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CHAPTER III.

Theory of the Polar Planimeter.

The mechanical construction of the Polar Planimeter and its various essential parts having been described in detail in the preceding chapter, the general theory of the instrument will now be taken up and the mathematical relation of the different parts to each other and to the operation of the Planimeter will be described in as simple and clear a manner as possible.

This demonstration together with the description of the instrument just referred to should show not only how the instrument described mechanically performs the operations demanded by the theoretical considerations involved in its principle and operation, but also the relation each essential part of the instrument bears to each other part and to the Planimeter as a whole, the relative importance of each such part, and the nature and extent which mechanical defect or non-adjustment of any part of the instrument would have on the theoretical degree of attainable accuracy of operation and result.

Before taking up the strictly theoretical consideration of the Polar Planimeter however it may prove of service in making the following explanations and demonstrations clearer to devote a few lines to the subject of the theory of Planimeters in general.

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