Scaling of the specific heat of confined helium near tλ

We have measured the specific heat of helium near the superfluid transition for films up to 56 thick and for samples confined to a cylindrical geometry of up to 2000 in diameter. The dependence of the shift in the transition temperature on size and the growth of the specific-heat maximum do not yield exponents as expected from simple scaling arguments. The data up to t|1-TTλ|=10-2 scale according to a form suggested by Fisher, but with an exponent 1θ=0.54±0.02.