  In this third paper of the series, which started with [N. P. Bailey et al.,
J. Chem. Phys. 129, 184507 and 184508 (2008)], we continue the development of
the theoretical understanding of strongly correlating liquids - those whose
instantaneous potential energy and virial are strongly correlated in their
thermal equilibrium fluctuations at constant volume. The existence of such
liquids was detailed in previous work which identified them, based on computer
simulations, as a large class of liquids, including van der Waals liquids but
not, e.g., hydrogen-bonded liquids. We here discuss the following: (1) The
scaling properties of inverse power-law and extended inverse power-law
potentials (the latter include a linear term which "hides" the approximate
scale invariance); (2) results from computer simulations of molecular models
concerning out-of-equilibrium conditions; (3) ensemble dependence of the virial
/ potential energy correlation coefficient; (4) connection to the Gruneisen
parameter; (5) interpretation of strong correlations in terms of the
energy-bond formalism.
