\magnification=\magstep1

$$
{{N_b}\over{N_a}} \quad = \quad \left( {{g_b}\over{g_a}} \right) \thinspace
       e^{-(E_b - E_a)/kT}
$$

$$
E \quad \sim \quad kT
$$

$$
{{N_{i+1}}\over{N_i}} \quad = \quad
    {{2 Z_{i+1}}\over{n_e Z_i}} \thinspace
    \left( {{2 \pi m_e k T}\over{h^2}} \right)^{3/2} \thinspace
    e^{- \chi_i/kT}
$$

$$
Z \quad = \quad g_1 \ + \ \sum_{j=2}^{\infty} \thinspace g_j \thinspace
                     e^{-(E_j - E_1)/kT)}
$$

$$
{{N_{II}}\over{N_I}} \quad \simeq \quad
    {{1}\over{n_e}} \thinspace
    \left( {{2 \pi m_e k T}\over{h^2}} \right)^{3/2} \thinspace
    e^{- \chi_i/kT}
 \quad \propto \quad
      T^{3/2} e^{- \chi_i/kT}
$$

\bye
