[davem]

One question that occured to me reading this chapter was: Why does Smeagol think Frodo is going to Mordor?

Or has he even considered this? Certainly he is by now, even if he wasn't during his long sojourn under the Misty Mountains, aware of the nature of the Ring & wath it can offer its possessor:

See, my precious: if we has it, then we can escape, even from Him, eh? Perhaps we grows very strong, stronger than Wraiths. Lord Smeagol? Gollum the Great? The Gollum! Eat fish every day, three times a day, fresh from the Sea. Most Precious Gollum! Must have it. We wants it, we wants it, we wants it!"

He has also experienced the authority it gives to Frodo:

"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 Smeagol 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, Smeagol, 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, Smeagol!"
Sam looked at his master with approval, but also with surprise: there was a look in his face and a tone in his voice that he had not known before. It had always been a notion of his that the kindness of dear Mr. Frodo was of such a high degree that it must imply a fair measure of blindness. Of course, he also firmly held the incompatible belief that Mr. Frodo was the wisest person in the world (with the possible exception of Old Mr. Bilbo and of Gandalf). Gollum in his own way, and with much more excuse as his acquaintance was much briefer, may have made a similar mistake, confusing kindness and blindness. At any rate this speech abashed and terrified him. He grovelled on the ground and could speak no clear words but nice master.

Even Sam has experienced something similar:

For a moment it appeared to Sam that his master had grown and Gollum had shrunk: a tall stern shadow, a mighty lord who hid his brightness in grey cloud, and at his feet a little whining dog. Yet the two were in some way akin and not alien: they could reach one another's minds. Gollum raised himself and began pawing at Frodo, fawning at his knees.
'Down! down!" said Frodo. 'Now speak your promise!"
"We promises, yes, I promise!" said Gollum. "I will serve the master of the Precious. Good master, good Smeagol, gollum, gollum!" Suddenly he began to weep and bite at his ankle again.

So what does Smeagol think Frodo is going to do once he gets to Mordor with the 'Precious'? One thing that did occur was that Gollum is rather like Sauron, in that he seems uable to contemplate the possibility that anyone could wish to destroy the Ring. Gollum has fantasised about taking the Ring back & becoming all powerful - is this what he thinks Frodo is up to? Does he believe that Frodo is going to Mordor to challenge & throw down Sauron & set himself up in his place? This would account for his desires - as Smeagol, to help 'Master' (ie, to keep in with the new Dark Lord, so as not to find himself on the recieving end of his wrath) & as Gollum, to keep in with Frodo so as to be in position to take the Ring for himself if & when the opportunity arises.

We've seen Frodo succumbing to the seduction of the Ring. Two confrontations so far with Gollum, & both times (there will be a third at the Forbidden Pool) he uses the (threat of) the power of the Ring to dominate & subjugate him - using terrible threats, which he knows Gollum will believe. Aren't we seeing Frodo's ultimate failure at the Sammath Naur foreshadowed right here? If so, why do we continue with any hope? Do we share Sam's blind faith in Frodo, or is our faith, whether we realise it or not, in something (Someone) else?