= Solution
The liquid does not wet the glass because $\cos140^\circ<0$. The <liquid meniscus> is convex, with the capillary mercury level depressed below the reservoir. Balancing vertical surface-tension force against the hydrostatic column gives <Jurin's law>, using the inner radius $r=0.5\,\mathrm{mm}$:
$$
\boxed{h=\frac{2\gamma\cos\theta}{\rho gr}=\frac{2(0.436)\cos140^\circ}{(1.35\times10^4)(9.81)(5\times10^{-4})}=-1.01\times10^{-2}\,\mathrm m.}
$$
Thus the depression is approximately \b[$10.1\,\mathrm{mm}$]. The simple height law neglects small meniscus-volume corrections. Mercury's high <surface tension> reflects strong <metallic bonding>, not merely dispersion between weakly interacting molecular units.
\Image[/past-exam-of-the-quantum-condensed-matter-course-of-the-university-of-cambridge/2007-mercury-capillary.png]
{title=Nonwetting mercury is depressed in a glass capillary and has a convex meniscus}
{description=Original schematic with the tube width enlarged relative to the vertical scale. The arrow marks the approximate hydrostatic depression; the drawn meniscus shape is schematic.}
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