In Dept. Q episode 3, Merritt's kidnappers are obviously nervous now that Carl Morck has reopened her case, and they're ready to put more pressure on her to remember and realize just why she's in the chamber. Here's a recap of what happens in the episode on Netflix. Spoilers below.
Carl and Akram make their way to the same boat and area where Merritt was last seen, and realize something interesting. Carl throws Akram's hat as it's a windy day just like that fateful day four years ago, though the hat doesn't go overboard. Because of the wind, it actually flies back towards the parking lot. This is important because they realize the kidnappers had lucky timing of sorts where Merritt came down alone to get her brother's hat back, and that was the perfect time to take her.
Just like the woman they're investigating, a man with a bird on his hat is watching Carl and Akram, and he was there in the parking lot. The investigators also figure out that Merritt's trip home wasn't planned because she bought the ferry tickets the morning she disappeared. Next up is travelling to said home to talk to the local law enforcement there. Just as we saw at the institution William is staying at in episode 2, there's not much new information they learn.

Dept. Q gets their first major breakthrough
Growing up, the Lingard family was a sort of dark cloud. Though William was a good teen, Merritt was trouble. A boy named Harry Jennings is the one who beat up William, which is why he has aphasia now. He died as he trried to outrun police by getting on a ferry and jumping off while drunk. Merrit and William's father is still alive and they also go to question him. He also doesn't really have much information, though it's clear there's no love lost between father and daughter.
In the final moments of the second episode of Dept. Q, William broke out of the institution and ran away. He goes to their old home and finds a drawing he made of a bird, which matches the bird on the hat us viewers see in the man's pocket, watching Carl and Akram. There's squatters there now and they scare him off, though when Akram and Rose, who is now working with their department, show up he gets an answer out of them. Akram is a scary sort of calm for sure!

They find William hiding in Claire's shed, and are able to get their first clue of sorts in the investigation. Thanks to William, they learn that he saw someone wearing the hat with the bird on it at his and Merrit's home, as well as on the ferry. It then cuts to Merritt in the gas chamber equipment she's in, and the logo is there again.
William is taken back to the institution afterwards, though Rose may have found another clue. She figures out the bird is a Boobrie, and the name of a boat in Merritt's hometown is called, Boobrie II. That's what we call, a breakthrough!
Be sure to check out all of our episodic recaps of the series, here. Dept. Q is now streaming on Netflix.