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CHAPTER VII.

Quantities of Materials (Cont'd).

II. Volumes from Original Contours.

3. Contents and Areas of Reservoirs.

Method of Measurement.

If then we adjust the Planimeter to that length of Tracer Arm which will give a Reading of 1994.8 Vernier Units for each Sq. inch of Actual Area represented by the values within the parenthesis, and then trace the various A's in the manner indicated, it is evident that the resultant Reading due to the entire operation will be the volume in U. S. Gallons of the Contents of the Reservoir if filled up to the Contour selected as the An of the trial measurement.

For the reasons already given elsewhere, exactly the same result is obtained by using another length of Tracer Arm or Setting and multiplying the resultant Reading by a corresponding value of Vernier Unit, the Setting and Vernier Unit selected as best adapted to the particular case being given in Table 12 opposite the given scale.

Looking in Table 12 we find the Setting for the scale 1 in. = 20 ft. to be 39.2 with the value of the Relative Vernier Unit 30.0. Adjusting the Planimeter to this Setting and bringing the Instrument to a Zero Reading the Planimeter is then placed on the diagram in its most favorable position and the Tracer brought to the point selected for the point of beginning of the tracing.

It is evident that since we desire to find that Contour at which the surface of the water must stand in order that the Reservoir shall contain the desired number of gallons, this can only be done by trial, varying the number of prismoids or contours measured until we find that value of n which will give us the desired value of V in Eq. 22.

Since n must be an even number the first trial measurement is made by taking any even Contour as the An of Eq. 22, and the volume of all the prismoids, or its equal the Contents in Gallons of the Reservoir where the water line is the n Contour, is found as indicated by the Formula by tracing continuously the Contours marked A0 and the An selected for this trial measurement. This Reading which when divided by 2 is the “½ Sum of Extreme A's” of our formula is then recorded as the partial result.

Adjusting the Planimeter again to a zero Reading, each Even A up to the Contour selected as the An of this trial measurement is then traced once and each odd A twice— the tracing as in the previous measurements being continuous. At the completion of this tracing the total Reading is taken and from it is subtracted the partial result already recorded. The result when multiplied by the value given for the Relative Vernier Unit for the given scale in Table 12 is then the total number of Gallons which the Reservoir would contain, were it filled with water up the level of the Contour taken as the An of our trial measurement.

It is evident that the result of this trial measurement will at once show whether the Reservoir when filled to the Contour chosen for the An of the trial measurement holds less or more than the number of Gallons decided upon and will act as a guide in selecting another Contour for the second trial measurement. In most instances the results of a second trial measurement, which is of course made in exactly the same manner as described for the first trial, will be sufficient to definitely determine the water line of the Reservoir when holding the number of Gallons of water previously decided upon.

The desired contour having been determined in the manner just described, the next step is evidently to find the number of acres of land covered by water when the Reservoir is filled to the height thus found.

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