  By expressing thermodynamic functions in terms of the edge and density of
Lee--Yang zeroes, we relate the scaling behaviour of the specific heat to that
of the zero field magnetic susceptibility in the thermodynamic limit of the
$XY$--model in two dimensions. Assuming that finite--size scaling holds, we
show that the conventional Kosterlitz--Thouless scaling predictions for these
thermodynamic functions are not mutually compatable unless they are modified by
multiplicative logarithmic corrections. We identify these logarithmic
corrections analytically in the case of the specific heat and numerically in
the case of the susceptibility. The techniques presented here are general and
can be used to check the compatibility of scaling behaviour of odd and even
thermodynamic functions in other models too.
