A partial-wave analysis of 9082 $\ensuremath{\eta}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}n$ events produced in the reaction ${\ensuremath{\pi}}^{\ensuremath{-}}\stackrel{\ensuremath{\rightarrow}}{p}\ensuremath{\eta}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}n$ at $18.3 \mathrm{GeV}/c$ has been carried out using data from experiment 852 at Brookhaven National Laboratory. The data are dominated by ${J}^{\mathrm{PC}}{=0}^{\ensuremath{-}+}$ partial waves consistent with observation of the $\ensuremath{\eta}(1295)$ and the $\ensuremath{\eta}(1440).$ The mass and width of the $\ensuremath{\eta}(1295)$ were determined to be $1282\ifmmode\pm\else\textpm\fi{}5 \mathrm{MeV}$ and $66\ifmmode\pm\else\textpm\fi{}13 \mathrm{MeV},$ respectively, while the $\ensuremath{\eta}(1440)$ was observed with a mass of $1404\ifmmode\pm\else\textpm\fi{}6 \mathrm{MeV}$ and a width of $80\ifmmode\pm\else\textpm\fi{}21 \mathrm{MeV}.$ Other partial waves of importance include the ${1}^{++}$ and the ${1}^{+\ensuremath{-}}$ waves. Results of the partial wave analysis are combined with results of other experiments to estimate ${f}_{1}(1285)$ branching fractions. These values are considerably different from current values determined without the aid of amplitude analyses.