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CHAPTER IV.

Measurement of Plane Areas.

II. Measurement of Small Areas.

Adjustment of Drawing and Instrument.

The plan or map on which is the figure whose area is to be measured is smoothly laid on and attached to the drawing board or table, the surface of which should be level and free from irregularities: especial care being taken that the surface should be smooth and without unevenness due to warping. If the paper on which the plan or map is drawn is in good condition and lies smoothly on the board without wrinkles or tear it can be fastened to the board with the ordinary thumbtacks. If however the paper is torn, wrinkled, or badly creased so that it does not present an even surface or lay flat on the board it must be stretched and mounted with paste on the board, in same manner as when water colors are to be applied with a brush.

In the case of old and valuable maps or drawings which cannot be mounted without injury to the map itself, they should be tacked down as smoothly as possible to the board and a sheet of paper or card board tacked on that portion of it on which the Wheel will move during the tracing of the given figure as has already been described . The size and position of the paper thus used can be at once determined by observing the path of the Wheel while making a preliminary tracing of the figure.

The map or drawing having been fixed to the drawing board with its surface as true and even as its condition will admit of, the Carriage Vernier V is adjusted to the Setting as given in the Tables for the scale to which the figure is drawn, and the Tracer Arm firmly clamped to the Carriage by the proper screws. The Tracer is then placed near the center of the given figure and the Pole placed in its proper or most favorable position on the paper with respect to the area to be measured. The proper or “most favorable” position of the Pole with reference to any given figure is easily determined by the Rule already given as well as the selection of the point for beginning the measurement. That the Pole be placed in this position is a matter of considerable importance in obtaining the highest degree of accuracy of results, and to facilitate the finding of this position and illustrate the application of the Rule, Figs. Nos. 2, 3, 4 and 5 are given on Plate V which show the most favorable positions as well as the proper direction of the tracing and places for beginning of the four principal forms of Planimeters with respect to the given figures whose areas are to be determined.

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