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Quantities of Materials.

I. Volumes from Cross Sections.

3. Volumes of Continuous Prismoids.

b. Volumes from Field Notes direct.

Accuracy of Results.

What has been said as to the attainable degree of accuracy in results by the method of plotted cross-sections applies equally to the method just described when the template replaces the plotted sections and the measurements are made from the field notes direct.

To test the accuracy of this form of measurement, the volume of a section of Railroad excavation six hundred feet long, of which the notes of five cross-sections are given on page 71, was calculated very accurately by means of the prismoidal formula. The volumes of the six prismoids were then measured continuously by the Polar Planimeter in the manner just described, the scale of the cross section paper and template used being 1 inch to 8 feet. In the measurement of these prismoids with the Planimeter no attempt was made to secure a degree of accuracy higher than attainable by average care in the tracing and use of the Planimeter in this class of work, the design being to have all the conditions of the measurement the same as would be the case in any ordinary measurement or use of the instrument.

The results of the two measurements of the 600 ft.. section were as follows:

Volume by Prismoidal Tables ... 23,326 Cu Yds.
Volume by Planimeter ... 23,294 Cu. Yds.
making the difference in volume as given by the two methods of measurement
23,326 23,294 = 32 Cu Yds.
a difference so small as to be far within the strictest allowable limit for this class of work and showing a degree of accuracy in the Planimeter method far higher proportionately than the field operations by which the notes were obtained.

The saving in time and labor as between the two methods was also shown by this test to be well within the proportion of 1/2 to 4/5 already mentioned in the case of the method by plotted end sections; in fact, that proportion was almost doubled and with the further very important consideration that by this method the probability of error is reduced to a minimum.

The value of the Polar Planimeter in the class of measurements we have been discussing is so great that when once used and its capacity for furnishing results unequalled in accuracy and saving in time and labor by any other known method once recognized, the Engineer will never again return to the old methods; a fact requiring but a very short experience with the Planimeter to amply demonstrate, not alone of the instrument in this form of operation, but in every form of operation to which it is applicable.

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