The Round World Version is an alternative creation myth to the version of J.R.R. Tolkien's legendarium as it appears in The Silmarillion and The Lord of the Rings. In that version, the Earth was created flat and was changed to round as a cataclysmic event during the Second Age in order to prevent direct access by Men to Valinor, home of the immortals. In the Round World Version, the Earth is created spherical from the beginning.
Tolkien abandoned the Round World Version before completion of The Lord of the Rings but later regretted this decision. He felt that postulating an ancient flat world detracted from the believability of his writings. He planned a new round world version, but only got as far as an outline. He continued to redraft his published works to make them compatible with a round world version for most of the rest of his life. His son Christopher, editing The Silmarillion which he published after Tolkien's death, considered adjusting the text to comply with Tolkien's wish to return to the Round World Version, but decided against it, not least because the story of the submerging of Númenor relies intrinsically on the Flat World cosmology.
History
Tolkien gives the fullest account of the creation myth in the Ainulindalë ("Music of the Ainur"). He wrote the original version in the 1930s, calling it the "Flat World Version" or later the "Old Flat World Version" after he had created a new flat world version. In 1946 he wrote the "Round World Version", intending this to be the published version. Tolkien sent both the "Old Flat World Version" and the "Round World Version" to Katherine Farrer (wife of the theologian Austin Farrer) for review in 1948. Farrer replied to him in October strongly supporting the Flat World Version – "The hope of Heaven is the only thing which makes modern astronomy tolerable..." Farrer seems to have influenced Tolkien to abandon the Round World Version, which he did before completing The Lord of the Rings, or even starting its last volume, The Return of the King. Tolkien created a new manuscript from a heavily edited Old Flat World Version. He then produced a final polished version with illuminated capitals.
No version of the Ainulindalë was published during Tolkien's lifetime, but a heavily edited version later formed the first chapter of the 1977 The Silmarillion edited by Tolkien's son Christopher. The earliest version (not named Ainulindalë) was published in 1983 in The Book of Lost Tales volume 1. The Old Flat World Version was included in the 1987 The Lost Road and Other Writings. Both the Round World Version and the New Flat World Version were included in the 1993 Morgoth's Ring. The latter is a more faithful reproduction of Tolkien's manuscript than the version in The Silmarillion.
Tolkien also wrote a Round World Version of the Akallabêth ("The Downfall of Númenor"), possibly in 1948 to match the Ainulindalë Round World Version. This is an Atlantis-like story of the destruction of the island of Númenor, brought about by their deception by Sauron. This geographic change is part of the transition from flat to round world. Like Ainulindalë, Akallabêth was not published during Tolkien's lifetime, but it was included in The Silmarillion.
As late as 1966 Tolkien was still attempting to make the Round World Version work across his body of work. In The Hobbit he has the Wood-elves lingering in the twilight of the Sun (Round World) instead of lingering in the twilight before the raising of the Sun (Flat World).
Tolkien's dilemma
An internal problem: impossible to the Númenóreans
According to the lawyer and author on Tolkien Douglas Kane, the fundamental problem Tolkien had with the Flat World Version was that the Númenóreans, the ancestors of Men, were the means by which the legends of the earliest days were transmitted to later generations. Tolkien believed that the Númenóreans would understand that a flat Earth was impossible.
An external problem: incredible to the ordinary reader
The Tolkien scholar John D. Rateliff takes a different view of the problem, writing that Tolkien had changed his mind about what an ordinary reader would be able to believe, or the extent to which that reader might be able to suspend their disbelief, in the face of a medieval cosmology. Rateliff wrote that