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- Essential Parts of the Instrument.
- Polar and Tracer Arms.
- Pole and Its Forms.
- Tracer Arm and Its Graduation.
- Carriage, Carriage Vernier and Attachments.
- Settings.
- Tracer Rests and Adjustments.
- Integrating Wheel and Recording Mechanism.
- Vernier Units, Relative and Actual Vernier Units.
- Adjustment and Care of the Instrument.
- Test Plate and Its Uses.
- Influence of Surface on Wheel Movement.
- Most Favorable Position.
- Point of Beginning.

- Theory of Planimeters in General.
- Symbols and Notation.
- Instrument Constants.
- General Principle of the Polar Planimeter.
- General Equation of the Polar Planimeter.
- Analysis of Movements of Integrating Wheel.
- Revolutions of the Wheel and Their Significance.
- The Zero Circle.
- Relation of Roll of Wheel to Area Traced.
- Fundamental Equations.
- Range of the Instrument.
- Settings— Their Determination and Use.
- Vernier Units.
- Constants— Their Derivation and Use.

I. Measurement in General.II. Measurement of Small Areas.

- Adjustment of Drawing and Instrument.
- Tracing the Figure.
- Example of Measurement.
- Formula for Area.
- Conditions for Accuracy.
- Use of Guide or Template.
- Accuracy of Results.
III. Measurement of Large Areas.

- Application of General Principle of Planimeter.
- Demonstration of Principles Involved.
- Adjusting the Planimeter.
- Special Attachment for Measuring Av. Ht. of Diagrams.
- Method of Measurement.
- Example of Measurement.
- Discussion.
- Application To or Discharge of River and Similar Diagrams.
- General Notes on the Method.

- Application of the Prismoidal Formula.
- Method of Plotting the Cross Sections.
- Method of Measurement.
- Accuracy of Results.
- Deduction of Formula.
- Method of Measurement.
- Example of Measurement.
- Accuracy of Results.
- Advantages of the Method.
- Preparing the Templet.
- Form of Field Notes.
- Method of Measurement and Use of the Template.
- Accuracy of Results.

Mean End Areas and Prismoidal Methods of Measurement.

II. Volumes from Original Contours

1. General Method of Measurement.

2. Grading Over Extended Areas.3. Contents and Areas of Reservoirs.

- Description of Diagram.
- Application of Prismoidal Formula.
- Method of Measurement.
- Measurement of Area.
4. Displacement Diagrams.

III. Volumes from Original and Final Contours.

1. General Method of Measurement.

2. Grading Over Extended Areas.3. Volumes of Materials in Reservoir and Similar Construction.

IV. Special Methods of Measurement of Quantities.Method of Measurement.2. Weights of Metals.

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