  In this paper we construct explicit solutions and calculate the corresponding
$\tau$-function to the system of Schlesinger equations describing isomonodromy
deformations of $2\times 2$ matrix linear ordinary differential equation whose
coefficients are rational functions with poles of the first order; in
particular, in the case when the coefficients have four poles of the first
order and the corresponding Schlesinger system reduces to the sixth Painlev\'e
equation with the parameters $1/8, -1/8, 1/8, 3/8$, our construction leads to a
new representation of the general solution to this Painlev\'e equation obtained
earlier by K. Okamoto and N. Hitchin, in terms of elliptic theta-functions.
