Specific heat of helium confined to cylinders near the lambda point

We report measurements of the specific heat of helium-4 confined to Very un iform 8-micron diameter cylinders and to 0.26-micron diameter Anopore cylin ders in the temperature region near the lambda point. The data allow improv ed tests of the emerging theory of finite size phenomena and cross-over to lower dimensional states. We find generally good agreement with scaling usi ng exponents derived by renormalization methods. We also find reasonable ag reement with more detailed numerical calculations of cross-over behavior wi th explicit inclusion of boundary conditions. However, in the region near t he peak, the 8-micron data do not scale well relative to Anopore. We also c ompare the results With previous work on 1-dimensional systems.