The foundational motivations behind βVS and βPS offer pivotal context. Van Slyke (3) aimed to assess how additional H+ would alter pH of a test-tube solution.
From his perspective, the quantity, but not the source, of added H+ was essential. This led him to use Δ[AMINUS SIGN ] or Δ[HCO3MINUS SIGN ] as proxies for the H+ added during strong acid or CO2 titration.
Conversely, Stewart (4) aimed to understand how alterations in the three independent variables he identified [strong ion difference (SID), partial pressure of CO2 (PCO2), and total nonvolatile weak acid (Atot)] would impact plasma [H+] and pH in vivo.