  We use the Bethe ansatz equations to calculate the charge stiffness $D_{\rm
c} = (L/2) d^2 E_0/d\Phi_{\rm c}^2|_{\Phi_{\rm c}=0}$ of the one-dimensional
repulsive-interaction Hubbard model for electron densities close to the Mott
insulating value of one electron per site ($n=1$), where $E_0$ is the ground
state energy, $L$ is the circumference of the system (assumed to have periodic
boundary conditions), and $(\hbar c/e)\Phi_{\rm c}$ is the magnetic flux
enclosed. We obtain an exact result for the asymptotic form of $D_{\rm c}(L)$
as $L\to \infty$ at $n=1$, which defines and yields an analytic expression for
the correlation length $\xi$ in the Mott insulating phase of the model as a
function of the on-site repulsion $U$. In the vicinity of the zero temperature
critical point U=0, $n=1$, we show that the charge stiffness has the
hyperscaling form $D_{\rm c}(n,L,U)=Y_+(\xi \delta, \xi/L)$, where $\delta
=|1-n|$ and $Y_+$ is a universal scaling function which we calculate. The
physical significance of $\xi$ in the metallic phase of the model is that it
defines the characteristic size of the charge-carrying solitons, or {\em
holons}. We construct an explicit mapping for arbitrary $U$ and $\xi \delta \ll
1$ of the holons onto weakly interacting spinless fermions, and use this
mapping to obtain an asymptotically exact expression for the low temperature
thermopower near the metal-insulator transition, which is a generalization to
arbitrary $U$ of a result previously obtained using a weak- coupling
approximation, and implies hole-like transport for $0<1-n\ll\xi^{-1}$.
