Excerpt from Lectures and Essays, Vol. 2 of 2
Notwithstanding the very different characters of these quantities, they are all measured by reducing them to the same kind of quantity, and estimating that in the same way. Every quantity is measured by finding a length proportional to the quantity, and then measuring this length. This will, perhaps, be better understood if we consider one or two examples.
The measurement of angles occurs in a very large majority of scientific instruments. It is always effected by measuring the length of an are upon a graduated circle; the circumference of this circle being divided not into inches or centimetres, but into degrees and parts of a degree - that is, into aliquot parts of the whole circumference.
As a step towards their final measurement, some quantities, of which work is a good instance, are represented in the form of areas; and there seems reason to believe that this method is likely to be extended. Instruments for measuring areas are called Planimeters; and one of the simplest of these is Amsler's, consisting of two rods jointed together, the end of one being fixed and that of the other being made to run round the area which is to be measured. The second rod rests on a wheel, which turns as the rod moves; and it is proved by geometry that the area is proportional to the distance through which the wheel turns. Thus the measurement of an area is reduced to the measurement of a length.
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