From the well-recognized equivalence of the Williams-Landel-Ferry (WLF) equation and the Vogel-Tammann-Fulcher (VTF) equation, tau = tau(0) exp (B/[T - T-0]), we shall show that the parameter C-1 in the former is just the number of orders of magnitude between the relaxation time at the chosen reference temperature and the pre-exponent of the VTF equation. Thus C-1(g) = log(tau(g)/tau(0)) (a relation which is not found in the present polymer literature), measures the gap between the two characteristic time scales of the polymer liquid, microscopic and alpha-relaxation, at the glass transition temperature. For systems which obey these two equations over wide temperature ranges, tau(0) is consistent with a quasilattice vibration period in accord with theoretical derivations of the VTF equation and also with the microscopic process of mode coupling theory. Thus for such systems, C-1(g) is obliged to have the value 16-17 (depending on how T-g is defined), while C-2(g) scaled by T-g will reflect the non-Arrhenius character, i.e. fragility, of the system. In fact when C-1(g) has the physical value of 16-17, then (1 - C-2(g)/T-g), which varies between 0 and unity, conveniently gives the ’fragility’ of the polymer within the ’strong/fragile’ classification scheme. This is useful because it permits prediction from the WLF parameters of other properties such as physical ageing behaviour through the now-established correlation of fragility with other canonical characteristics of glassforming behaviour. Where the best fit C-1(g) is not 17 +/- 2, the corresponding best fit tau(0) must be unphysical, and then the range of relaxation times for which the VTF or WLF equations are valid with a single parameter set will be limited, and the predictions of other properties based on that parameter set will be unreliable.