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Let A = Area of FigureThen
r1 and r2 the first and 2nd Readings respectively
x = Value Actual Vernier Unit and y = Value Relative Vernier Unit
It is evident from the description just given that the operation of measuring an area with the Polar Planimeter is a very simple one and singularly free from liability to error, since but one mathematical operation is involved— (the multiplication of the Reading by the value of the Vernier Unit) and that operation usually a mental one as the value of the Vernier Unit is usually a single simple number, often Unity. It is also evident that with an instrument in good adjustment and condition, the accuracy of the measurement is entirely dependent on the accuracy and fidelity with which the Tracer is made to follow the periphery of the given figure.
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