CHAPTER IV.
Measurement of Plane Areas.
III. Measurement of Large Areas.
Tracing the Figure.
The Setting for the scale to which the given figure is drawn being taken
from the column of Settings opposite the given scale,
the Planimeter is then placed at or near the center of the given figure,
care being taken to see that every point on the perimeter of the figure
can be reached by the Tracer from one position selected for the Pole, which
can easily be determined by a rough preliminary tracing of the figure.
A place of beginning is then selected and marked and the Tracer having
been brought to this point the Reading of the Instrument is taken. Then
carefully and in the manner described and with due attention paid to those
details
already given as requisite for accuracy, the Tracer is made to trace
the periphery of the given figure in exactly the same manner as
described for the tracing of the small area. When the Tracer has traced
the entire circumference of the figure and arrived at the place of beginning,
the Reading for the given area is obtained as in the
first method by subtracting the first Reading from the second or final
Reading. Unlike the first method however the area of the figure is not
the product of the Reading of the given area by the value of the Vernier
Unit for the given scale. The area recorded by the instrument during this
operation is actually difference in area between the area of the figure
traced and the area of the Constant Circle, and hence to obtain the area
of the figure, we must add to the Reading given the area of the Constant
Circle for the scale of the Tables for that given
scale. The sum of these two values will then be the area of the given figure
expressed in Vernier Units and this sum multiplied by the value of one
Vernier Unit given in the Table for the scale of the figure will then be
the area required.