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\subsubsection{The ${\rm Z \to \bbbar}$ partial width}  An electroweak correction of great interest is the vertex correction to the $b$ ${\rm Z \to \bbbar$  partial width, which width. This correction  affects $\Gamma_Z$, the total Z width $\Gamma_{\rm Z}$, the leptonic branching fraction  $R_\ell$, the peak hadronic cross-section and, cross section $\sigma^{\rm peak}_{\rm had}$, and  most sensitively, $R_b $R_{\rm b}  \equiv \frac{\Gamma_b}{\Gamma_{had}}$. \Gamma_{\rm Z \to bbbar}/\Gamma_{\rm had}$.  $R_b$ was measured at LEP and SLC by tagging $b\bar{b}$ by the presence of one tagged $b$-jet and the efficiency was controlled by double tag. The present experimental value is $R_b = 0.21629 \pm 0.00066$ with a roughly equal sharing between systematic and statistical errors. The double $b$ tagging method is self-calibrating, and indeed most of the systematics are based on experimental tests related to the modeling of events, and should decrease with accumulated statistics. The SLD detector at SLC was the most efficient by the double effect of having a more precise detector, and the beam spot being smaller, thus allowing a more precise determination of the impact parameter of secondary hadrons. We expect the experimental conditions at TLEP to be similar to LEP with the exception that the beam size at the IP is smaller in all dimensions, ensuring that the $b$-tagging abilities should be rather similar to those of SLD than to those of LEP. \\ {\em A precision of $2-510^{-5}$ seems to be a reasonable goal for the measurement of on $R_b$ at TLEP}