A compressible continuum model for the limiting electrical conductivity, Lambda(0), is presented. Solvent density as a function of the radial distance r from a solvated, spherical ion is calculated via the compressible continuum model developed by Wood and co-vv co-workers. The viscosity of the solvent around an ion is calculated as a sum of electrostrictive and electroviscous components which are also taken as functions of r. The viscosity change due to electrostriction is obtained with the viscosity equation for water mu[rho(r),T]. Hubbard＇s expression for the electroviscous effect in an incompressible solvent is adapted to calculate the viscosity enhancement arising from the presence of an electric field at constant local solvent density. With only one adjustable parameter, this model reproduces, within experimental uncertainty, the experimental infinite dilution equivalent conductance data for aqueous NaCl from 140 to 800 degrees C at densities greater than 0.5 g cm(-3). Recent measurements of the Debye relaxation time allow this parameter to be eliminated with very small changes in the prediction. Below densities of 0.5 g cm(-3), the calculated values are too high by as much as 30%. Far 140-800 degrees C and 1.0 > rho(0) > 0.5 g cm(-3) the model correctly predicts that (1) Walden＇s rule is not obeyed, (2) Lambda(0) varies linearly with density, (3) Lambda(0) is a very weak function of temperature at constant density, and (4) for small ions (r < 2 (A) over cap) Lambda(0) is a very weak function of ionic radius. Electrostriction and electroviscosity effects an shown to be very important in this region.