"It is known that very distant nebulae, probably galactic systems like our own, show remarkably high receding velocities whose magnitude increases with the distance. This curious phenomenon promises to provide some important clues for the future development of our cosmological views. It maybe of advantage, therefore, to point out some of the principal facts which any cosmological theory will have to account for. Then a brief discussion will be given of different theoretical suggestions related to the above effect. Finally, a new effect of masses upon light will be suggested which is a sort of gravitational analogue of the Compton effect."