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Relationships observed between variables are inextricably linked to the ways in which the variables are measured. In an earlier paper it was argued that the development of a rigorous and consistent system of measurement is a necessary, although not a sufficient, condition for the discovery of mathematical relationships in human geography [ 5 ] . This note will examine the measurements presently in use in the subject to substantiate the claim that the types of variables we investigate do not facilitate mathematical synthesis. Consideration of geographical variables leads to questioning the extent to which the discovery of mathematical relationships is an appropriate goal.The primitive terms from which all measurements can be derived are known as dimensions. It was suggested in [ 5 ] that a working set of primary dimensions for human geography might be mass M , distance L, time T, value $, population N, and information 1. From these primitives it is possible to construct most, if not all, of the variables of interest. Population density, for example, is population divided by the product of two distances (NL-2), land rent is value per area per time ($L-'T-l), and so on. Analyzing variables in this manner emphasizes the compatibility of their measurements and clarifies how it is that many different quantities may combine together in an elegant and parsimonious mathematical relationship. According to the principle of dimensional homogeneity, all quantities that are added, subtracted, or equated must have the same dimensions or, in other words, must be measured in the same units [ 6 ] . Population, for example, cannot equal area, but can equal area multiplied by population density (L2.NL-'= N). Population density here is a constant that has the effect of linking the measurement of population and area and so makes possible a mathematical relation between them. A collection of variables that are made up of different combinations of the same primary dimensions is rich in theoretical possibilities. On the other hand, a field in which the most commonly used measures are not compatible with each other is unlikely to develop mathematical theory. R. M. Haynes is lecturer in environmental sciences, Unioersity of East Anglia. 0 1978 Ohio State University Press 0016-7363/78/0778-0288$00.50/0 GEOGRAPHICAL ANALYSIS, vol. X, no. 3 (July 1978)

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