  We examine the scaling of the linear dimension of the system size of a real
polymer solution at constant excess free energy and in two different spacial
dimensionalities, d=d0 and d=d1. Standard results for the functional form of
the excess free energy lead to the conclusion that the scaling exponent nu(d)
satisfies nu(d0) - nu(d1) = 1/d0 - 1/d1. Taking the critical dimensionality as
a point of reference (nu(4)=1/2) gives a scaling exponent nu(d) = 1/4 +1/d, in
agreement with the accepted result for two-dimensions (nu(2) = 3/4) and the
first term in the epsilon (d-4) expansion. For the unsolved case of three
dimensions it predicts nu(3)=7/12. Several simplifying features of this result
are pointed out.
