λ transition in confined 4 He:ratio of surface specific heats above and below the bulk transition point

We calculate the ratio of the surface specific heats above and below the bulk $\ensuremath{\lambda}$ point for the superfluid transition in confined liquid ${}^{4}\mathrm{He}$ in a wafer geometry. Our calculation is valid for the first departure from thermodynamics. A comparison with presently known experimental results is shown.