A recent experiment has provided clear evidence for a large maximum in the adsorption just below the critical micelle concentration of the surfactant hexadecyl trimethyl ammonium bromide (C16TAB) to the surface of sapphire. This observation is interesting as it is expected that when micelles are present the activity in solution is approximately constant and a plateau in absorption is expected. No minimum was observed in surface tension at the air/solution interface of solutions of the surfactant. This proposal seeks to provide an explanation of this phenomenon by studying systematically the effects of pH and added salt. The new data will allow sensitive tests of new models of adsorption that depend on ionic asociation and surface potential close to the critical micelle concentration.