Measurement of $B^0_d - \overline{B^0_d}$ oscillations

${B}^0_d$ meson oscillations are measured in hadronic $\Zz$ decays using the charge of a lepton or the mean charge of an event hemisphere to sign the presence of a $b$ or a $\overline{b}$ quark when it is produced, and using the charge of a lepton emitted at large p$_t$ or of a D$^{\ast \pm}$ to sign the presence of a B or a $\bar{\mbox{B}}$ meson when it decays. With 3.2 million hadronic $\Zz$ decays registered by DELPHI between 1991 and 1994, the mass difference $\Delta m_d$ between the two physical $\mbox{B}^0_d$ states is measured in four channels: \begin{eqnarray} \Delta m_d &=& 0.523 \pm 0.072 \pm 0.043 ~ \mbox{ps}^{-1}~~(\Dstar - Q_{hem})\nonumber \\ \Delta m_d &=& 0.493 \pm 0.042 \pm 0.027 ~ \mbox{ps}^{-1}~~(\ell - Q_{hem})\nonumber \\ \Delta m_d &=& 0.499 \pm 0.053 \pm 0.015 ~ \mbox{ps}^{-1}~~((\pimora-\ell)-Q_{hem})\nonumber \\ \Delta m_d &=& 0.480 \pm 0.040 \pm 0.051 ~ \mbox{ps}^{-1}~~(\ell - \ell).\nonumber \end{eqnarray} Taking into account the statistical overlap between these measurements and the common systematic uncertainties, the combined result is: \Delta m_d = 0.496 \pm 0.034 ~ \mbox{ps}^{-1}.