A model for the reaction $\ensuremath{\pi}+N\ensuremath{\rightarrow}2\ensuremath{\pi}+N$ at low energies, with $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ scattering lengths as parameters, discussed in a previous analysis is extended by removing the assumption that $\frac{{a}_{0}}{{a}_{2}}=\frac{5}{2}$. The parameters are determined by using the ${\ensuremath{\pi}}^{+}$ angular distribution from ${\ensuremath{\pi}}^{\ensuremath{-}}+p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}+{\ensuremath{\pi}}^{+}+n$ at 430 Mev and the total cross section for ${\ensuremath{\pi}}^{+}+p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}+{\ensuremath{\pi}}^{+}+n$ at 470 Mev. We find two acceptable sets for the $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ scattering lengths: ${a}_{0}=0.50$ ${\mathrm{\ensuremath{\mu}}}^{\ensuremath{-}1}$, ${a}_{1}=0.07$ ${\mathrm{\ensuremath{\mu}}}^{\ensuremath{-}1}$, ${a}_{2}=0.16$ ${\mathrm{\ensuremath{\mu}}}^{\ensuremath{-}1}$ and ${a}_{0}=0.65$ ${\mathrm{\ensuremath{\mu}}}^{\ensuremath{-}1}$, ${a}_{1}=0.07$ ${\mathrm{\ensuremath{\mu}}}^{\ensuremath{-}1}$, ${a}_{2}=\ensuremath{-}0.14$ ${\mathrm{\ensuremath{\mu}}}^{\ensuremath{-}1}$. The total cross sections for the various charge channel and for single partial waves are computed. The predictions of this model are in qualitative agreement with experiment.