Republication of: A homogeneous universe of constant mass and increasing radius accounting for the radial velocity of extra-galactic nebulae

This is an English translation of a paper by Georges LemaItre, first published in French in 1927, in which the author, having re-discovered and generalised the Friedmann models, for the first time related them to the then-already-available observations of expansion of the Universe. The translation published in 1931 in MNRAS was not perfectly faithful to the original text-it was updated. As it turned out very recently, the updates were done by LemaItre himself, but the discrepancies between the two texts caused a temporary stir among historians. Our translation follows the 1927 version exactly. The paper has been selected by the Editors of General Relativity and Gravitation for republication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by Jean-Pierre Luminet that, among other things, lists and explains the differences between the 1927 and 1931 versions.