A method reported previously for obtaining the residual chemical poten
tial (the amount by which the chemical potential exceeds that for the
ideal fluid) based on the use of the Shing-Gubbins method in conjuncti
on with an estimation of the value of the chemical potential of a rela
ted hard core model is applied to very dense Lennard-Jones fluid syste
ms at two reduced temperatures (T = 1.2 and 1.0, where T* = kT/epsilo
n). Convergence to steady values is obtained economically. Results are
shown to be in good accord with previously reported determinations at
T = 1.2 up to reduced densities (rho* = rho sigma(3)) of 0.95. It is
shown that the limit of the range of the present method is probably p
approximate to 1.0.