The chapter begins with a three-day float through wooded river-banks that offered at least some semblance of security.  But the mood remained somber, even funereal, and even the irrepressible hobbits remained essentially silent.

The boats left the woods and entered a land of startling contrast, with the vast and desolate Brown Lands on the east bank, and the green and grassy plains of Rohan on the west bank.  Birds lined the west bank, and a phalanx of black swans flew overhead.

Aragorn gives Frodo and Sam and the readers a geography lesson, and tells us about the Rohirrim.  But he also tells us about the orcs on the east bank.  Yet for some reason the orcs rarely dare to cross the river, despite the fact that the Rohirrim "do not dwell by the River or ride often to its shores."  Sam feels that he is on a frontier of war, but if so Rohan is protected, and the Anduin patrolled, by powers unseen.

Boromir begins to exhibit strange behavior, muttering to himself, biting his nails, and driving his boat close behind Aragorn's.  Pippin and Merry notice and one would think others notice as well, but no one comments on it or brings it to Boromir's attention.  The atmosphere remains funereal.

Sam sees Gollum, but waits until bedtime to tell Frodo.  They decide to split watch for the night without bothering the others, and when Frodo relieves Sam he sees Gollum too.  Frodo draws Sting, Gollum leaves, and Aragorn awakes and reveals that he knew about Gollum all along, and indeed would like to catch him because he could be useful.  Aragorn decides to take more precautions, and the party begins paddling, journeying by night, and hiding their camp.

As they enter the grey hills of the Emyn Muil (which means, of course, grey hills), they see flocks of birds circling and an eagle high in the sky.  Aragorn decides to risk one more night journey, moving slowly in case they run into rapids, which they indeed do.  The current takes them toward the east bank where orcs unleash a volley of arrows.

The company's elf-boats and elf-cloaks defeat the night eyes of the orcs and they escape to the west bank, where Legolas shoots down a mysterious winged creature on the east side of the River.  Legolas's mighty shot dismays the orcs, and the wide river and developing fog seemingly protect the Fellowship.  No attack takes place that night or the next day, when the company makes a difficult portage (described in great detail) in heavy fog.

Boromir, by the way, briefly argues for abandoning the river above the portage, but agrees to stay with the party because Aragorn wants to make the portage and Frodo plans to follow Aragorn.  Aragorn apparently intends to enter Gondor by carrying one or more boats to the bottom of Rauros Falls, and continuing the river journey.

The party reenters the river, and encounters the Argonath, the Pillars of the Kings.  All but Aragorn bow their heads in fear: Aragorn sits straighter, and declares his kingly heritage.  He also, perhaps unconsciously, reveals to Frodo his desire to go to Minas Tirith, which he refers to as Minas Anor, "my own city."

Finally, the party reaches the lake of Nen Hithoel, the island peak of Tol Brandir, and the hills on either side of the lake, Amon Hen the Hill of Sight on the west and Amon Lhaw the Hill of Hearing and the east.

At the beginning I asked what is the point of this chapter.  Several noted that Tolkien is reintroducing the various threats to Frodo, and building the tension about which way Frodo will go, and who will go with him.  I would also note that we do get a lesson about geography, and the stark contrast between the east and west side of the River.  Even if we do not associate it with the Valar or any ancient power it is obvious that the two banks of the Anduin, the Great River, are as different as night and day, or life and death.  Frodo must choose, and it looks very much as if he must choose the land of death.  Which might explain the funereal atmosphere of this ten-day journey, and the fact that the company overlooks even Boromir's strange behavior.

Another note about the geography lesson: Reverend noted that the place names in this chapter often translate to simple descriptions of the land, such as grey hills, white mountains, or brown lands.  There are few places in all of LotR which are named after people.  Even ancient names often trace their roots to people.  I found a website which discusses the origins of place names in London here.

I would also note that Rohan and Wilderland use names in English or archaic English, while Gondor uses names in Sindarin.  Lorien also used Sindarin names, but everything was translated and explained for the visitors.  But in Gondor the names are used often with no translation or explanation.  Tolkien also introduces some more archaic names for the scenery in this chapter, or says that Aragorn "descried" rather than "saw" an eagle.  These archaisms will become even more common in Rohan and Gondor.

We also see Aragorn revealed as a king, returning to his land, and so does Frodo.  The phalanx of black swans may even be a sign that the king has returned, although the future looks dark.  We hear him reveal his desire to go to Gondor, and again, so does Frodo.  This may very well influence Frodo's actions in the next chapter.  And we hear Aragorn tell Frodo some other things which may foreshadow Frodo's future actions.  Aragorn tells Frodo not to mention Galadriel's ring, even among friends.  How much more important is it, then, for Frodo to keep his own plans secret?  Aragorn tell Frodo that Gollum could be useful.  Aragorn says he would like to climb Amon Hen, the Hill of Seeing, to plot his next course of action.  Frodo says little during this chapter, but it becomes apparent later that he was listening to everything Aragorn said.

Indeed this chapter also marks the beginning of a distance between the reader and Frodo.  No longer are we privy to all of Frodo's inner thoughts.  Instead, we hear more of Sam's inner thoughts about the trip, and how exposed he feels, and how he sees a log with eyes, and how he hates boats and water.  The reader, too, is left wondering what Frodo is thinking, and what his decision will be.  From now on, the reader will hear as much or more of Sam's inner dialogue than of Frodo's.

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"‘I think he was a silly little man,' said Councillor Tompkins.  ‘Worthless, in fact; no use to Society at all.'

"‘Oh, I don't know,' said Atkins, who was nobody of importance, just a schoolmaster.  ‘I am not so sure: it depends on what you mean by use .'

"‘No practical or economic use,' said Tompkins.  . . .

. . .

"‘It is proving very useful indeed,' said the Second Voice.  ‘As a holiday, and a refreshment.  It is splendid for convalescence; and not only for that, for many it is the best introduction to the Mountains.  It works wonders in some cases.  I am sending more and more there.  They seldom have to come back.'"