CHAPTER III.
Theory of the Polar Planimeter.
General Equation of the Polar Planimeter.
The mathematical statement of this General Principle
is what we shall term the “General Equation of the Polar Planimeter”
and is
A = c × r × t ... (1)
in which
A = Area of figures traced
c = Circumference of Integrating Wheel
r = Revolutions of the Wheel for that tracing
t = Length of Tracer Arm of the Planimeter which is always taken as
being the distance between the Carriage Pivot F and
the Tracer T.
The demonstration of the truth of this General Principle
will now be given as concisely as is consistent with a clear understanding
of the subject, after which the application of the
principle as expressed mathematically in the General Equation of the
Polar Planimeter will be fully discussed, the relation
of the various essential parts of the instrument to each other and
to the operation of the Planimeter described, and the derivation
and significance of the factors with the methods for obtaining and
applying their values fully described.