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We used the University of New South Wales Infrared Fabry-Perot (UNSWIRF) to investigate the photodissociation region (PDR) associated with the `elephant trunk' features in the M16 H ii region (the Eagle nebula). Images were made in the H2 1--0 S(1) and 2--1 S(1) lines at 2.122 and 2.248 μ m, respectively, and in the H i Br γ line at 2.166 μ m. The trunk-like features have an average H2 number density of ∼ 104 cm-3 and are irradiated by a far-UV field ∼104× the ambient interstellar value. The H2 intensity profile across the trunks is consistent with a simple model in which cylindrical columns of gas are illuminated externally, primarily by a direct component (the stars of NGC 6611), with an additional contribution from an isotropic component (scattered light). We find that most of the H2 emission from the source is consistent with purely fluorescent excitation, however a significant fraction of the H2 emission (∼ 25 per cent) from the northernmost column shows evidence for `collisional fluorescence', i.e. redistribution of H2 level populations through collisions. This emission is confined to clumps up to ∼ 0.01 pc in diameter, with densities ≥ 105 cm-3, and perhaps > 106 cm-3, filling at most a few per cent of the volume of the trunks. The line intensities and ratios are consistent with steady-state and not time-dependent PDR models.