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Various Forms of Planimeters and their Characteristics.

Compensating Planimeter.

All that has been said either here or in previous chapters of the Polar Planimeter, just mentioned, can be repeated with even greater truth and force of that form of the instrument designed by Mr. G. Coradi of Zurich, and termed by him the “Compensating Planimeter.”

Reference to this statement has been made in a previous Chapter and its advantages over other forms of Polar Planimeter due to the elimination from its results of those errors inherent in the ordinary Polar type are quite sufficient to place it within the Precision class.

No. 6.

Mr. Coradi regards this instrument as “destined little by little to replace the Polar Planimeter”— a prediction which the instrument seems fully to justify. The theoretical considerations involved in the design of the Compensating Planimeter are easily understood from the mathematical discussion of the principles of the Planimeter given in Chaps. II and III and the manner in which the tendency to error in the results of Planimeter measurements due to non-parallelism of the axis of the Integrating Wheel and other causes are compensated for in the working of this form of instrument will be readily seen from the two diagrams given in Plate IX, Figs. 5 and 6.

These Figs. show the Compensating Planimeter as placed in position for the measurement of the area J. As explained in Chap. II, when the axis of the Integrating Wheel in any Planimeter is not in adjustment or not parallel to the Tracer Arm, it produces an error in the results of any measurement, the size of the error being directly proportional to the amount of the displacement.

By taking the mean of two Readings, one taken with the Planimeter on the right of the base XX', as shown by the full lines in Figs. 5 and 6, and the dotted lines in the given Figs., any error in the results due to the causes named is evidently eliminated, since in one position the sign of the error would be positive, and in the other negative. Detail drawings of the Compensating Planimeter are given on Plate IX from which the construction of the instrument can be readily understood.

The Pole of the Planimeter is a very fine needle point projecting from the bottom of the Polar Weight P shown in Fig. 4. This Polar Weight is permanently attached to the Polar Arm and revolves with the Arm about the needle point as a center, the bottom of the Polar Weight being wedge shaped in order to reduce friction to a minimum.

The special arrangement by which the length of the Tracer Arm is made equal in length to the base of any diagram whose average height is to be measured has already been described on Page 55 of Chapter V, as has also the special form of graduation by which the “Setting” of the Planimeter for any case is also the length of the Tracer Arm, an improvement of much value when making the calculations of the factors for any given operation.

The workmanship of this instrument is all that could be desired and of the kind which characterized all of this maker's productions.

No. 7.

A special form of the Compensating Planimeter has recently been produced which has an adjustable Polar Arm which may be shortened or lengthened as desired. By this arrangement the value of p in the Equation of the Constant Circle (Figs. 1 and 2 of Plate III), can be made such that the Constant for any given scale or operation shall be a round number or any number desired.

A further advantage of the adjustable Polar Arm lies in the ability to extend it and thus increase the size of the Area which may be measured with the instrument.

As giving an idea of the actual size of the Figure whose area can be measured in one operation of the Planimeter it can be said that the Compensating Planimeter as described above is capable of measuring with one tracing and with the Pole on the outside of the given figure a figure in the form of a square having a side 25 centimeters in length or an area of, say, 625 Sq. Centimeters, equivalent to about 97 Sq. inches, which is also about the same capacity as the Polar form of instrument which we have been using for illustration and description.

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