Enter Fortinbras, Captain, and army:
Fortinbras, on the march to Poland, pauses for a moment to order one of his captains to go speak with the Danish King. Fortinbras already has permission to cross Danish territory, and all he needs now is a Danish "conveyance," that is, an escort. After delivering his command, Fortinbras marches on.
As Fortinbras and his army exit the stage, in comes Hamlet with his escort--Rosencrantz, Guildenstern, and some others. Hamlet stops the Norwegian Captain and questions him. He learns that Fortinbras is marching against Poland, but not the "main of Poland." They go only "to gain a little patch of ground / That hath in it no profit but the name" (4.4.18-19). The Norwegian Captain bitterly remarks that it isn't worth five ducats, and Hamlet guesses that the battle will cost twenty thousand ducats and two thousand men. Hamlet then remarks, "This is the imposthume [abscess] of much wealth and peace, / That inward breaks, and shows no cause without / Why the man dies" (4.4.27-29). In short, the battle is absolutely meaningless.
Exeunt all but Hamlet:
From this point on, Hamlet's basic thought is that if Fortinbras can do what he's doing, Hamlet should be able to do what he's supposed to do. But Hamlet undercuts his own argument at every step, because he views Fortinbras as a damn fool. Fortinbras will expose himself "To all that fortune, death and danger dare, / Even for an egg-shell" (4.4.52-53). To Hamlet's shame, Fortinbras is marching off to war, but only to gain a piece of ground "Which is not tomb enough and continent / To hide the slain" (4.4.64-65). In other words, the piece of ground is not large enough to serve as a graveyard for the soldiers who will die in the battle. This seems to be war's ultimate absurdity, and this idea gives a hollow ring to Hamlet's final words of the scene, "O, from this time forth, / My thoughts be bloody, or be nothing worth! (4.4.65-66). Then Hamlet walks off--not to kill the King, but to continue his journey to England with Rosencrantz and Guildenstern.