  We analyze, without resort to any model field-mixing scheme, the leading
temperature-dependent term in the "diameter" of the coexistence curve
asymptotically close to the vapor-liquid critical point. For this purpose, we
use a simple non-parametric equation of state which we develop by meeting
several general requirements. Namely, we require that the desired equation (1)
lead to correct asymptotic behavior for a limited number of the fluid's
parameters along selected thermodynamic paths, (2) reveal a Van der Waals loop
below the critical point, and (3) be consistent with a rigorous definition of
the isothermal compressibility in the critical region. For the temperature
interval in question, the proposed equation approximates experimental data with
an accuracy comparable to those given by Schofield's parametric equation and by
other authors' equations. The desired term is obtained by applying the Maxwell
rule to the equation and can be represented as D_{2 \beta} | \tau |^{2 \beta},
where | \tau | = | T - T_{c} | / T_{c}, and \beta is the critical exponent for
the order parameter. The amplitude D_{2 \beta} is determined explicitly for the
volume-temperature and entropy-temperature planes.
