  In this note we identify the leading terms of the (reduced) K-energy map with
a universal linear combination of the principal and subdominant coefficients of
the weight of the $mth$ Hilbert point. This shows that the weight
$F_{1}(\lambda;X)$ introduced by Donaldson in [SKD02] is just the weight of the
CM-polarisation.The equivalence between the CM-(semi)stability and the K-(semi)
stability follows from this. Also, using our previous work, we are able to
describe this subdominant coefficient in terms of the weights of some
generalised Chow forms, under a multiplicity free hypothesis on the
degeneration. This is accomplished by introducing a parameter dependent lift of
the CM-polarisation, and letting this parameter tend to infinity. This could be
thought of as a ``quantized'' version of the virtual bundle introduced in
[Tian94].
