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CHAPTER X.

Various Forms of Planimeters and their Characteristics.

Precision Disk Planimeter.

Another form of instrument which, like the Rolling Planimeter just described, is included in the Precision Class on account of the high degree of accuracy of which it is capable, is the Precision Disk Planimeter.

With this instrument as with others of its class this high degree of accuracy is due to the elimination of those sources of error present in the simpler forms of Planimeter, chief of which being the irregular and slipping movements of the instrument caused by unevenness and lack of uniformity of the contact surface when the integrating wheel receives its motion from direct contact with the surface over which it moves.

This Planimeter consists of two distinct partsó the Polar Disk P having a rim on which are cut very fine teeth and the Planimeter proper AFHSM.

The Tracer Arm F of this instrument is of the form common to all Planimeters and like them is adjustable in length and capable of being adjusted to any desired Setting, and has also the usual Tracer Rest, Binding and Slow Motion screws.

The Polar Arm is supported on the paper by the small wheel L and the Tracer Rest S, and on the Polar Disk P by means of the small spherical bearing at p, the exact center of the disk, and turns about a finely polished pivot at this point which forms the center of revolution of Pole of the instrument. Any movement of the Tracer f produces a revolution of the entire instrument about the point p and this movement being communicated to the disk S through the Wheel r causes a corresponding movement of the Integrating Wheel R which moves around the edge of the Disk Só the extent and nature of the movement of the Tracer f being thus measured and recorded by the wheels R and Z.

Since the Rest S and the small wheel L are mere supports of the Tracer Arm they have no effect on the movement of the instrument, and since the motion of the Integrating Wheel R is produced entirely from its contact with the Disk S the surface of which is uniform, the accuracy of the instrument is seen to be entirely independent of the character of the surface traced.

The diameter of the Polar Disk is about 15 cms. and the total length of the Tracer Arm 35 cms. while the area which can be traced from one position of the instrument would be that of a figure 25 cms. in height by 20 cms. in length or about 80 sq. inches.

Referring again to the relative degrees of accuracy of these Precision Planimeters as compared with the Polar form used throughout the preceding discussion to illustrate the various operations of which it is capable, it can be said that in most cases equally accurate work can be done with the Polar or Compensating Instruments as with the instruments included within the so-called Precision class, provided that in the use of the simpler instrument the conditions for accuracy given in detail in a previous chapter are carefully complied with and that the surface or paper upon which the integrating wheel rolls is of the nature proved by experience to be most favorable for accurate results. The special value of the Precision Planimeters being as already stated their independence of these conditions.

The class of instrument known as Mechanical Integraphs and Integrators while differing from Planimeters already described, must still be included with them since they possess most, if not all, of the properties of Planimeters.

In addition to an ability to perform those operations of which the ordinary form of Planimeter is capable, the Integraph and Integrator have a range of operation impossible to the simpler instrument and which makes them of the greatest interest and value besides rendering their aid almost indispensable in certain forms of calculation.

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