ABSTRACT
Measurement of magnitudes is, in its most general sense, any method by which a unique and reciprocal correspondence is established between all or some of the magnitudes of a kind and all or some of the numbers, integral, rational, as the case may be. Concerning measurement in the most general sense, there is very little to be said. Since the numbers form series, and since every kind of magnitude also forms a series, it will be desirable that the order of magnitudes measured should correspond to that of the numbers, i.e. that all relations of between should be the same for magnitudes and their measures. There are two general metaphysical opinions, if accepted, shows that all magnitudes are theoretically capable of measurement in the sense. The importance of the numerical measurement of distance, at least as applied to space and time, depends partly upon a further fact, by which it is brought into relation with the numerical measurement of divisibility.
