On the History of Quantity Calculus and the International System

A brief presentation is given of the most important developments in the history of quantity calculus. Starting with the early introduction of the concept "physical quantity" by Maxwell in his work on electricity and magnetism, attention is focused in particular on the foundations of the calculus with physical quantities given by Wallot in the 1920s. For illustration and better understanding of the praxis of quantity calculus, special attention is paid to the three- and four-dimensional systems of physical quantities used for theoretical description in the fields of electricity and magnetism. Special emphasis is placed on understanding controversies and confusion caused by differences in interpretation of the concepts "quantity" and "unit" in physical language and in the mathematical description of physical phenomena. A short presentation is given of the further development of various studies on the algebraic structure and the axiomatic foundation of the calculus with physical quantities developed by Landolt, Stille, Fleischmann and others. Quantity calculus constituted the basis for obtaining consensus on the introduction of the International System of Units (SI) and allowed the formulation of international standards on definitions and symbols for quantities and units by the various international scientific and standardizing organizations.