How does Hamlet test the conscience of the king?

Actually, according to the text, Hamlet intends to
"catch the conscience of the King." (II, ii, 601)  This is
an important distinction, because in "catching" rather than "testing" the King, Hamlet
demonstrates to the audience that he is no longer wavering over whether the ghost he met
in Act I was, in fact, his father, and the story and challenge of revenge that the ghost
issued him was true.

In Act Three, Hamlet stages a play he
calls The Mousetrap, which is the story of a King who is poisoned
by his nephew as he sleeps in the garden.  The villainous nephew pours poison in the
King's ear -- exactly the method described by the Ghost to Hamlet concerning the method
used by Claudius to kill Hamlet Senior.  This performance is meant to be the means by
which Hamlet catches Claudius.  Here, in Act III, scene ii, just before the play is
performed, Hamlet instructs Horatio in testing for King
Claudius:

readability="15">

There is a play tonight before the
King:

One scene of it comes near the
circumstance

Which I have told thee of my father's
death.

I prithee, when thou seest that act
afoot,

. . .Observe my uncle.. . . Give him heedful
note.

And when Claudius
witnesses the murder in the play, he jumps up, and abruptly exits the room.  Hamlet is
convinced that this is evidence of Claudius' guilt, and ultimately follows Claudius with
the intent to exact the revenge.  He catches Claudius at prayer, however, and refuses to
kill him as he is asking forgiveness of his sins.  This moment is ironic however, as, in
fact, Claudius is not forgiven his sins since he is unable to send his words up to
heaven, but rather they "remain below."

For more on Act
III, scene ii, please follow the links below.