the tilt of the bottom of the wine bottle as well as the depth of the second minimum. We have then at our disposal four parameters in the effective Lagrangian: $\lambda, c, \epsilon_1$ and $\epsilon_2$. These parameters must be restricted so as to give the proper pion mass, pion decay constant, a reasonable value for the $\sigma$ mass, PCAC in the weak field limit, and the condition that the ground state of the theory occur at $\sigma = f_{\pi}$ and $\mbox{\boldmath $\pi$} = {\bf 0}$. We obtain $$\begin{aligned}
m_{\pi}^2 &=& \lambda f_{\pi}^2 - c^2 \, ,\\
m_{\sigma}^2 &=& 2 \lambda f_{\pi}^2 + m_{\pi}^2 - \epsilon_2 \, ,\\
f_{\pi} m_{\pi}^2 &=& \epsilon_1 + \epsilon_2 f_{\pi} \, .\end{aligned}$$ The numerical values chosen in this paper are $m_{\pi} = 140$ MeV and $f_{\pi} = 94.5$ MeV. Lin and Serot [@lin] have emphasized that the $\sigma$ meson in this model is [*not*]{} to be identified with the exchange of two correlated pions in the isoscalar - scalar channel in the nucleon - nucleon interaction. That exchange is rather broadly distributed in mass with a peak around 600 MeV. Good phenomenology for low energy pion and nucleon dynamics is obtained if the $\sigma$ meson has 