A search for the indirect effects of the gravitational
interaction in extra dimensions on the process 
${\mathrm e}^+{\mathrm e}^-\rightarrow{\mathrm e}^+{\mathrm e}^-$
is presented. Data from the OPAL experiment at LEP at centre-of-mass
energies between 183~GeV and 209~GeV are compared with the predictions
of models including quantum gravity in extra dimensions. The data are
found to be consistent with the Standard Model, and 95\% confidence level
lower limits on the scale $M_{\rm s} >$ 1.00~TeV for 
$\lambda = +1$ and $M_{\rm s} >$ 1.15~TeV for $\lambda = -1$ are derived. 
These results are combined with limits derived from $\mu^+\mu^-$, 
$\tau^+\tau^-$, 
$\gamma\gamma$ and ZZ final states at OPAL. The combined 95\% confidence 
level lower limits are $M_{\rm s} >$ 1.03~TeV for $\lambda = +1$ and 
$M_{\rm s} >$ 1.17~TeV for $\lambda = -1$.