  We provide a simple derivation of the constant factor in the short-distance
asymptotics of the tau-function associated with the $2$-point function of the
two-dimensional Ising model. This factor was first computed by C. Tracy in
\cite{T} via an exponential series expansion of the correlation function.
Further simplifications in the analysis are due to Tracy and Widom \cite{TW}
using Fredholm determinant representations of the correlation function and
Wiener-Hopf approximation results for the underlying resolvent operator. Our
method relies on an action integral representation of the tau-function and
asymptotic results for the underlying Painlev\'e-III transcendent from
\cite{MTW}.
