CLAUDIUS      Love! His affections do not that way tend.

Nor what he spake, though it lacked form a little,

Was not like madness. There’s something in his soul

O’er which his melancholy sits on brood

And I do doubt the hatch and the disclose

Will be some danger – which for to prevent

I have in quick determination

Thus set it down. He shall with speed to England

For the demand of our neglected tribute.   (3.1.161-169)

In some editions Ophelia exits after her speech, which necessitates her re-entering later on; it’s perhaps more effective if Claudius and (perhaps, probably) Polonius ignore her distress when they reappear from where they’ve been watching and listening. Claudius certainly isn’t going to engage with her, and he’s completely dismissive: Love! His affections do not that way tend. I completely reject that as an explanation for Hamlet’s behaviour (which has been Polonius’s pet theory). Of course it’s particularly brutal to say this in Ophelia’s hearing: no, doesn’t sound anything like love to me. No question. But Claudius is properly suspicious now: nor what he spake, though it lacked form a little, was not like madness. And actually, he’s not sounding that mad, even though what he was saying was a bit—all over the place? (The suggestion can be that Hamlet’s knee-jerk, conventional misogyny, for instance, sounds entirely reasonable and commonplace to Claudius.)

No, there’s something in his soul o’er which his melancholy sits on brood. Claudius is musing more to himself here: there’s some deeper cause, Hamlet’s obsessed with something; he’s plotting. (Melancholy imagined as a bird sitting on a nest, but it’s sinister; serpents also hatch from eggs, of course.) And I do doubt the hatch and the disclose will be some danger—my main concern is that when his plotting comes to fruition, the eggs hatch—he’s going to do something untoward, reckless—and then Claudius seems to interrupt himself, stop before he says that the danger, the plotting will likely be directed towards him, specifically, because this would be to incriminate himself. Which for to prevent—getting ahead of this possible outcome—I have in quick determination thus set it down. I’ve made a decision, I have a strategy, and this is what’s going to happen. I’m sending Hamlet on a diplomatic mission, immediately: he shall with speed to England for the demand of our neglected tribute. (This makes sense of the business with the ambassadors in 1.2, Claudius more confident, and successful, in pulling the levers of government and diplomacy, than in dealing with tensions closer to home.)

Assuming Ophelia’s on stage still, she can be trying to recover some semblance of self-control; Polonius might be looking at her with concern, or he might be hanging on Claudius’s every word, taking notes, preparing to implement his boss’s decision.