Heat Capacity of Helium Confined to 8-μm Cylinders near the $\lambda$ Point

We report the results of heat capacity measurements on helium confined in 8-μm diameter cylinders in the temperature region spanning the $\lambda$ point. The data allow improved tests of the emerging theory of finite size phenomena and crossover to lower-dimensional states. In contrast to earlier work with much smaller holes, we find good agreement with scaling using exponents derived by renormalization methods. We also find reasonable agreement with more detailed calculations of crossover behavior based on explicit inclusion of boundary conditions.