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Vintage ALLBRIT Fixed Arm Planimeter measuring instrument, compensating polar version, with weighted arm, with original wooden box and magnifying glass.
Box size 45cm x 10cm
Mathematical Measuring instrument
Dated around 1970\'s
Serial Number 41221and marked Allbrit and Made in England
Very good condition, with only superficial tarnishing and scratches. Appears complete and in working order.
Although much has been written on the subject of polar planimeters, they still remain relatively obscure instruments. This is unfortunate: not only do they provide a remarkably quick and precise method for measuring areas, they have a fascinating history and are a delightful example of Green’s theorem to show calculus students (or colleagues, for that matter). Perhaps part of the reason polar planimeters are not discussed in calculus courses is that an explicit computation with the relevant vector field using Green’s theorem is somewhat complicated. (There are geometric explanations of planimeter operation that avoid Green’s theorem, but it is debatable whether they are simpler.
A brief description of planimeter operation
A polar planimeter is a mechanical device used to measure the area of a region by tracing the boundary of the region.
The instrument consists of three major components: a (1) pole arm, (2) tracer arm, and (3) measuring wheel. The pole arm merely rotates about the pole, the tracer arm is connected to the free end of the pole arm by a pivot joint (a ball and socket joint in the case of the compensating polar planimeter pictured), and the measuring wheel is attached to the tracer arm with its axis parallel to the tracer arm. The area enclosed by a simple closed curved is measured by moving the tracer along the curve clockwise and recording the amount the measuring wheel moves which, as we will see, is proportional to the area enclosed by the curve. The dial keeps track of how many complete rotations are made by the measuring wheel, and the guide wheel merely balances the instrument so that it does not tip over while tracing.
The polar planimeter was invented by Jakob Amsler in 1854 and Amsler published a paper describing it in 1856 The polar planimeter is not the only type of planimeter; there are other types of planimeters.
