The Second Quantification of Physics

Historians traditionally trace the quantification of physics to the period 1780–1830, during which time many quantitative physical concepts, such as latent heat or electrical capacity, were invented and operationalized. I identify and characterize a subsequent “Second Quantification” during the remainder of the nineteenth century that distinguishes itself from the traditional one along three key lines: (1) Substantive conceptual, physico-mathematical and operational issues posed by the historical definition and realization of “absolute” units, or the integration of measuring scales. (2) Development of novel algebraic practices for representing physical quantities and the results of measurement in experimental physics. (3) Pursuit of a widespread program of theoretical and experimental implementation by William Thomson and his mathematically-minded allies across epistemic discontinuities between different communities of physical practice, e.g. telegraphic engineers. I cement the historical reality of the Second Quantification by briefly explaining how some of its facets are readily discernible in modern metrology.