  The paper describes an experiment aimed at studying muon capture by
${}^{3}\mathrm{He}$ nuclei in pure ${}^{3}\mathrm{He}$ and $\mathrm{D}_2 +
{}^{3}\mathrm{He}$ mixtures at various densities. Energy distributions of
protons and deuterons produced via $\mu^-+{}^{3}\mathrm{He}\to p+n+n + \nu_{\mu
}$ and $\mu^-+{}^{3} \mathrm{He} \to d+n + \nu_{\mu}$ are measured for the
energy intervals $10 - 49$ MeV and $13 - 31$ MeV, respectively. Muon capture
rates, $\lambda_\mathrm{cap}^p (\Delta E_p)$ and $\lambda_\mathrm{cap}^d
(\Delta E_d)$ are obtained using two different analysis methods. The
least--squares methods gives $\lambda_\mathrm{cap}^p = (36.7\pm 1.2) {s}^{-
1}$, $\lambda_\mathrm{cap}^d = (21.3 \pm 1.6) {s}^{- 1}$. The Bayes theorem
gives $\lambda_\mathrm{cap}^p = (36.8 \pm 0.8) {s}^{- 1}$,
$\lambda_\mathrm{cap}^d = (21.9 \pm 0.6) {s}^{- 1}$. The experimental
differential capture rates, $d\lambda_\mathrm{cap}^p (E_p) / dE_p $ and $
d\lambda_\mathrm{cap}^d (E_d) / dE_d$, are compared with theoretical
calculations performed using the plane--wave impulse approximation (PWIA) with
the realistic NN interaction Bonn B potential. Extrapolation to the full energy
range yields total proton and deuteron capture rates in good agreement with
former results.
