  We define two tau functions, $\tau$ and $\hat{\tau}$ , on moduli spaces of
spectral covers of $GL(n)$ Hitchin's systems. Analyzing the properties of
$\tau$, we express the divisor class of the universal Hitchin's discriminant in
terms of standard generators of the rational Picard group of the moduli spaces
of spectral covers with variable base. The function $\hat{\tau}$ is used to
compute the divisor of canonical 1-forms with multiple zeros.
