Interpreting unit symbols in the language of science

This paper compares Maxwell’s description of unit systems with the modern interpretation based on abstract physical quantities. In doing so, it identifies the source of certain difficulties in interpreting unit notation. The main finding is that unit symbols in the modern interpretation do not always denote quantities of the same kind as the measurand; rather, they denote metrological references that exhibit the same scaling behaviour under a change of units as values for the measurand. A second finding is that the dimension of a quantity within a unit system represents the measure of one reference quantity in terms of another (i.e., the ratio of reference quantities). The individual quantities are not specified but must be of the same quantity kind. Dimensional terms, such as $M$, $L$, and $T$, may therefore be treated as numeric variables and can be manipulated and simplified according to the rules of arithmetic.