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, or real, as the case may be. (It might be thought that complex numbers ought to be included; but what can only be measured by complex numbers is in fact always an aggregate of magnitudes of different kinds, not a single magnitude.) In this general sense, measurement demands some oneone relation between the numbers and magnitudes in question-a relation which may be direct or indirect, important or trivial, according to circumstances. Measurement in this sense can be applied to very many classes of magnitudes; to two great classes, distances and divisibilities, it applies, as we shall see, in a more important and intimate sense.
