Shakespeare enjoyed irony. In Act1 Scene 2,Polonius says, "Since brevity is the soul of wit...I will be brief." How is this ironic?

In Shakespeare's Hamlet, Polonius
says in Act 2.2.91-96 (rather than 1.2): 

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Therefore, since brevity is the soul of
wit

And tediousness the limbs and outward
flourishes,

I will be brief:  your noble son is
mad.

Mad call I it, for, to define true
madness,

What is 't but to be nothing else but
mad?

But let that
go. 

It is ironic when
Polonius says he will be brief, because he is anything but brief.  This passage is just
the beginning of Polonius' speeches in which he tries to convince Gertrude and Claudius
that Hamlet is mad, but even in just these few lines we see how full of "art" he is, and
how empty of substance.  He's talking in circles, defining and redefining.  He uses the
word mad to define
mad. 

Gertrude recognizes this
immediately, telling him:

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More matter, with less
art.

Polonius is a
nonsensical windbag, who talks much while saying little.  And he is anything but
brief.