Believe it or not, a colleague just knocked on my door to ask (for a talk she's writing) what the name of the body of water is where Déagol finds the Ring. I'm at work and without my LOTR, so I thought I'd ask the question here. Thanks!
The Gladden river, a tributary of the Anduin River.
"Spirits in the shape of hawks and eagles flew ever to and from his halls; and their eyes could see to the depths of the seas, and pierce the hidden caverns beneath the world."
Thank you both very much: and the Academy thanks you!
She's a wonderful person and a brilliant scholar, my friend across the hall who needed this bit of info, and she'll be presenting this paper on special effects in LOTR (and elsewhere) in Chicago.