\magnification=\magstep2


$$
\eqalign{
{\rm surface\ brightness\ \sigma} \quad & \equiv \quad 
         {\rm {{energy} \over {sq.arcsec\ sec } } } \cr
      \cr
                 & {or} \quad
         {\rm {{photon} \over {sq.arcsec\ sec } } } \cr
      \cr
                 & {or} \quad
         {\rm {{magnitude} \over {sq.arcsec } } } \cr
}
$$

$$
\eqalign{
\sigma \quad & = \quad {\rm{counts\ from\ star}\over{area}} \cr
      \cr
             & = \quad {\rm{ 1247\ counts\ per\ sec}\over{9\ sq.\ arcsec}} \cr
      \cr
             & = \quad {\rm{ 138\ counts\ per\ sec\ per\ sq.\ arcsec}} \cr
}
$$


$$
    {\rm E5\ means \ }\quad \quad 5 \quad = 
              \quad 10 \left( {{a - b}\over{a}}  \right) 
$$


$$
  \Phi(L) \thinspace dL \quad 
         = \quad { { {\rm number\ of\ galaxies\ in\ } [L, \thinspace L+dL] }
                        \over  { V } }
$$

$$
  \Phi(M) \thinspace dM \quad 
         = \quad { { {\rm number\ of\ galaxies\ in\ } [M, \thinspace M+dM] }
                        \over  { V } }
$$


$$
\eqalign{
{\rm N_{total}}  \quad  &= \quad \int{ \Phi(L) \thinspace dL }  \cr
     \cr
                        &= \quad \int{ \Phi(M) \thinspace dM }  \cr
}
$$


$$
  \Phi(L) \quad = \quad {{\Phi^*} \over{L^*}} 
                       {\left( {{L}\over{L^*}} \right)}^{\alpha}
                       e^{-{L/{L^*}}} 
$$


\bye
