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


Measurement of Plane Areas.

II. Measurement of Small Areas.

Tracing the Figure.

The Planimeter having been placed in position and a preliminary tracing of the figure to be measured having been roughly made to see that every point on its perimeter can be reached by the Tracer, the Tracer Rest is adjusted to the proper height and the Tracer brought to the point of beginning. With the Tracer at the point of beginning and before commencing the tracing the Reading of the instrument is taken which, as we have already seen, is the Reading of the Counting Wheel O and the graduated drum of the Integrating Wheel W. Then carefully and in the directions of the hands of a watch the Tracer is conducted along the outlines of the given figure by taking the Tracer Rest E (Plate I, Fig. 3) between the thumb and first finger of the right hand and guiding the Tracing Needle slowly but steadily and with a uniform motion along the center of the bounding lines, steadying the motion by resting the palm and the other fingers of hand upon the paper, until the Tracing Needle has traced the entire circuit of the given figure and arrived again at the point of beginning. A second Reading of the Planimeter is then taken and the difference between the first and second Readings, obtained by subtracting the Reading taken before the tracing from the Reading taken at the completion of the tracing, is evidently the Reading due to the tracing of the given figure or the “Reading for the given area.” This Reading which, as has already been explained in Chap. III, is the number of “Wheel Units” or “Vernier Units” recorded by the Planimeter while tracing the given figure, when multiplied by the value of the Relative Vernier Unit given in the Table for the scale to which the figure is drawn gives the desired area of the given figure traced. The description just given of the method of measuring the area of any plane figure will perhaps be more clearly understood by means of the following practical example. It will also illustrate the simplicity and ease with which the area of any figure regardless of its shape or the nature or irregularity of its periphery can be at once obtained with the Polar Planimeter and with a facility and accuracy unequalled by any other known method.

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