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We have reconstructed the radiative decays $\chi_{b}(1P) \to \Upsilon(1S) \gamma $ and $\chi_{b}(2P) \to \Upsilon(1S) \gamma $ in $p \bar{p}$ collisions at $\sqrt{s} = 1.8$ TeV, and measured the fraction of $\Upsilon(1S)$ mesons that originate from these decays. For $\Upsilon(1S)$ mesons with $p^{\Upsilon}_{T}>8.0$ GeV/$c$, the fractions that come from $\chi_{b}(1P)$ …