 Early measurement theorists formulated axioms that describe these qualitative empirical structures, and used these axioms to prove theorems about the adequacy of assigning numbers to magnitudes that exhibit such structures. Specifically, they proved that ordering and concatenation are together sufficient for the construction of an additive numerical representation of the relevant magnitudes. An additive representation is one in which addition is empirically meaningful, and hence also multiplication, division etc. Campbell called measurement procedures that satisfy the conditions of additivity “fundamental” because they do not involve the measurement of any other magnitude (1920: 277). Kinds of magnitudes for which a fundamental measurement procedure has been found—such as length, area, volume, duration, weight and electrical resistance—Campbell called “fundamental magnitudes”. A hallmark of such magnitudes is that it is possible to generate them by concatenating a standard sequence of equal units, as in the example of a series of equally spaced marks on a ruler.