In Act IV, scene i of Macbeth, what do the apparitions of the bloody child and the crowned child stand for?

Macbeth is most concerned with two things when he visits
the Witches in Act IV, scene i:  Will he be murdered as he murdered Duncan?  And, since
he and Lady Macbeth have no children, who will follow him as king?  The two children
apparitions are symbolic representations of those who might bear the power to take his
life.

The bloody child is called the Second Apparition, and
it says:

Be
bloody, bold, and resolute; laugh to scorn

The power of
man, for none of woman born

Shall harm
Macbeth.

The image of a
bloody child, besides being just the sort of gore that Shakespeare's audience enjoyed,
suggests a child who is born in blood, naturally birthed from his mother's
womb.

The crowned child, or Third Apparition, carries a
tree in his hand.  He says:

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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.

This apparition is
crowned to suggest that the kingship is at stake.  It carries a tree to suggest the wood
that it speaks of, but also to foreshadow how the seemingly impossible task of the wood
"coming" from one place to another.  It will be carried as camouflage for the soldiers
who make a sneak attack upon Macbeth.

Both apparitions are
technically correct in their assessments.  Macbeth is not killed by a man of woman born,
but a man born by Cesarean section, and the wood moves from one place to another, not
because it grows legs and walks, but because its sticks and branches are carried by the
soldiers coming to defeat Macbeth.