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As they arrive at the Shivering Sands, Sergeant Cuff tells Betteredge not to worry about Rosanna.
Even if the evidence does point at Rosanna, Cuff doesn't suspect Rosanna of having stolen the diamond for herself; he thinks that she was acting for someone else.
Who? asks Betteredge.
But Cuff won't say.
All he does is explain what he thinks Rosanna has been up to: when Seegrave pointed out the smudge on the door to all the female servants, Rosanna realized that it might be on her own dress.
So she pretended to have a headache to give herself time to make a new one.
She slipped out of the house and went to town to buy the materials, and then spent the rest of the afternoon sewing and ironing it in her room.
She wouldn't have wanted to risk burning the stained one, since the smell would tip off the other servants; so, instead, she is probably hiding the piece of clothing somewhere.
In fact, Sergeant Cuff saw her sneak out in this direction earlier, stopping at a cottage in a tiny fishing village on her way.
And that's why he asked Betteredge to come with him to the Shivering Sands: to trace Rosanna Spearman and find the article of clothing.
But they can't find anything on the beach, even though they do see some footprints.
So they head to the cottage in the fishing village where Cuff say Rosanna stop earlier.
It's the cottage of some friends of hers, the Yollands.
The Yollands' daughter, Lucy, has a physical disability, like Rosanna, and the two girls seem to have bonded over it.
Mrs. Yolland is there, and is happy to meet a real-live detective from London.
Cuff chats with her about this and that, and finally leads the conversation to the Verinder house and Rosanna Spearman.
He makes Mrs. Yolland understand that he likes poor Rosanna and wants to help her, and so Mrs. Yolland trusts him.
She tells him that Rosanna is leaving her position at the Verinder house soon.
When Rosanna was there earlier, she borrowed paper to write a long letter, and then bought a few things that she would need for traveling.
Cuff manages to wheedle out of her exactly what the things were: a waterproof metal case and some chains.
Cuff and Betteredge then leave the cottage, and Cuff admits that he's confused.
It seems clear to him that Rosanna planned to hide the stained dress in the case, tie the case with the chains, and sink the case in the ocean or in the quicksand so that it would remain hidden until she came back for it.
But why would she not just throw the stained piece of clothing into the quicksand for good? Why might she want to pull it up again?
Betteredge suggests that she's hiding the diamond there, not the stained clothing, but Cuff disagrees.
He says that it must be the stained clothing, though he doesn't explain why.
He says that the next step will be to go to Frizinghall to see what kind of fabric Rosanna bought – that way they'll know whether she was making a nightgown or a petticoat, and that might shed more light on the matter.
When they get back to the house, they ask around and discover that Rosanna had returned to the house about an hour before.
Cuff wanders around the garden for a while, and notices that the lights are on in Rachel's room, and that there seems to be a lot of bustle going on in there.
Cuff tells Betteredge that he bets that Rachel has just decided to leave the house.
They go inside, and Lady Verinder sends for Betteredge. Sure enough, Rachel has decided to leave.