In Elvish cosmology, the World of Arda was surmounted and enclosed by a region named Ilmen or Tarmenel, the highest of the 'airs', within which the stars were set and the Sun and Moon followed their courses. This Over-heaven separated the World from the Outer Void, and corresponds with the medieval idea of a 'Firmament' that held the stars in an arc above the World.
It should be noted that this idea of a Firmament is only mentioned once, and then only in a metaphorical sense (the final chord of the Music of the Ainur was 'deeper than the Abyss, higher than the Firmament', according to the Ainulindalë). This makes it difficult to identify the intended meaning with certainty, but the similarity of the concept the Elves' notion of Ilmen is striking, and unlikely to be coincidental.
The English word 'firmament' derives from Biblical Latin firmamentum, itself an indirect translation of Hebrew raqia. The exact meaning of the Hebrew original is not entirely clear, but it seems to refer to something that has been fashioned to spread out (as for example through the beating thin of a sheet of metal). Tolkien's usage takes this derivation literally: his Firmament is an actual dome separating the World from the Outer Void.
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