We study the cosmological solutions of the two-dimensional Brans-Dicke
equations considering a gas of c = 1 strings in S1 x R as the source
of the gravitational field. We also study the implications of the R-du
ality invariance on the solutions. To this purpose we conjecture that,
as it happens for massless fields in finite boxes, the free energy of
a gas of massless string excitations is not given by the correspondin
g toroidal compactification.