Polonius panics at the sight of Hamlet.  He recognizes instantly that if Claudius and Gertrude talk to Hamlet, one of them will inevitably ask Hamlet about the letters.  One of them will say, "Hamlet, is it true what you wrote in those letters?"  Hamlet will reply, "What letters?"  Hamlet will then be told, "Your love letters to Ophelia that Polonius has.  He read one to us, and showed us more.  Is it true, what you wrote?"  Hamlet will look at Polonius, and say, in a very displeased tone, "You have ''my'' love letters to Ophelia?"

Polonius panics at the sight of Hamlet.  He recognizes instantly that if Claudius and Gertrude talk to Hamlet, one of them will inevitably ask Hamlet about the letters.  One of them will say, "Hamlet, is it true what you wrote in those letters?"  Hamlet will reply, "What letters?"  Hamlet will then be told, "Your love letters to Ophelia that Polonius has.  He read one to us, and showed us more.  Is it true, what you wrote?"  Hamlet will look at Polonius, and say, in a very displeased tone, "You have ''my'' love letters to Ophelia?"

Uh-oh.  The jig will be up.  But Polonius has not yet persuaded Claudius to get involved to make Hamlet marry Ophelia.  Also, Polonius is sure Hamlet is mad, but he doesn't know how mad.  Is Hamlet so mad, at that point he would exclaim, "You rat!  Dead, dead for a ducat!" and then draw his sword and kill Polonius?  If Hamlet is ''that'' mad, Polonius doesn't want to find it out, here and now.

Uh-oh.  The jig will be up.  But Polonius has not yet persuaded Claudius to get involved to make Hamlet marry Ophelia.  Also, Polonius is sure Hamlet is mad, but he doesn't know how mad.  Is Hamlet so mad, at that point he would exclaim, "You rat!  Dead, dead for a ducat!" and then draw his sword and kill Polonius?  If Hamlet is ''that'' mad, Polonius doesn't want to find it out, here and now.  So, Polonius panics, and he begs Claudius and Gertrude to leave.