  We investigate theoretically the properties of a trapped gas of fermionic
atoms in both the normal and the superfluid phases. Our analysis, which
accounts for the shell structure of the normal phase spectrum, identifies two
observables which are sensitive to the presence of the superfluid: the response
of the gas to a modulation of the trapping frequency, and the heat capacity.
Our results are discussed in the context of experiments on trapped Fermi gases.
