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Measurement of Plane Areas.

III. Measurement of Large Areas.

Example of Measurement.

Example 2.   Let it be required to measure the area of a plane figure drawn to a scale of say 1 in. = 40 ft. the size of which is too great to allow of measurement by the first or Exterior pole method.

From Table 1, we find the Setting for the scale 1 in. = 40ft. to be 92.6, with 20.0 as the value of the Relative Vernier Unit.

Adjusting the instrument to 92.6, the given Setting, the Pole is placed at or near the center of the given figure and in such a position that the Tracer can reach every point of the periphery of the figure without moving the Pole.

In this form of measurement owing to the fact that when the area of the figure to be measured is approximately equal to the area of the Constant Circle the resulting Reading of the Planimeter is small, (being only the difference between the two quantities named) it is well to cause the Integrating Wheel, or both Integrating and Counting Wheels to read Zero, as it not only facilitates taking the final Reading but also diminishes the chance for error and admits of the algebraic sign of the Reading being more readily determined.

The Tracer having been brought to the point of beginning and the instrument either being set to a Zero Reading or the Reading taken as in the first method, the Tracer is guided and caused to trace the periphery of the figure to be measured in exactly the same manner as already described for the measurement of small areas.

At the arrival of the Tracer at the starting point after having traced the entire periphery of the given figure the Reading of the instrument is again taken. If the instrument has been brought to a Zero Reading as recommended before beginning the tracing, it is evident that the final Reading is the reading for the given figure. If the instrument had not been made to read Zero but a first Reading taken, the Reading for the given area is, as in the first method, the difference between the first and second or final Readings.

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