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CHAPTER II.

The Polar Planimeter.

Test Plate and Its Use.

Enclosed in the case with each Planimeter will be found what is know as a Test Plate. This Test Plate may have the form of a circular metal disk having a groove cut along its edge as shown in Fig. 2 of Plate I, or it may consist of a metal strip of the form shown in Fig. 3 of Plate IX. The intent or purpose of the Test Plate is to furnish an accurately known constant area by means of which the accuracy of the Planimeter and its adjustments can be tested. In the case of the circular grooved disk the area of the circle of which the groove is the circumference is accurately know, and by placing the point of the Tracing Needle in the groove, this known area is accurately traced by moving the Tracer along the groove until it has made a complete circuit and returned to the starting point. The other form of Test Plate consists, as has been said, of a short metal strip or plate. At one end of the plate, and held in position by means of the large screw head shown, is a very fine needle point which projects a short distance from the face of the plate. Along the center of the plate, and at different distances from the needle point, are very minute conical receptacles into which the point of the Tracer fits without play. These points are so spaced that when the needle point at the end of the strip is firmly pushed into the paper the distance from the needle point to any given receptacle is the radius of a circle, the area of which is a known quantity; the circle itself having for its circumference the path of that particular receptacle when the strip is revolved about the projecting needle point as a center.

The method of using the Plate is very simple and is as follows: Having pressed the needle point of the Test Plate firmly into the paper, the Tracer of the Planimeter is placed in the receptacle selected, and either a mark made on the paper opposite a line cut in the outer end of the Plate or a pin is pushed into the paper to mark the point of beginning. The Test Plate is then caused to revolve about the needle point at its end by pushing the other end of the plate with the finger until the mark at the end of the plate having made a complete revolution about the needle point has returned to the marked starting point. It is evident that by this operation the receptacle and the Tracer have traced the circumference of a circle the area of which is accurately known and the Test Plate has fulfilled the purpose desired.

The number usually found engraved at the each receptacle on the Plate is in most forms of plate the actual area of the circle whose circumference is the path traveled by that point during the revolution of the plate; this area is usually expressed in terms of the Unit of graduation of the Tracer Arm which in most cases is square millimeters.

When using this form of Test Plate in the manner described the plate is often moved through its revolution by taking hold of the Tracer with the fingers. This practice is objectionable for several reasons as not being conducive to the greatest possible accuracy during the operation, and a much better plan is to keep the Tracer firmly in the receptacle during the movement by placing small weights on the Tracer Arm and then to cause the revolution by moving the Test Plate with the fingersó not touching the Tracer at all with the fingers during the entire operation.

Of the two forms of Test Plate just described the second or strip form is preferable to the grooved disk for a number of reasons and is the form usually supplied with the best grade of Planimeters.

It often happens that the area to be measured may be on an old map drawn on wrinkled or torn paper and otherwise not conducive to accurate working of the Planimeter. In this or any similar case the path taken by the Wheel while the Tracer traces the outline of the given area can be easily determined by trial and a sheet of paper having a proper surface can be laid down in such a manner that the entire travel of the Integrating Wheel shall be on this paper and not on the objectionable surface.

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