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We present the first direct measurements of ${\mathit{T}}_{\mathit{c}}$ as a function of uniaxial stress ${\mathit{p}}_{\mathit{i}}$ (i=a,b,c) along the crystal axes for an untwinned ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ single crystal. ${\mathit{T}}_{\mathit{c}}$ is linear in ${\mathit{p}}_{\mathit{i}}$ with slopes ${\mathit{dT}}_{\mathit{c}}$/${\mathit{dp}}_{\mathit{a}}$=-2.0\ifmmode\pm\else\textpm\fi{}0.2 K/GPa, ${\mathit{dT}}_{\mathit{c}}$/${\mathit{dp}}_{\mathit{b}}$=+1.9\ifmmode\pm\else\textpm\fi{}0.2 K/GPa, and ${\mathit{dT}}_{\mathit{c}}$/${\mathit{dp}}_{\mathit{c}}$=-0.3\ifmmode\pm\else\textpm\fi{}0.1 K/GPa. These results confirm predictions based on thermal expansion measurements [C. Meingast et al., Phys. Rev. Lett. 67, 1634 (1991)] and show that the small hydrostatic pressure dependence of ${\mathit{T}}_{\mathit{c}}$ in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ is due to a cancellation of large and opposite effects in the a-b plane.

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