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Various Forms of Planimeters and their Characteristics.

Area Planimeter.

As has previously been stated, there are many forms of the Planimeter varying from the simple Area Planimeter whose capacity is usually limited to a single operation, to the complicated Precision Instruments whose range of operation and attainable degree of accuracy is almost unlimited.

A brief description of these various forms of the instrument together with the operations possible to each and any particular application to which they may be especially adapted should be of interest here.

The simplest form of Planimeter consists of two arms of unchangeable length connected at the end by some form of pivot joint. The free end of one arm terminates in a vertical needle, which on being pressed into the paper, becomes a center about which the entire Instrument can revolve. At the free end of the other arm is the vertical Tracing Needle or Tracer which is used to follow the outline of the figure whose area is required.

No. 1.
Polar Planimeter, German Silver, to measure square inches.

At the other end of the Tracer Arm and near the pivot joint connecting the two arms is the Integrating Wheel having its axis parallel to the Tracer Arm to which it is attached.

The drum of the Integrating Wheel is divided into one hundred equal parts, and the relation of the areas and Wheel is such as to cause the Wheel to record one hundred of these parts, or to make one complete revolution when the Tracer has traced an area of ten square inches. By this arrangement the figures on the Wheel represent square inches, the intermediate graduations tenths, and the vernier hundredths of a square inch of area traced.

Having no recording wheel the limit of the area which can be traced and recorded is evidently ten square inches while the length of the Tracer Arm being constant restricts the measurement to one unit of area for all measurements, usually one square inch.

No. 2.

The addition of a recording wheel to this form of Planimeter which records the number of complete revolutions of the Wheel for any tracing allows of the measurement and recording of an area of one hundred square inches for those instruments having this attachment.

The simplicity of this form of Planimeter restricts its use to the simple operations of measuring areas within its capacity, although it performs that operation with a degree of accuracy unapproachable by any other method when applied to the measurement of areas having more or less irregular bounding lines.

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