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An electroweak correction of great interest is the vertex correction to the ${\rm Z} \to \bbbar$ partial width. This correction affects the total Z width $\Gamma_{\rm Z}$, the leptonic branching fraction $R_\ell$, the peak hadronic cross section $\sigma^{\rm peak}_{\rm had}$, and most sensitively, $R_{\rm b} \equiv \Gamma_{\rm Z \to \bbbar}/\Gamma_{\rm had}$. At LEP and SLC, $R_{\rm b}$ was measured by tagging the presence of one b-quark jet, and the efficiency was controlled by the ``double tag'' method. The present experimental value, $R_{\rm b} = 0.21629 \pm 0.00066$, has a roughly equal sharing between systematic and statistical uncertainties.   Because the double b-tagging method is self-calibrating, its accuracy is expected to improve with accumulated statistics. The SLD detector at SLC had the best efficiency for this selection, by the twofold effect of a more granular vertex detector and a smaller beam spot, which allowed a more precise determination of the impact parameter of secondary hadrons. While the experimental conditions at TLEP are expected to be similar as those at LEP, the beam spot size will be very significantly smaller in all dimensions than at SLC, and a next-generation vertex detector will be used. The b-tagging capabilities should therefore be similar to or better than those of SLD.\\  {\em {\bf\it  A precision of ${\it 2}$ to ${\it 5 \times 10^{-5}}$ seems therefore to be a reasonable goal for the measurement of $R_{\rm b}$ at TLEP.}