We have measured the heat capacity of He-4 films adsorbed in Vycor gla
ss for temperatures down to 10 mK and coverages close to the critical
coverage for the onset of superfluidity at T = 0. The data show that t
he critical coverage corresponds to a mobility edge in the chemical po
tential, below which the He-4 film is an insulator with a gap. We find
no evidence for the existence of a gapless Bose glass phase.