= Andrews's carbon dioxide experiment
{c}
The 1869 <The Bakerian Lecture: On the Continuity of the Gaseous and Liquid States of Matter by Thomas Andrews> describes dried <carbon dioxide> trapped above <mercury (element)> in a sealed <capillary tube>. A steel screw pressurized <water> in a strong <copper> tube; movable <mercury (element)> transmitted the load. A second <capillary tube> held air as a <pressure> gauge. Flowing <water> around the visible <capillary tubes> controlled <temperature>; a <thermometer> read the bath. A <cathetometer> read column positions, converted to <volume (thermodynamics)> readings using weighed-<mercury (element)> calibration.<The Bakerian Lecture: On the Continuity of the Gaseous and Liquid States of Matter by Thomas Andrews>[Andrews, pp. 576–578 and Plate LXIII, figures 3 and 5–7: sample preparation, screw, coupled capillaries, water jackets and optical readout]{ref}
Below the critical <temperature>, compression produced a visible <liquid>–<gas> boundary; above it, large density changes occurred without that boundary. Three trials gave $30.92\,{}^\circ\mathrm C$ as his critical <temperature>. Purity checks detected residual air; <mercury (element)> height corrections accounted for unequal <hydrostatic pressures>. He explicitly left air nonideality and pressure-induced tube-capacity corrections unresolved, so his air-gauge <pressures> were approximate. These readouts support a <liquid-gas critical point>; they do not measure a homogeneous unstable loop or establish universal quantitative accuracy of the later <Van der Waals equation>.<The Bakerian Lecture: On the Continuity of the Gaseous and Liquid States of Matter by Thomas Andrews>[Andrews, pp. 576, 578–580 and 583: residual air, approximate air-gauge pressure, hydrostatic corrections and three critical-temperature trials]{ref}
\Image[/andrews-carbon-dioxide-critical-apparatus.png]
{title=<Andrews's carbon dioxide experiment>: control, readout and the <liquid-gas critical point>}
{description=Original functional schematic, not a scale reconstruction. The <water> circuit transmits compression through <mercury (element)> to two samples; separate <temperature> jackets permit control of the sample and air gauge. The right panels distinguish a visible <liquid>–<gas> <liquid meniscus> from a single <thermodynamic phase>. Interpret alongside the experimental limitations above.}
A disappearing <liquid meniscus> by itself has more than one possible explanation: in ordinary subcritical condensation or evaporation, one <thermodynamic phase> can simply run out. The stronger critical-point inference combines <temperature> control, compression readings and the existence of a continuous route around the endpoint of the <phase coexistence curve>. On that route a dilute <gas> can become dense without crossing a two-phase boundary. This is what continuity of <liquid> and <gas> means; it does not remove their distinct equilibrium <number densities> below $T_c$.
In his 12 December 1910 Nobel lecture, <Johannes Diderik van der Waals> explained <gases> and <liquids> through the same moving <molecules>, with attraction and finite size modifying their <pressure>. He also rejected the idea that constant $a,b$ should give universal numerical agreement. His critical-volume discussion explicitly retained <derivatives> of a volume-dependent $b$: the familiar $v_c=3b$ follows only when those <derivatives> are neglected. Thus the elegant constant-parameter <Van der Waals critical point> is a model result whose limitations were already part of its author's account.<The Equation of State for Gases and Liquids by Johannes Diderik van der Waals>[The equation of state for gases and liquids, Nobel lecture delivered 12 December 1910, pp. 254–257: molecular continuity, constant-parameter caveat and critical-volume derivatives]{ref}
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