  The $2\times 2$ Schlesinger system for the case of four regular singularities
is equivalent to the Painlev\'e VI equation. The Painlev\'e VI equation can in
turn be rewritten in the symmetric form of Okamoto's equation; the dependent
variable in Okamoto's form of the PVI equation is the (slightly transformed)
logarithmic derivative of the Jimbo-Miwa tau-function of the Schlesinger
system. The goal of this note is twofold. First, we find a symmetric uniform
formulation of an arbitrary Schlesinger system with regular singularities in
terms of appropriately defined Virasoro generators. Second, we find analogues
of Okamoto's equation for the case of the $2\times2 $ Schlesinger system with
an arbitrary number of poles. A new set of scalar equations for the logarithmic
derivatives of the Jimbo-Miwa tau-function is derived in terms of generators of
the Virasoro algebra; these generators are expressed in terms of derivatives
with respect to singularities of the Schlesinger system.
