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CHAPTER VI.

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Quantities of Materials.

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I. Volumes from Cross Sections.

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1. Methods of Measurement in General.

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Mean End Area and Prismoidal Methods of Measurement.

The two methods in general use for obtaining the volume or quantity of
any materials in Engineering or Construction work are what are know as
the “Average” or “Mean End Area” method and the Prismoidal method.
Of these, the first or Method of Mean End Area is only accurate in the
very few instances, when conditions may make it a special form of the second
or Prismoidal method. While often used, and indeed, having its use in some
States legalized by statute, the method is at best but an approximation,
and when used except as an approximation, is liable to work great injustice
to either the Contractor or to those whose interests are represented by
the Engineer. In almost every case the results of the measurements of a
quantity by this method are larger than the true quantity, and although
attempts to counteract this are made by applying a correction, the error
not being a constant one can not be eliminated, and is often productive
of any amount of subsequent trouble and disagreements.

The extended use of this Average End Area Method is due entirely to
the rapidity with which calculations for the determination of quantities
of materials can be effected, as compared to the second or Prismoidal Method,
which while rigid and mathematically accurate, necessitates a much longer
time to obtain any desired result than does the first.

Owing to the extended use of the Average method just mentioned, and
to the fact that the method has a certain value where confined to rough
preliminary estimates or approximations, the use of the Planimeter in connection
with the solution of problems by that method will be included in our discussion,
although it will later be seen that the use
of the Polar Planimeter in all this form of computation entirely eliminates
every advantage as to time possessed by the Average Method, allowing an
absolutely accurate result by the Prismoidal method to be obtained in exactly
as short a time as an inaccurate result by the Average Method.