The particular case we are using for illustration would evidently require three distinct sets of measurement operations; the first operation would give the volume of excavation above the level or elevation taken as grade; the second would be to find the volume of excavation in the basin proper below the grade level, the result of which being added to the first result would give the total number of cubic yards of material to be excavated; while the third operation would be for finding the number of cubic yards of embankment required for the given construction.

With the examples already given of the use of the Polar Planimeter in the measurement of volumes of prismoids, no difficulty will be encountered in applying the instrument to the measurement of any quantity which can be treated by any of the methods described, and with the principles involved clearly understood there is almost no limit to the number or variety of problems to the solution of which the Planimeter cannot be most easily adapted and with the same degree of accuracy and almost incredible saving in time, labor and mental effort which characterizes its use in those applications already discussed.

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