Sylvia appears, and spotting the Doctor starts yelling. She remembers to tell him Merry Christmas before telling him to GTFO -- which is very cute, and a good reminder about how the Doctor already got Sylvia to lay off Donna and mind her manners, another gift he gave her; the actress really does work to make the different versions of Sylvia make sense -- and they all three agree one more time that Donna's the thing and that the Doctor needs to disappear. Donna comes looking for them, since now everybody's outside, and roams the house yelling for them; Wilf takes the opportunity to head for the TARDIS with the Doctor, which pisses Sylvia off, but before she can scream them to death, they're gone, and Donna appears: "Are you shouting at thin air?" she asks, adorably, and Sylvia nods awesomely: "Yes? Possibly. Yes."
Wilf stares around the TARDIS long enough for them to have the usual Companion meet-cute about how crazy big the TARDIS is, inside, and welcome aboard, and all that ritual. He asks if they can't just take the TARDIS back to yesterday and catch the madman, but the Doctor explains about how you can't move around in your own timeline -- "I have to stay relative to the Master within the causal nexus, understand?" -- and they're off.
At the Naismith mansion, they've got the Master on a collar and leash, in a straight jacket. They finally light up the giant alien tech, which is clearly not from Earth. When Naismith points out that neither is the Master, the two sketchy scientists stare at each other, and they run off to freak out about him downstairs, releasing the shimmers that make them look human and revealing themselves to be spiky and green and annoying. Verdict: "What if this visitor is some sort of genius? We're hijacking this project, maybe we can use him, too. Harold Saxon, or whatever he is, might be exactly what we need." I guarantee this is not the case, but to be honest I hate the Vinvocci more than I hated the Slitheen, so I could care less.
The Gate was found inside a spaceship, buried at the foot of Mount Snowdon, and taken by Torchwood One and subsequently "acquired" by Naismith, after the whole Void thing. The Master likes the cut of Joshua's jib, but any bonding that might occur as a result is undercut by the Master noting also that he would taste delicious. The Master's turkey is delivered and he pounds the whole thing, which is totally disgusting, and then Naismith explains the Nuclear Bolt. And we're using "explains" rather loosely here: Basically, it's some kind of two-cell plastic unit that houses the power supply of the Gate. Somebody has to monitor the energy feedback 24/7, so it doesn't explode or vent, which means when one door locks the other one unlocks. "The power feeds through to the Gate, where it encourages some sort of cellular regeneration." He shows the Master a lady whose arm used to be burnt and now isn't. Naismith then explains that he wants the Master to fix it up entirely and then they can use it to make his daughter immortal. Apropos of nothing, the little weirdo goes, "Abigail. It means Bringer of Joy." I fuckin' hate the Naismiths.