ARSTV are then traced and one-half the resulting number of Vernier Units recorded is set down as a partial result.

The Planimeter is then adjusted to a zero Reading and all the bases of the constituent prismoids are traced— those bases designated as odd being traced twice and those designated as even being traced once. At the completion of this last tracing which is continuous and without intermediate readings, the total Reading is taken and from it is subtracted the partial Reading already recorded. The resulting number of Vernier Units is then multiplied by the relative value of the Vernier Unit for the scale in question, which in this case is .001, and the product thus obtained is the total value of the 10 prismoids or the total number of Cu. Yds. of material which will have to be excavated to bring the surface of the given lot to the required surface.

In the description just given of the use of the Polar Planimeter in the measurement of quantities of materials in grading and similar operations, the example chosen to illustrate this method of measurement while of very frequent occurrence was purposely made of very simple character in order that the method should be clearly understood, but the extension of the method and its application to much more complicated conditions is quite as simple and involves no principle other than those already described.

It will take but little thought to discover how easily this form of measurement can be extended to cover every form of operation similar to the one above described, no matter how complicated it may be and how perfectly the Planimeter is adapted to the solution of all problems of similar nature.

In the case of grading and leveling operations the Planimeter when used with any topographical map and by the simple operation of tracing the contours will give at once not only the volume of material necessary to be excavated to bring the surface of the ground to any desired level but also the amount of material necessary to fill in any depressions, thus enabling the quantities for cutting and filing to be compared and greatly facilitating the entire operation.

The facility and ease with which the Planimeter measures the volumes of materials in all these forms of operation has also the very great advantage of allowing cross-sections or contours to be taken much closer together than is customary and hence giving a much more accurate and satisfactory result, since by the use of the Planimeter we are able to measure at least three prismoids in the same or less time than it takes to measure one by any other method and with a far greater degree of accuracy.

As already stated the extension of this method of measurement to other problems of like nature is evident and will not require further description except to say that the value of the Polar Planimeter in every such problem will be found to be quite as great as is apparent in the simple case we have been discussing— a remark equally applicable to each and every application possible to the instrument.

Table 9 gives the Settings, Constants and other factors for adjusting the Planimeter to this form of measurement and for all the usual scales.

The factors there given are calculated in all cases on the assumption that the vertical distance between the Contours or End Sections is one foot which would make L = 1.0 ft. in Eq. 19. The correction applied to the final result for any other value of L is evident and consists simply of multiplying the result obtained by using the factors given in the Tables by the vertical distance in ft. between the parallel cutting planes. Thus in the example just given the results obtained by using the factors in the Table would be the total volume of all the prismoids if the contours thus found must be multiplied by 2 to obtain the correct volume for this particular case.

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