The phase space multi-histogram method is a new technique to study phase transitions in hard particle systems. The method constrains the phase space using a Monte Carlo approach by smoothly varying a potential between the ideal gas and the hard particle limit. Using a small sphere system, we give an example of computing chemical potential at the liquid state. However, we find that the method fails for a dense sphere system at the coexisting liquid-solid state. We conclude that the method is appropriate for dilute hard particle systems, but it fails when the volume fraction of the system is too high.