Experimental data on the dependence of the surface tension of water on the adsorption of n-alkanes (methane to butane) from the vapor phase over a range of temperatures are re-interpreted to obtain improved estimates of the two-dimensional second virial coefficients for comparison with calculations based on the Lennard-Jones (L-J) formalism in two dimensions. The analysis includes the fugacity corrections for the alkane gases and takes the L-J parameters as known for the three-dimensional gases. The new L-J calculations use a closed-form analytical solution of the basic equation for the two-dimensional second virial coefficient. These older published computations are correct and, as expected, are in complete agreement with the results by numerical integration with modern computer software. Together with estimates of the standard entropies of adsorption, the results indicate that no significant structuring of the surface water molecules occurs upon adsorption of the alkanes. The two-dimensional second virial coefficients are in fair accord with the L-J predictions, except for butane. The reduction of the attractive component of the potentials of mean force between physisorbed molecules arising from the frequency-dependent interaction with their electrostatic images in the bulk aqueous phase, as described by McLachlan (Mol. Phys. 1964, 7, 381), or from the polarization of the adsorbates by a surface electric field (surface field polarization) is minor for methane, ethane, and propane. For butane, these effects may be significant but possible changes in conformation upon adsorption may weaken the validity of the gas-phase L-J parameters in estimating the two-dimensional virial coefficients for this alkane.