Excited state bond orders calculated in the previous paper (McCoy and Ross 1962) are used in a necessarily approximate attempt to predict the locations of intersections between potential energy surfaces for all the lower excited states of benzene, naphthalene, azulene, and anthracene, and thus to investigate the mechanism of degradation of electronic excitation energy. It is concluded that excited states commonly, but not invariably, intersect in such a way that there is no barrier to passage from the zero-point level of one state to some state below it. Quite often, however, tunnelling, as suggested by Robinson (1961), is necessary to effect the passage. Diagrams are presented showing the preferred routes for descent through the singlet and triplet states. The radiative properties of the compounds considered are then successfully correlated with the distances through which tunnelling needs to take place, and an approximate empirical relationship emerges in which the tunnelling rate (multiplied by 106 if there is a spin change) decreases exponentially with barrier width. The mechanism of tunnelling is briefly discussed.