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


Measurement of Plane Areas.

I. Measurement in General.

Examination and Adjustment of the Planimeter.

Before beginning any operation with the Planimeter, and especially if the Planimeter has not been in very recent use, the condition of the instrument and its adjustment should be carefully examined, and with particular reference to the conditions mentioned in Chapter II.

After a general examination of the instrument for apparent injury or defect due to accident, such as a bent needle or arm, rust or dent on the rim of the Integrating Wheel, binding of the carriage pivot, etc., the Planimeter should be tested for sources of error not discoverable by ordinary inspection. It is to the latter that we must look for cause and correction in almost every case when the Planimeter fails to give a result with its customary degree of accuracy, and the instruments must be subjected to a series of tests to determine the source and extent of the inaccuracy and the means of correction.

To test the accuracy of the Planimeter the Test Plate is fixed on the paper, a starting point accurately marked, and the Tracer being placed in one of the small holes already described, the Test Plate and Tracer is made to revolve a certain number of even times about the needle point fixed in the end of the Test Plate as a center. The Reading of the counting and Integrating Wheels being taken at both the beginning and end of these revolutions, the difference of these two Readings is evidently the Reading of the Planimeter for the number of Revolutions of the Tracer thus made. If at the end of these revolutions the Tracer is caused to make an equal number of revolutions in the opposite directions from the first, and the Reading of the Instrument due to the reverse revolutions is equal to the Reading due to the first or direct revolutions, the assumption is that the Planimeter is in good adjustment.

If, however, these Readings differ, or what is the same thing, if the reverse tracing of any figure does not give the same Reading as did the direct tracing of the same figure, the instrument is evidently either not in adjustment, or else one or more of what we have termed the conditions for accuracy have not been complied with.

This discrepancy in the readings thus obtained may then be due to irregular slipping of the Integrating Wheel, lost motion, irregularities in the surface of the paper on which the Wheel rolls, non-parallelism of Wheel Axis with Tracer Arm, or lack of sensitiveness in the Wheel Axis bearings due to causes already discussed in Chapter II.

If we measure any given area which is placed first on the outside of the Constant Circle and then on the inside of the Constant Circle, and the Reading for both positions of the same area are the same, it proves that the defect in or lack of accuracy is not due to any displacement of the axis of the Wheel from its proper position, and that the axis of the Wheel is parallel to both surface and Tracer Arm.

The unfavorable effect of the surface of the paper on which the Integrating Wheel moves is easily determined by pinning to the drawing board a piece of paper, having what experience has proved to be a favorable surface for the purpose, and of such shape and size as to contain within its area the entire path of the Wheel during the measurements in question.

Should the axis of the Wheel be too loose or shake in its bearings, it can easily be detected by forcing the Tracer Needle into the paper, and then after having fastened the binding screw, trying to shake the axis in its bearings by moving the other end of the Tracer Arm laterally with the fingers.

Lack of sensitiveness of the Wheel Axis with its cause and method of correction has already been treated in a previous chapter and need not be repeated here except to say, that when the requisite degree of sensitiveness has not been restored by any of the methods described, it is safe to assume that the defect is due to dullness, or is the result of injury by shock or accident to the wheel axis or its bearings, and the only remaining remedy is to place the instrument at once in the hands of a competent maker.

All errors or inaccuracies in results of Planimeter measurements due to the non-parallelism of Wheel Axis with Tracer Arm, or to imperfect working of Integrating Wheel or its axis from dirt or looseness in its bearings are, however, easily discoverable by the testing methods just described, and disappear when the axis and its bearings are properly adjusted. These adjustments are made by means of the bearing and set screws in the Carriage, and by them the Wheel and its attachments can be adjusted with the greatest nicety, and with mathematical and mechanical precision.

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