The Polar Planimeter and Its Use in Engineering Calculations; Together with Tables, Diagrams and Factors for the Immediate Adjustment of the Instrument for the Solution of Problems Etc., Etc., Etc
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1908 edition. Excerpt: ...includes amongst its many forms almost every form of operation having for its object the securing of a maximum degree of accuracy in the determination of the true value of a quantity by the operation of averaging; this is best illustrated, perhaps, by the method of repetition in the case of the measurement of an angle and processes of similar nature. To this class also belong problems such as the determination of the average or mean height of an indicator and similar diagrams, the finding of the center of gravity of a plane figure, problems involving the principles of probability and probable error, the reduction of the records of self1 registering instruments, and in fact every form of problem in which the relation of two variables can be expressed in the form A--X X y, and which is capable of graphical representation by an area. Application Of General Principle Of Planimeter. That principle which, as we have said, makes the Planimeter especially applicable to this class of problem, is that which we have elsewhere demonstrated and termed the "General Principle of the Polar Planimeter," and is given with its demonstration and discussion in Chap. III. To more clearly illustrate its relation in this connection, this General Principle can be stated as, the Area of any figure measured by the Polar Planimeter is equal to the Area of a rectangle having for its base the length of the Tracer Arm and for its height a distance equal to the distance rolled by (he wheel during the tracing of a given figure. This principle stated mathematically is what we have termed the "General Equation of the Polar Planimeter," and is repeated here on account of its especial significance in the operation under discussion. Demonstration Of Principles...
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