Derivation of Jurin's law revisited

The capillary rise/fall of a liquid within a thin capillary tube is described by the well-established Jurin's law. The liquid reaches an equilibrium height/depth as the capillary pressure is balanced by the hydrostatic pressure. When the adhesion force at the three-phase contact line is counteracted by the liquid weight, the liquid column also stabilizes. Both descriptions evidently coincide although they are based on different physical quantities. Most undergraduate textbooks do not mention why these two routes draw two identical results; besides, the proofs become conceptually incorrect. We review the underlying ideas in Jurin's law and the two possible derivations.