  It is shown that the M$^{2+}$ ion yield in the double photoionization of the
aromatic hydrocarbons, pyrene and coronene, can be expressed as a superposition
of a contribution from a resonance involving carbon atoms on the perimeter and
coherent contributions from carbon atoms inside the perimeter. In the case of
pyrene, the two interior atoms are associated with a resonance peak at 10 eV
and linear behavior above 75 eV. The resonance peak is an optically excited
state of the interior carbon pair. The linear behavior arises from the coherent
emission of two electrons with equal energy and opposite momenta, as occurs in
pyrrole. Coronene has a low energy peak along with two pairing resonances,
however, the linear region as in the case of pyrene is absent. The low energy
resonance is associated with the atoms on the perimeter and the high energy
resonance is associated with the hexagonal array of six carbon atoms at the
center of the molecule. It is proposed that the quasi-independence of the
contributions from the perimeter and interior atoms is related to H\"uckel's
Rule for the stability of aromatic hydrocarbons.
