In Macbeth, in Act 4, scene 1,what is the significance of the tree which the third apparition appears with?

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This third prophecy comes in Act IV scene 1 when Macbeth wishes any sort of destruction upon the world in order to gain the "truth" from the witches. However, it is important to note how the truth that is revealed plays with his insecurities and leads him on into ever greater acts of darkness and evil. When the third apparition comes, described as "Third Apparition, a child crowned, with a tree in his hand" in the stage directions, Macbeth responds:

What is this,

That rises like the issue of a king;

And wears upon his baby brown the round

And top of sovereignty?

It is important to note that the crown not only completes and rounds, as with the perfection of a circle, the claim to sovereignty, but it is figuratively the summit of his ambitious hopes. Macbeth can thus interpret this sign in terms of his own success in keeping the crown and producing an heir, though the significance of the tree is explained by the third apparition itself:

Be lion-mettled, proud, and take no care

Who chafes, who frets, or where conspirers are:

Macbeth shall never vanquish'd be, until

Great Birnam wood to high Dunsinane hill

Shall come against him.

Therefore the tree represents the danger in the future prophecy of Dunsinane wood moving against Macbeth and attacking him - the prophecy that becomes terrifyingly true in Act V. Note how this prophecy gives Macbeth false hope and confidence - it is as if the witches are deliberately playing with Macbeth's mind, giving him faith and hope, yet knowing that he will be deposed and the future that Macbeth is clinging on to will come to naught.