Hmm. How to reconcile what would seem at first glance to be an
error on the color of the Smaug-killing arrow? Now what would
Tolkien do...
Wait! The arrow was of course black, but after being eventually
retrieved from The Long Lake it remained forever coated with Smaug's
blood and was therefore renamed the "Red Arrow."
Fun Fact: In the $$$ successful Peter Jackson 2-part movie of The
Hobbit it is Legolas who retrieves and renames the arrow.
