The King and Queen enter with Rosencrantz and Guildenstern and others. King Claudius has summoned Hamlet's two school chums to Elsinore to have them spy on the Prince and report back to Claudius, recounting Hamlet's every move. The Queen promises them handsome compensation for their spying and assures them that Hamlet's own good requires the service. Rosencrantz and Guildenstern agree. The two leave to seek Prince Hamlet, and the King and Queen turn their attention to Polonius, who claims to have the answer to Prince Hamlet's affliction He promises to elaborate further after Claudius receives his newly arrived ambassadors from Norway.
When Polonius exits, Gertrude scoffs at the old man's intimations. She remains certain that Hamlet's woes are caused by the old king's death and her hasty remarriage. Polonius returns with Ambassadors Voltemand and Cornelius. They bring news from Norway that the old and ailing king, brother to the slain King Fortinbras, has managed to restrain his nephew, young Fortinbras, from invading Denmark. In return, however, the old man asks that Denmark provide some assistance in Fortinbras' campaign against Poland — that Claudius allow Fortinbras to pass through Denmark on his way to Poland.
As soon as the ambassadors leave, Polonius launches into an elaborate discussion on the meaning of life and duty, promising to be brief and then launching into further wordiness. Finally, Polonius asserts that Hamlet is mad. Having no patience for Polonius, Gertrude admonishes him. Again promising to be less loquacious, Polonius makes showy, wavy motions with his arms and then reads a letter he confiscated from his daughter, written in the Prince's hand. Polonius criticizes the highly dramatic, artificial prose with random rhymes in which Hamlet has written the note and tells Claudius and Gertrude that he has forbidden Ophelia to accept any advances from the Prince. That is the order, Polonius claims, that has led poor Hamlet into madness.
Polonius then suggests that he and Claudius hide themselves behind a needlework wall hanging so they can eavesdrop on the couple when Ophelia meets with Hamlet to return his love gifts. Claudius agrees, just as Hamlet enters reading. Polonius asks the King and Queen to leave them so that he may speak to Hamlet himself.
In the encounter that follows between Hamlet and Polonius, Hamlet warns Polonius to watch his daughter carefully and then toys with Polonius' limited wit. The exchange convinces Polonius that Hamlet is lovesick when, in actuality, Hamlet's responses have done little but ridicule Polonius. Polonius leaves, and Rosencrantz and Guildenstern enter. Hamlet greets them as his "excellent good friends" and asks why they have come to his prison. They grouse at his choice of words, but he tells them, "Denmark's a prison." Rosencrantz wittily replies, "Then is the world one." Hamlet breaks through his friends' resistance, and the two finally admit that the King and Queen sent them to observe Hamlet and provide them with details of his behavior. Hamlet's melancholy then erupts in a blank verse complaint that he has lately "lost all my mirth." He laments that a foul and sickening fog now besmirches the heavens, which he once saw as a canopy "fretted with golden fire." Hamlet then indicts the very nature of mankind.
Rosencrantz seizes the opportunity to announce the arrival of the players, and Hamlet's mood shifts yet again. Ecstatic at the opportunity for diversion, Hamlet asks who the players are and why they are on the road. Rosencrantz answers that they are on the road because a company of child actors has usurped the London stage. Hamlet responds by saying that he welcomes Rosencrantz and Guildenstern as he welcomes the actors and hopes he can be a worthy host. Polonius enters to announce the arrival of the players.
When the players enter, Hamlet requests that the lead player perform a speech from Virgil's Aeneid in which Aeneas tells Queen Dido the story of Phyrrus, whose father Achilles was killed at Rome. The player performs the speech and moves himself to tears over Hecuba's horror at seeing her husband dismembered. Hamlet asks Polonius to see to the players' lodging, and, as soon as the Lord Chamberlain has left, he tells the small group of players remaining on-stage his plans for their performance of The Murder of Gonzago. He tells them that he will provide them with twelve to sixteen original lines that he wants them to add to the play. They agree, and they leave.
Hamlet then reveals his real intentions for The Murder of Gonzago. The players will perform the play with an enhanced scene, which will enact the murder the Ghost has described. Hamlet hopes that seeing his crime reenacted in front of the assembled audience will make Claudius act guilty and reveal that he murdered King Hamlet. Such an admission will prove to Hamlet, once and for all, that the Ghost is real and not simply a devil or the figment of his imagination.
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