Specific heat of helium confined to a 57-mu m planar geometry near the lambda point

We report measurements of the specific heat of liquid helium confined to 57 -mu m planar. gaps; extending to within a few nanokelvin of the bulk lambda transition. The data are in fair agreement with Monte Carlo estimates for finite-size effects and with renormalization-group-theory predictions above the transition. Far from the transition, we find surface specific heat exp onents, alpha(s) = 0.64 +/- 0.05 below, and 0.65 +/- 0.2 above, which compa re well with the prediction of 0.658. Comparison with other recent data on small Length soles shows some areas of agreement.