  We introduce an alternative definition of the relative height h^\kappa(x) of
a one-dimensional fluctuating interface indexed by a continuously varying real
paramater 0 \leq \kappa \leq 1. It interpolates between the height relative to
the initial value (i.e. in x=0) when \kappa = 0 and the height relative to the
spatially averaged height for \kappa = 1. We compute exactly the distribution
P^\kappa(h_m,L) of the maximum h_m of these relative heights for systems of
finite size L and periodic boundary conditions. One finds that it takes the
scaling form P^\kappa(h_m,L) = L^{-1/2} f^\kappa (h_m L^{-1/2}) where the
scaling function f^\kappa(x) interpolates between the Rayleigh distribution for
\kappa=0 and the Airy distribution for \kappa=1, the latter being the
probability distribution of the area under a Brownian excursion over the unit
interval. For arbitrary \kappa, one finds that it is related to, albeit
different from, the distribution of the area restricted to the interval [0,
\kappa] under a Brownian excursion over the unit interval.
