 Solution

A clean narrow tube dipped in a wetting liquid displays a curved meniscus and a rise above the external free surface. With a nonwetting liquid, such as Mercury against clean glass under the usual conditions, there is a convex meniscus and a depression. The material pair and surface cleanliness matter; small diameter alone does not determine the sign.

For a circular tube of radius $r$, surface tension $\gamma$, and equilibrium contact angle $\theta$ measured through the liquid, the vertical force at the contact line is $2\pi r\gamma \cos \theta$. Neglecting the small meniscus-volume correction, its balance with the excess column's gravitational weight gives Jurin's law:Thus the signed height is inversely proportional to radius for a fixed liquid, wall, temperature and contact angle. Increasing the tube length beyond the required column does not increase the equilibrium height. A short tube that cannot contain that column is a different boundary problem.

The same result follows from the Young–Laplace equation: a curved interface supports a capillary pressure difference, balanced by the hydrostatic head. Molecular interactions establish the surface tension and the preference for wetting the solid, encoded in the contact angle. The force balance does not require molecules to attract across the whole height of the column. To test the inverse-radius law, use tubes of several measured radii with the same surface preparation, and compare $hr$ after equilibrium; different cleaning or contact-angle hysteresis can otherwise imitate a failure of the radius law.