In Hamlet, what are three metaphors used in  Act 4 Scene 1?  

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In this important scene in the play, Gertrude narrates to her new husband, Claudius, what happened when she attempted to reason with Hamlet, her son, herself, whilst Polonius listened behind a tapestry. Of course, Polonius is killed by Hamlet as Hamlet hears someone eavesdropping and assumes it is his Uncle.

Interestingly, this passage contains far more examples of similes than metaphors, and I assume this is what you are trying to identify. Remember that both similes and metaphors are comparisons, but the only difference is that similes compare one thing to another with the words "like" or "as".

Gertrude describes her son's state of mind to her new husband as:

Mad as the seas, and wind, when both contend

Which is the mightier.

It is interesting that in comparing her son to the weather during a storm, she is perhaps trying to excuse her son's behaviour, for if it is as if the elements are battling for sovereignty within him, he can hardly be held accountable for his actions.

Claudius describes his regret at not acting to stop Hamlet sooner as follows:

But like the owner of a foul disease,

To keep it from divulging, lets it feed

Even on the pith of life.

Hamlet is described in explicitly negative terms here - as a foul disease that the owner lets spread out of fear of others knowing about it, even as it swallows up "the pith of life." Clearly, from the King's perspective, Hamlet is a cancer who threatens to eat up his sovereignty and position.

The final example I will point to comes from Gertrude when she tells Claudius where Hamlet has gone:

To draw apart the body he hath kill'd,

O'er whom his very madness like some ore

Among a mineral of metals base

Shows itself pure.

Note again how this simile presents Hamlet in a positive light - he shows himself to be "pure" in spite of his madness, and his condition is compared to a precious ore in a bed of worthless minerals that shows how precious and valuable it is, in spite of the surrounding rubbish.

Hopefully this will help you identify others. Enjoy!