Act III scene 1 is a very important scene in this play as it represents the final attempt of Claudius and Polonius to discover whether Hamlet's supposed madness is the result of his love for Ophelia or not. To this end, they create a situation where Hamlet will stumble across Ophelia, apparently by chance, whilst they eavesdrop on the conversation they have. Before this happens, Hamlet delivers his famous soliloquy, "To be or not to be," where he contemplates suicide and philosophises about the value of life in general. When the conversation with Ophelia starts, Hamlet, although he begins it fairly innoccuously, then turns on Ophelia, insulting her and cursing her, before leaving her distraught. Polonius and Claudius then enter, talking about what they have learnt from this and how to proceed. Claudius significantly says:
There's something in his soul
O'er which his melancholy sits on brood,
And I do doubt the hatch and the disclose
Will be some danger...
Now that they have shown Hamlet's madness is not because of his thwarted love for Ophelia, it is clear that Claudius begins to suspect that Hamlet is plotting something against him, and therefore he determines to send him to England to get him away from Denmark so that he cannot threaten Claudius. Key issues that arise from this scene are the nature of the relationship between Hamlet and Ophelia and then also Hamlet's state of mind, as revealed through his soliloquy.