We carry out the calculation of the surface tension for a model electrolyte
to first order in a cumulant expansion about a free field theory equivalent to
the Debye-H\"uckel approximation. In contrast with previous calculations, the
surface tension is calculated directly without recourse to integrating
thermodynamic relations. The system considered is a monovalent electrolyte with
a region at the interface, of width h, from which the ionic species are
excluded. In the case where the external dielectric constant epsilon_0 is
smaller than the electrolyte solution's dielectric constant epsilon we show
that the calculation at this order can be fully regularized. In the case where
h is taken to be zero the Onsager-Samaras limiting law for the excess surface
tension of dilute electrolyte solutions is recovered, with corrections coming
from a non-zero value of epsilon_0/epsilon.Comment: LaTeX, 14 pages, 3 figures, 1 tabl