  Mayer's convergence method for virial expansion and condensation is studied
using a new generating function for canonical partition function, which
directly depends on irreducible cluster integral, $\beta_k$, unlike Mayer's
work where it depends on reducible cluster integral, $b_l$. The virial
expansion, criteria for it's validity and criteria for condensation, etc. are
derived from our generating function. All earlier Mayer's results are obtained
from this new generating function.
