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Measurement of Plane Areas.

II. Measurement of Small Areas.

Conditions for Accuracy.

Experience has shown that the accuracy of the Tracing is increased and the operation greatly facilitated by the observance of the following details during the operation of tracing the figure.

Whenever possible the tracing of any line should be watched or viewed in the direction of the line, as by observing this precaution the Tracer can be kept to the center of the line with greater accuracy and any deviation from its true path is more readily detected by the eye.

At each angle of the figure, or when there is any decided change in the direction of the periphery, the finger should be placed on the top of the Tracer and the point of the Tracer pressed down into the paper at the given point, thus allowing the guiding hand to be rested and to assume the most convenient position for guiding the Tracer along the new direction without danger of moving the Tracer while making the change.

The motion of the Tracer along the periphery should be slow and uniform, and if from any cause the Tracer should deviate slightly at any point from its path by accident, it can be compensated for by causing an equal deviation to the opposite side of the path and for a length along the path equal to the length of the accidental deviation. A new tracing is, however, evidently preferable when a high degree of accuracy is desirable in the given operation.

While tracing any given figure, it should be noted whether the Counting Wheel O has passed its 0 mark during the operation. If it has done so, and its index points to a figure beyond 0, the reading for the given figure must be obtained by subtracting the first reading from 10,000 and adding the second reading to the difference.

To avoid complication and minimize the possibility of error, the Integrating Wheel is often set to Zero before beginning the tracing, and often the entire instrument is set to read Zero by turning the Counting Wheel to Zero as well as the Integrating Wheel. The advantage of this procedure is, however, doubtful, except in the case of very long and continuous tracings in one operation, as the temptation is always present to turn the wheels with the fingeró an operation to be rigidly excluded. If, however, the Zero of the Integrating Wheel is sufficiently near Zero as to require little turning to bring it there, it can be so set without injury to the Planimeter by placing the Instrument in its proper position with the Tracer at the point of beginning and then causing the wheel to read Zero by slightly shifting the position of the pole, the Tracer being pressed down at the starting point during the shifting of the pole. This has the advantage of making the second Reading the reading for the given figure by the simple mental subtraction of the two readings of the Counting Wheel alone, and is often of advantage when performed in the manner specified.

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