<< Previous Section Table of Contents The Polar Planimeter Page Numbers Next Section >>

CHAPTER III.

Theory of the Polar Planimeter.

Fundamental Equations.

From the “General Equation of the Polar Planimeter”just demonstrated, which is simply what we have termed the “General Principle” mathematically stated, we are able to at once determine the relation existing between the various parts of the instrument, and deduce the formulae by which the values of the different factors for the various practical applications are obtained.

As already given this General Equation of Equation 1 is

A = c × r × t ... (1)
from which
c = A ÷ (r × t) ... (2)
r = A ÷ (c × t) ... (3)
t = A ÷ (c × r) ... (4)
r × t = A ÷ c ... (5)

Since the above five Equations show the relation of the various parts of the Planimeter to each other, and the relation of each to the operation of the instrument, they may be termed the “Fundamental Equations” of the Polar Planimeter, and will now be discussed.

<< Previous Section Table of Contents The Polar Planimeter Page Numbers Next Section >>