CHAPTER V.
Problems Involving Averaging.
Application of General Principle of Planimeter.
That principle which, as we have said, makes the
Planimeter especially applicable to this class of problem, is that which
we have elsewhere demonstrated and termed the “General
Principle of the Polar Planimeter,” and is given with its demonstration
and discussion in Chap. III. To more clearly illustrate its relation in
this connection, this General Principle can be stated as,
the Area of
any figure measured by the Polar Planimeter is equal to the Area of a rectangle
having for its base the length of the Tracer Arm and for its height a distance
equal to the distance rolled by the wheel during the tracing of a given
figure.
This principle stated mathematically is what we have termed the “General
Equation of the Polar Planimeter,” and is repeated here on account of its
especial significance in the operation under discussion.