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CHAPTER V.

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Problems Involving Averaging.

There is perhaps no class of problem to whose solution the principle underlying
the construction and operation of the Polar Planimeter is so peculiarly
applicable as it is to that large class of problems so common to Engineering
and experimental work, which involves the determination of the average
or mean value of a variable quantity.
This class is a large and important one, and includes amongst its many
forms almost every form of operation having for its object the securing
of a maximum degree of accuracy in the determination of the true value
of a quantity by the operation of averaging; this is best illustrated,
perhaps, by the method of repetition in the case of the measurement of
an angle and processes of similar nature.

To this class also belong problems such as the determination of the
average or mean height of an indicator and similar diagrams, the finding
of the center of gravity of a plane figure, problems involving the principles
of probability and probable error, the reduction of the records of self-registering
instruments, and in fact every form of problem in which the relation of
two variables can be expressed in the form A = x × y, and which is
capable of graphical representation by an area.