\magnification=\magstep1 


$$
L \quad = \quad {{1}\over{n \pi d^2}}
$$


$$
L \quad = \quad {{1}\over{n \pi d^2}} \quad = \quad {{1}\over{n \sigma}}
$$


$$
{\rm Luminosity\ } \quad = \quad 4 \pi R^2 \ \sigma \thinspace T_{eff}^4
$$

$$
f(v, v+\Delta v) \quad = \quad \left( {{m}\over{2 \pi k T}} \right) \thinspace
                       e^{(-m v^2 / 2 k T)} \thinspace
                       4 \pi v^2 \Delta v
$$

$$
v_{\rm rms} \quad = \quad \sqrt{ {{3 kT}\over{m}} }
$$

$$
dI \quad = \quad - I \thinspace \rho \kappa ds
$$

$$
{{dI}\over{I}} \quad = \quad - \rho \kappa ds
$$

$$
{{I}\over{I_0}} \quad = \quad e^{- \rho \kappa s}
$$

$$
\rho \kappa s \quad = \quad 1 \qquad \Rightarrow  \qquad
            s \quad = \quad {{1}\over{\rho \kappa}}
$$

$$
{\rm mfp} \quad = \quad {{1}\over{\rho \kappa}} 
     \qquad \qquad
{\rm mfp} \quad = \quad {{1}\over{n \sigma}} 
$$


$$
I \quad = \quad I_0 \ e^{- \rho \kappa s}  \qquad {\rm becomes \ } \qquad
     I \quad = \quad I_0 \ e^{- \tau} 
$$

$$
\sigma_{bf} \quad  = \quad
         1.31 \times 10^{-19} \ {{1}\over{n^5}} \ 
         {\left( {{\lambda} \over{5000 \thinspace \AA}} \right)}^3  \  {\rm m}^2
$$
        


\bye
