Just this morning I was reflecting on the incantatory lines at the heart of the Ring verse:
One Ring to rule them all, one ring to find them
One Ring to bring them all, and in the darkness bind them
The emphatically repeated 'them' refers as much to the bearers of the other Rings of Power as it does to the Rings themselves. The intent to enslave the bearers was imperfectly realized of course, except in the case of Men. It occurs to me, however, that these verses also reflect the relations of the three agents of the eucatastrophe at Mt Doom, Frodo, Gollum, and Sam, all of whom of course are Ringbearers. The Ring brought them all together and bound them in the literal darkness of Mordor. Frodo 'wouldn't have got far without Sam' (TT 4.viii.712) and 'but for [Gollum]' Frodo 'could not have destroyed the Ring' (RK 6.iii.947). Frodo, however, 'was meant to have the Ring' as much as Bilbo had been (FR 1.ii.55), but it was not the maker of the Ring who intended this.
'[T]here was something else at work', as Gandalf tells Frodo. That 'something' read the Ring verse ironically, in a sense no one else grasped, much like the words that in truth prophesied the Witch-king's death rather than his invulnerability. Just as Éowyn, Merry, and the barrow-blade were brought together as if by chance to belie the obvious meaning of 'not by the hand of man shall he fall' (RK 5.vi.840; App. A 1051), so too, the coming together of Frodo, Gollum, and Sam at Mt Doom reveals new meaning in the Ring verse.
It is a new meaning such as Eru prophesied to Melkor before the world was made (Silm. 17) :
'.... And thou, Melkor, shalt see that no theme may be played that hath not its uttermost source in me, nor can any alter the music in my despite. For he that attempteth this shall prove but mine instrument in the devising of things more wonderful, which he himself hath not imagined.'
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*The use of this word here should not be taken to imply that Sauron was ever a mentsh to anyone, anywhere, at any time.