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Recent studies have shown that there exist precise connections (or covariance relations) between adsorption properties for substrates with different shapes. This occurs, for example, when a fluid is adsorbed in a linear wedge. In this case, the influence of the geometry is to shift effectively the contact angle from theta to theta−alfa, where alfa is the tilt angle. Despite the fact that these relations are obeyed both at mean-field level and also exactly in two dimensions (when fluctuation effects dominate), their fundamental origin has been unclear. Here, we show that they can be traced to a symmetry present in interfacial Hamiltonian models, and further relate this to surface thermodynamics and the nonlocal nature of interfacial interactions in systems with short-ranged forces.