Frodo, Too, Tips His Hand -- The Threat Outside the Black Gate (TT 4.iii.640)

When Frodo, Sam, and Gollum reach the Black Gate and Frodo declares that he must try to enter Mordor that way, a panic-stricken Gollum slips up and tells Frodo to give him the Ring rather than do anything so foolish. Frodo does not respond to Gollum's suggestion at first, not until he has learned that Gollum knows another way in. After grilling Gollum about it, he decides to trust him once again. Then and only then does he return to the suggestion Gollum had made about the Ring.

‘But I warn you, Sméagol, you are in danger.’

‘Yes, yes, master!’ said Gollum. ‘Dreadful danger! Sméagol’s bones shake to think of it, but he doesn’t run away. He must help nice master.’ 

‘I did not mean the danger that we all share,’ said Frodo. ‘I mean a danger to yourself alone. You swore a promise by what you call the Precious. Remember that! It will hold you to it; but it will seek a way to twist it to your own undoing. Already you are being twisted. You revealed yourself to me just now, foolishly. Give it back to Sméagol you said. Do not say that again! Do not let that thought grow in you! You will never get it back. But the desire of it may betray you to a bitter end. You will never get it back. In the last need, Sméagol, I should put on the Precious; and the Precious mastered you long ago. If I, wearing it, were to command you, you would obey, even if it were to leap from a precipice or to cast yourself into the fire. And such would be my command. So have a care, Sméagol!’

(TT 4.iii.640, italics mine)

Since Gollum is almost the last person Frodo would want to know that he was planning to throw the Ring into the fires of Mount Doom, neither he nor Sam have told Gollum why they must get into Mordor. In fact earlier in this very scene Sam reflects on just this: "‘And it’s a good thing neither half of the old villain don’t know what master means to do,’ he thought. ‘If he knew that Mr. Frodo is trying to put an end to his Precious for good and all, there’d be trouble pretty quick, I bet'" (TT 4.iii.639). It was only the night before Sam had overheard Gollum's two sides talking to each other about, among other things, 'what's the hobbit going to do with it, we wonders, yes, we wonders' (TT 4.ii.633).* 

Somehow it never crossed my mind until yesterday that Frodo reveals himself here just as much as Gollum had by suggesting Frodo give him the Ring back. His threat about commanding him to leap from a precipice might well pass unnoticed, but 'cast yourself into the fire' draws attention to itself. What fire? What fire large enough to cast oneself into? Gollum doesn't reply, doesn't ask. Frodo's taunting and threatening him and invoking the power of the Ring thoroughly cows him for the moment. He'll figure it out, however, as he follows Frodo and Sam across Mordor towards the fire of Mount Doom. There, on the road to the Sammath Naur, Gollum will grasp what fire his wicked master had been talking about.

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*It's interesting to note that the phrase, 'we wonders ... we wonders' pops up twice before this moment. 

When Gollum first meets the hobbits, he says 'And where are they going in these cold hard lands. We wonders, yes, we wonders' (TT 4.i.615).

After Gollum attempts to escape, Sam hurls the words back at him: 'And where were you off to in these cold hard lands, Mr. Gollum.... We wonders, aye, wonders' (TT 4.i.617).