  We discuss the properties of the Liouville theory coupled to the c=1 matter
when perturbed by an operator, the screening operator of the $SL(2;R)$ current
algebra, which is supposed to generate the mass of the two-dimensional black
hole. Mimicking the standard KPZ scaling theory of the Liouville system
perturbed by the cosmological constant operator, we develop a scaling theory of
correlation functions as functions of the mass of the black hole. Contrary to
the case of KPZ, the present theory does not have the $c=1$ barrior and seems
somewhat insensitive to the delatils of the matter content of the theory; the
string succeptibility equals 1 independent of the matter central charge. It
turns out that our scaling exponents agree with those of the deformed matrix
model proposed recently by Jevicki and Yoneya.
