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

CHAPTER VI.

Quantities of Materials.

I. Volumes from Cross Sections.

3. Volumes of Continuous Prismoids.

a. Volumes from Plotted Sections.

Method of Measurement.

The actual method of tracing as indicated by the quantity within the parenthesis would be as follows: After having adjusted the Planimeter as described to that Setting which will give a Reading of 1580.2 units for 1 square inch of actual area, we bring the instrument to a Zero Reading, and having placed it in its most favorable position as elsewhere described, we select a beginning point and trace the plotted sections marked A0 and A6, as shown on Fig. 3 of Plate IV as already mentioned. After having traced A0 and A6 once each as described, the reading of the Planimeter due to the tracing of these two sections is then taken and being divided by 2 is set down for later use.

The Planimeter is again set to a Zero Reading, and following the operations indicated by the quantities within the parentheses of Eq. 16 we trace A0 once, then A1 twice, then A2 once, A3 twice, and so on, tracing each A having an odd subscript twice and each A having an even subscript once until we have arrived at and traced the last section A6 once as indicated.

The entire operation of tracing these sections in the manner indicated is continuous, no intermediate Readings other than the one for the quantity (A0 + An) ÷ 2 as already described are taken, and no attention need be paid to the Wheel movements throughout the entire operation except to note whether and how many times the counting wheel may have passed its 0 mark and begun a new revolution.

At the completion of the entire tracing the Reading of the Planimeter is taken, and from this Reading is subtracted the Reading first set down for the quantity (A0 + A6) ÷ 2. This subtraction having been made the resulting quantity is multiplied by the Relative Vernier Unit given for the scale to which the cross-sections are plotted.

The product is then the entire volume of the six prismoids or the volume of the R'y. section between Section A0 and A6.

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