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The relative spin level populations of the lowest $\pi \pi \ast$ triplet state have been measured for five aromatic hydrocarbons using a pulsed phosphorescence-microwave double resonance technique. Since the populations are sampled in a time which is short compared to spin-lattice or $T1\to S0$ relaxation times, they are proportional to the intersystem crossing transition probabilities to each spin level. It is found that 80-90 percent of the inter-system crossing occurs to the two levels having spin alignment in the two magnetic planes perpendicular to the molecular plane. Several theoretical treatments predict that these levels should be the least populated, since intersystem crossing to them is forbidden in first order perturbation theory. Because an out-of-plane distortion is required to account for our findings, we suggest that a second order out-of-plane vibronic coupling mechanism is responsible for intersystem crossing in planar aromatic hydrocarbons. The molecules studied are benzene, naphthalene, phenanthrene, coronene, and triphenylene.