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Measurement of Plane Areas.

II. Measurement of Small Areas.

Use of Guide or Template.

In many cases of measurement with the Planimeter, and especially in cases where the figure to be measured has an outline composed of long straight lines, the Tracer is guided along these lines by causing the edge of a flat thin straight-edge or ruler to coincide with the line to be traced and the side traced by carrying the needle along the edge of the ruler thus placed.

There is considerable difference of opinion as to the value of this method of tracing. M. Coradi, certainly an authority, condemns the practice as being a source of error rather than an aid to accuracy, arguing that owing to the more or less spring or bend of the Tracing Needle due to its being pressed against the edge of the Ruler, there will exist a constant error in the result of the measurement of any area whose periphery has been thus traced. He further supports his contention by deducing the error due to this “spring” of the needle in tracing a circle of 8 cm radius. Assuming the spring due to pressure of the needle against the guiding edge to amount to a deviation of the point of 0.02 mm from its normal position, he finds the error in the area of the circle in question due to this deviation to be 1/2000 = 10 Vernier Units, and remarks that “when one thinks that it takes but the slightest effort to put the Tracer 0.1 mm out of its true position, I believe that what has been stated has been fully verified.”

The experience of the writer has been, however, that the use of a ruler as a guide to the Tracer not only greatly facilitates the tracing, but that repeated tests made by measuring a figure of known area, both with and without the aid of the guide, have in very case not only failed to detect any error due to spring of the needle, but have shown an increased accuracy in every case where guide was employed. Certain it is that the amount of deviation due to any such spring can be minimized and practically eliminated by giving a conical shape to the Tracer, by pressing the point of the Tracer against the guide with only sufficient force to cause it to keep in constant contact with the guide, and by the simple precaution of moving the guide sufficiently away from the line traced as to cause the deviated path of the needle to coincide with the center of the line traced.

The accuracy of the results obtained in measuring with the Planimeter volumes of continuous prismoids, discussed in a later chapter, which necessitates the continuous use of a template or guide, is also proof that when properly used and with the precautions given above properly taken, the use of a guide when tracing straight sided figures is conducive to increased rather than deceased accuracy in the measurement.

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