In the aftermath of the duel, the Raiders flee, their hostages are freed, and it turns out the parrot isn't dead. Squawwakak! (That's parrot-talk for "hallelujah!")
Daphne and Mau do some reflecting. The past few weeks have been tough, sure, but neither would change anything—they're better today for all of it.
Interrupting that happy moment, yet another ship arrives. Hey, look! It's Daphne's father!
Of course, His Excellency thinks that Daphne has been at the mercy of savages, but she assures him that she's fine. That blood on her? Oh, that's just a splash from when she had to amputate a leg.
She leads her father to the cave of the gods. It takes a lot of persuasive talk, but she convinces him not to just take everything and cart it back to England.
Instead, he should set up a Royal Society on the island. They should come here because the island is the important place, the birthplace of humanity.
Over the next couple of weeks, His Excellency and his men explore the island and play games like cricket with the islanders. (The islanders kick their butts.)
This happy moment is interrupted by even another ship: the Cutty Wren, carrying the Gentlemen of Last Resort and Daphne's Grandmother, who is like the Dowager Countess from Downton Abbey but without the warmth and tact.
(The Dowager Countess doesn't have any warmth and tact.)
The Gentlemen inform His Excellency that he's now King, even though his mother still makes him feel like a useless twit.
Bolstered by this news, His Excellency manages to tell her off in a most hilarious fashion.
Daphne is thrilled to learn that Cookie, the cook from the Sweet Judy, is still alive, rescued by the men of the Cutty Wren.
Mau arrives (with Pilu to translate) to bargain with the king. In exchange for the cave's Golden Door, Mau wants a few items of scientific interest: a big telescope, a giant boat, timber, metals, books, and, oh yeah, a doctor.
Using the figurehead from the Sweet Judy, the carpenters build a new door to the cave.
A week later, Mau and Daphne say their goodbyes: "We both walk away, without regrets, and when we meet again, it will be as old friends" (15.345).
The ship sails away with Daphne on it, and Mau goes fishing. Of course.