Measurements are presented of the long time-averaged transfer function (or mutual coherence function) of the atmosphere, taken at Mauna Kea Observatory, Hawaii, using a coherence interferometer. Over the 10 nights of observation the seeing was variable, ranging from typical widths of the transfer function at the 25 per cent level of approximately 0.23 cycles/arcsec (2.5 cm in the pupil) to approximately 1.00 cycles/arcsec (11.0 cm in the pupil). The latter values correspond to sub-arcsec seeing. The variation with zenith angle and the form of the atmospheric transfer function were briefly investigated.