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The importance of these calculations and the necessity of a high degree of accuracy in their results is too evident to need expression and but illustrates the need and enormous value of any aid capable of lessening the time and mental labor necessarily involved. The value of such aid is even more evident when we stop to consider how often problems arise in which the final decision in any given case is dependent on the results of the calculation of comparative costs: such for example as the final location of a section of railroad when several locations are feasible— the choice of a Reservoir site, and innumerable problems of similar nature. In too many instances the enormous amount of labor and time necessary for the calculation of the relative quantities of materials involved in making such comparative estimates limits the number considered, and in many instances causes the selection of a location which is afterwards found to have been by no means either the best or the cheapest.

A further result of the use of any efficient aid in this form of calculation is easily seen to be a much more accurate and intelligent preliminary report and estimate in any given case and the lessening of the drudgery involved in the making of the inevitable “monthly estimate.”

The attempt to supply such an aid as we have been discussing is seen in the almost innumerable number of Tables, diagrams and similar devices which have appeared, each claiming to best serve the purpose intended, and many of which are of more or less assistance to the Engineers: but of the many with which the author is familiar there are none which can from any point of view compare with the Polar Planimeter. In degree of accuracy, saving of time and labor, and adaptability to every condition, the value of the Planimeter in this connection cannot be over estimated.

While perhaps the most frequent use of the Polar Planimeter in this
class of problem is in computing the volumes of Earth work or other material
from cross-sections, since these computations are the most frequent and
occupy the larger share of the Engineer's time, the instrument is by no
means limited to that particular form of operation, but is adapted with
equal facility and accuracy to *every* calculation in which the measurement
of volumes or quantities of materials is involved. On this account and
on account of the invaluable aid of which the Planimeter is capable in
*every*
application of this form of computation the use of the Instrument
will be described in those calculations of most frequent occurrence in
the Engineer's practice.

Very complete factors for the immediate adjustment of *any* Planimeter
and for *all* scales are given in the Tables
for all of these operations and applications and these factors together
with the following descriptions of the use of the Planimeter will at once
admit of the intelligent use of the instrument in all calculations of similar
nature.

The operations selected to illustrate the use of the Polar Planimeter in the various calculations of the quantity or volume of materials are as follows and will be taken up in the order here given:

1. Methods of Measurement in General.II. Vols. from Original Contours.

2. Vols. of Single Prismoids.

3. Vols. of Continuous Prismoids.a. From Plotted Sections.

b. From Field Notes direct.

1. General Methods of Measurement.III. Vols. from Original and Final Contours.

2. Grading over Extended Areas.

3. Contents and Areas of Reservoirs.

4. Displacement Diagrams.

1. General Method of Measurement.IV. Special Methods of Measurement.

2. Grading over Extended Areas.

3. Vols. of Materials in Reservoir and Similar Construction.

1. Vols. of Brickwork.

2. Weights of Metals.

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