  We use the Rayleigh-Schr\"odinger perturbation theory to calculate the
corrections to the adiabatic geometric phase due to a perturbation of the
Hamiltonian. We show that these corrections are at least of second order in the
perturbation parameter. As an application of our general results we address the
problem of the adiabatic geometric phase for a one-dimensional particle which
is confined to an infinite square well with moving walls.
