On Young's (1805) equation and Finn's (2006) ‘counterexample’

In 1805, Thomas Young considered the balance of forces acting on the contact line formed at the intersection of a liquid-fluid interface with a solid surface and introduced a macroscopic concept of “contact angle”. From Young's reasoning it follows that in equilibrium the contact angle is a material property of the liquid/fluid/solid system independent of a particular configuration. Two centuries later, Robert Finn considered a model problem which seems to suggest that there is a fundamental flaw in Young's force diagram and the reasoning behind it. In the present note, we show that the apparent paradox in Finn's model problem disappears once Young's original concepts are applied in a correct way.