This paper considers the effect of a perturbed wall in regard to the classical Benard convection problem in which the lower rigid surface is of the form $z={\epsilon }^{2}g\left(s\right)$, s=ε r, in axisymmetric cylindrical polar coordinates (r,ϕ,z). The boundary conditions at s=0 for the linear amplitude equation are found and it is shown that these conditions are different from those which apply to the nonlinear problem investigated by Brown and Stewartson [1], representing the distribution of convection cells near the center....