Measurements of the geocoronal absorption at the center of the solar Lyman-&agr; line, performed by the University of Paris instrument on board OSO-5 are compared to aspherical models. The deduced values of the minimum hydrogen density were analysed over periods of one year, between 1969 and 1972. They indicate a systematic departure up to 40% from exospheric models. This feature corresponds to a dayside sub-solar hydrogen bulge characterized by a 25% decrease of the hydrogen density at 50¿ away (northward or southward) from the solar direction. This bulge could be due to solar direction related anisotropies of the hydrogen production, diffusion, transport and loss mechanisms which are neglected in the exospheric theories.