  This investigation follows up the suggestion that the equation of state for
superconducting cosmic strings provided by Witten's prototype biscalar field
model can be well represented by an effective Lagrangian of simple logarithmic
form depending on only 3 independent parameters. The numerical work described
here confirms the validity of this approximation, and initiates the evaluation
of the 3 required parameters, as functions of the masses and other parameters
specifying the underlying U(1) x U(1) scalar field model in the limit for which
the relevant gauge coupling constants are small.In this limit, subject to
calibration of the relevant length and mass scales, the scalar field model is
characterised by just 3 dimensionless ratios which (in order to provide
conducting strings) must be subject to three inequalities (of which two have
obvious analytic expressions). It is found here that when all three of these
inequalities are satisfied by a reasonably large margin, there is a simple
empirical formula that can be used to provide a fairly accurate prescription
for the algebraic dependence on these 3 dimensionless ratios of the 3
parameters required for the logarithmic equation of state.
