  Using positional data from video-microscopy we determine the elastic moduli
of two-dimensional colloidal crystals as a function of temperature. The moduli
are extracted from the wave-vector-dependent normal mode spring constants in
the limit $q\to 0$ and are compared to the renormalized Young's modulus of the
KTHNY theory. An essential element of this theory is the universal prediction
that Young's modulus must approach $16 \pi$ at the melting temperature. This is
indeed observed in our experiment.
