A simple version of the linear hypervertex approximation (LHA) is used
to estimate the location of ferroelectric transitions in dipolar syst
ems. The well known result of the mean-spherical approximation is used
to develop an explicit expression for the core parameter that appears
in our mean-field theory of dipolar systems (J. S. Hoye and G. Stell,
1976, J, chem. Phys., 64, 1952). The full self-consistent version of
the LHA, not as yet assessed numerically, promises to be of higher qua
ntitative accuracy. For the comparatively low values of the dielectric
constant that characterize real molecular dipolar fluids, the LHA may
well be the best analytic theory currently available for that quantit
y.