Careless Singing Costs Lives
 

Nice version of it sung http://uk.youtube.com/watch?v=onC-hCcYtsg

My point is that should Gandalf really be singing about the star in Galadriel's right hand right in front of Wormtongue? Wormtongue would tell Saruman every word of the encounter and Saruman (clever bloke he is) would work out what the star was. And Sauron could probably garner the information from Saruman using the palantir. Some uncharacteristic foolishness from Gandalf brought about by his annoyance of Grima perhaps?

I've just realised Saruman could have already known where the Elven Ring was, but then wouldn't Sauron know where it was?

Well, Gandalf did say "in" not "on," so Wormtongue might not quite know what he was talking about. :)

But I doubt there was much question in Saruman's mind as to where the Three might be. As I recall, there's a statement, possibly in the Silmarillion (don't have the books on hand to check) that says the Wise (in whose numbers Saruman was counted) discerned before the end of the Third Age that one was with Elrond in Rivendell, another with Galadriel in Lorien, and the third possibly with Cirdan at the Havens. As the head of the White Council, Saruman would likely have had plenty of opportunity to figure this out. Saruman also had discerned that Gandalf had the third, likely before he became enmeshed with Sauron, as it was one of the roots of his jealousy toward Gandalf. So no surprise there. By the time Gandalf sang his little ditty (for which I also wrote a tune maybe 30 years ago), Saruman doubtless had a clear idea where the Three were located, but whether or not Sauron got that information from him... I wonder. I know Sauron attacked Lothlorien more than once, so he might have suspected a Ring was there, but I can't recall if there were similar attacks on Rivendell (I know, I should bestir myself to go upstairs and check the books, but it's almost nap time :)).

It is hard to imagine that Sauron hadn't figured it out that at least Galadriel had an Elven Ring. He wasn't that stupid - and the choice was so obvious. He knew her personally (as Annatar), he knew Celebrimbor - how could the head of the Mirdain not give a Ring to Galadriel?

Then Lorien, with its closely guarded borders and its magic fences. I guess Amroth's realm (before Galadriel came there) had nothing of the kind. Must be quite obvious that Galadriel had a Ring.

And finally here is a quote from UT "the Hunt for the Ring: Note how casually the magic fences and Galadriel's Nenya are mentioned - not a hint of doubt that this info was fully available in Mordor..

Actually, not! It may seem funny, but it is quite precisely stated in FotR that Sauron did NOT know:

Quite plain. Strange perhaps, but it was so. Well, why not? Galadriel was a Noldo, and there was Celeborn too, who knows what may have protected Lórien - not necessarily the Elven magic, eh? Elrond, Círdan, Glorfindel... Sauron had no idea what Elven lords and hidden realms may actually lie west of Misty Mountains. He was quite uninformed when it came to things like Isildur's heir as well. So why not the Elven Ringbearers?

When it comes to Saruman, then I am quite inclined to think he knew - but then, perhaps not? What is clear is that the Ringbearers didn't talk openly about their Rings with anybody, so no things like "ah, he knew because they were on the same Council" will hold. He figured out about Gandalf, though, so it is possible he may have learned about Galadriel - but then, not sure if "learned" was possible there until he would actually get a hold of the Ring itself. So, he may have "suspected", like Sauron, but not be 100% sure.

Underestimation of the Enemy, my precious... Ahh.. this arrogant Glad...:p

Well he'd know if Frodo blurted it out to an orc or Gandalf sang about the wrong thing surely. Aragorn scolded Frodo about talking about the ring outside Lorien didn't he?

Yes, that's true. Although Aragorn maybe was a little more careful, you know, being too much of a "simple man" (meaning in contrary to the really Wise, like Gandalf, Saruman, Galadriel, Elrond...). I think in Aragorn's case it may have been really closer to "simple man's superstition" - just because he heard from Gandalf and others, rather than the thing proved by his own rational reflection, if you know what I mean? "It is taboo to speak about the Rings aloud," but why in particular, few people actually ever thought about that.

Anyway, I don't think one Orc knowing about Galadriel's Ring this way would help. You see, desinformation is always a threat, and also verified sources are necessary. If an Orc came to Sauron, saying: "I heard a hobbit saying that Galadriel has an Elven Ring," would he take it as a proof? Hardly. Of course he presumed already the possibility, but this thing does not help him at all. In the best case, he would at least go and catch the Hobbit. And when interrogating him, as a (reputedly) first-hand witness, he could ask some things to verify, like "what stone did it have", "what was inscribed on the ring" etc. Sauron, like the Ring-loremaster, could then perhaps have some more evidence. But still, I cannot think now, for myself, about any thing that I would consider proving 100% that Galadriel is the one having the Ring - except for meeting her in person. This is perhaps why Sauron did not know. It would have to be, possibly, some "high divination magic" - like, I could imagine something like a special Mirror of Galadriel, if it was possible to attune it the right way, you could let's say see in it somebody wearing a Ring of Power, and the Ring would shine on its finger (so the Mirror would bring your attention to it). But it was hard to have such thing in M-E, and the Rings and similar things were usually capable of rather "hiding" themselves from the sight of the observer.