

\subsection{\bf The Real World and $\chi^2$ Minimization}
\subsection{\bf Example of Two Variables---II}
\subsection{\bf Pictures of Two Variable Case}

\begin{slide}
\begin{itemize}
\item so that as a function of $\alpha_1$, we get

\vspace*{10pt}
\centerline{\psfig{figure=fig16.phys.ps,clip=true,width=2.5in}}
\vspace*{10pt}

\item and as a function of $\alpha_2$, we get

\vspace*{10pt}
\centerline{\psfig{figure=fig17.phys.ps,clip=true,width=4.0in}}
\vspace*{10pt}

with a valley with steep walls in $\alpha_1$ and gentle walls in
$\alpha_2$ direction.  

\item The predicted shift from Equation~(30), $\Delta\alpha_2 \sim
\frac{1}{A_2}$ and is typically large compared to $\Delta\alpha_1 \sim
\frac{1}{A_1}$.
\end{itemize}
\end{slide}

