  We study a potential introduced by Darboux to describe conjugate nets, which
within the modern theory of integrable systems can be interpreted as a
$\tau$-function. We investigate the potential using the non-local
$\bar\partial$ dressing method of Manakov and Zakharov, and we show that it can
be interpreted as the Fredholm determinant of an integral equation which
naturally appears within that approach. Finally, we give some arguments
extending that interpretation to multicomponent Kadomtsev-Petviashvili
hierarchy.
