Claudius tells some of his advisers that while Hamlet is a dangerous presence in Elsinore, he is beloved by the people—Claudius can’t do anything to Hamlet that might upset Denmark’s subjects. He plans to make sending Hamlet away to England look like it is something he’s been planning for a long time.
Claudius wants to get rid of Hamlet and legitimize his claim to the throne—but he can’t kill Hamlet without erasing the latter possibility and so resolves to merely send Hamlet away.
Rosencrantz enters and tells Claudius that while Hamlet refuses to divulge where he has buried Polonius, he is outside under guard. Claudius orders Hamlet be brought inside, and Guildenstern brings him in. Claudius asks Hamlet directly where Polonius is, and Hamlet replies that he is “at supper.” Claudius asks where he is eating, and Hamlet replies that Polonius is not eating, but rather being eaten. Claudius, growing even angrier as Hamlet continues to taunt him, demands to know where Polonius is. Hamlet replies that Polonius is in heaven—but if his body isn’t found within a month, the residents of Elsinore may begin to smell him in the main hall. Claudius orders his attendants to search for the body.
Hamlet’s macabre jokes about Polonius’s death and decay lend credence to Claudius’s belief that Hamlet is truly mad. At the same time, Hamlet has some merriment about him as he knows, surely, that Claudius can’t kill him—he will not face any consequences for murdering Polonius, no matter how irreverently he speaks of the man’s death.
Claudius says that he is concerned for Hamlet’s “safety,” and so has decided to send him away to England. Hamlet bids Claudius farewell, calling him “dear mother.” When Claudius tells Hamlet that he is his father, Hamlet insists that in marrying his mother, Claudius joined his flesh with hers. Hamlet hurries away, and Claudius bids his attendants to follow Hamlet and make sure he gets on the ship—he wants Hamlet gone tonight.
Hamlet continues taunting and ridiculing Claudius until the last moment—but doesn’t take any decisive action against him. Hamlet is not suited to revenge in the traditional sense—what he does best is chipping away at the man’s honor bit by bit.
Alone in the hall, Claudius speaks aloud, hoping that the King of England will follow the instructions in the letter Hamlet is carrying—and kill Hamlet on sight. Claudius states that he will never be joyful again until he is certain of Hamlet’s death.
Claudius reveals that he does actually intend to have Hamlet killed, but by cowardly means that will ensure he’s not implicated in the murder.