A single lipid molecular bilayer of 17 or 18 carbon chain phosphocholines, floating in water near a flat wall, is prepared in the bilayer
gel phase and then heated to the fluid phase. Its structure (electron density profile) and height fluctuations are determined by using x-ray reflectivity and nonspecular scattering. By fitting the offspecular signal to that calculated for a two-dimensional membrane using a Helfrich Hamiltonian, we determine the three main physical quantities that govern the bilayer height fluctuations: The wall attraction potential is unexpectedly low; the surface tension, roughly independent on chain length and temperature, is moderate (10^-4 J.m^2) but large enough to dominate the intermediate range of the fluctuation spectrum; and the bending modulus abruptly decreases by an order-of-magnitude from 10^-18 J to 10^-19 J at the bilayer gel-to-fluid transition.