= 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>:
$$
2\pi r\gamma\cos\theta=(\rho_l-\rho_g)g\pi r^2h,
\qquad
\boxed{h=\frac{2\gamma\cos\theta}{(\rho_l-\rho_g)gr}.}
$$
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.
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