Heat capacity measurements of the liquid helium lambda transition in c
onfined geometries have long been in disagreement with scaling theorie
s of second order phase transitions. We present measurements of a 19 m
icron film which extend the results of Chen and Gasparini (CG) to near
macroscopic size. We find that the new data as well as most of the CG
data are in reasonable agreement with recent renormalization group th
eory calculations.