This paper discusses in detail the speculative suggestion that the influx of extraterrestrial hydrogen to the Earth's atmosphere constitutes a significant variable source of atmospheric water vapour (sometimes called ‘solar rain’ or ‘extraterrestrial rain’) which can be invoked to explain Sun-weather relationships. The continual influx of solar-flare protons with energies in the range 1–100 MeV, which penetrate down to the mesosphere or upper stratosphere, makes a negligible contribution to the normal water vapour concentration at these altitudes. During the most intense solar-proton event yet recorded (August 1972) this solar-flare contribution to atmospheric humidity amounted to no more than 2 parts in 10 9. Moreover, the long-term average influx of solar-flare protons, or galactic-cosmic-ray protons, has been totally inadequate to produce an appreciable change in the concentration of atmospheric water vapour. The continuous influx at the magnetospheric clefts of solar-wind protons with a mean energy of about 1 keV, which cannot penetrate below 150 km and hence cannot form water vapour directly, only constitutes a highly-localized reduction, or reversal, of the global efflux of hydrogen atoms from the Earth's atmosphere: a similar conclusion holds for auroral protons (∼10keV). At the present time the influx of interstellar hydrogen atoms is trivial compared with the global efflux of terrestrial hydrogen atoms. However, the influx of interstellar hydrogen could be greater than the efflux of terrestrial hydrogen if the Solar System encountered a dense interstellar cloud, but the atmospheric implications of such a large influx of interstellar hydrogen require further consideration. Apart from this one possible exception, which could only be advanced as a tentative explanation for very long-term (∼10 6y) changes of climate, the hypothesis that Sun-weather relationships can be attributed to atmospheric water vapour of extraterrestrial origin is untenable.