Actually, the Eldar had hordes of children in Middle-earth. The descendants of Finwe are an extremely poor example of Elvish fertility. The numbers of the Noldor were constantly being increased according to Tolkien (in the interludes between the devastations of war).

: For all their wisdom and power Celeborn and Galadriel produced
: only one child, likewise Thingol and Melian. Gil-galad none.
: Fingon none. Of the seven sons of Fëanor, only three even
: married, let alone produced children.

Elrond and Celebrian had three children.

: On the basis of a sperm count perhaps the Eldar were not
: impotent, but on the basis of a child count they weren't far
: from it. And, I am suggesting, that the onset of 'fading'
: exacerbated this problem.

It could not have been a problem while the Three Rings were effective, however. Their power to work against fading was in force throughout the Second and Third Ages.

: Mithrellas's children were (like Arwen's) sired by a Man, not
: an Elda.

I don't see any reason why male Elves would be affected more than female Elves.

: : Legolas may have been born in the Third Age as well. He is
: : not mentioned by Tolkien in the passages discussing
: : Thranduil and his father Oropher.

: We don't know when Legolas was born. Although, because he
: recognized the Balrog of Moria for what it was, I tend to think
: it may not have been the first he had seen. That pushes his
: birth back into, at least, the Second Age.

I don't see how it pushes his birth into the Second Age. The stories of the First Age were still being told in the Third Age. Legolas need only have been properly educated to recognize a Balrog -- and that he appears to have been.

In order to have seen any other Balrogs, however, Legolas would have to have been born in the First Age. We hear of no other Balrogs in the Second Age. A First Age birth for Legolas is not really feasible -- he should have marched with Thranduil in the War of the Last Alliance, and Tolkien doesn't mention that at all. By the same token, unless he was born very late in the Second Age (so that he would be too young to go to war), a Second Age birth doesn't really work either.

Legolas was at least 500 years old, if his words about the leaves falling 500 times in Mirkwood since the Rohirrim left their northern lands are meant to imply that he had actually seen them fall 500 times). That is all we really know concerning his age. He does refer to his companions as "children" at one point and he speaks of having watched acorns grow to old age, but neither statement implies an age greater than 3,000 years.

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