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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline22355}%
$45^\circ$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline22357}%
$\tan^{-1} 4$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline22359}%
$\sim 76^\circ$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline22363}%
$\zeta<80^{\circ}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline22365}%
$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.01$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline22367}%
$\zeta<60^{\circ}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline22371}%
$\zeta<45^{\circ}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline22628}%
$\sim\!76^\circ$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline22638}%
$25^\circ$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline22640}%
$50^\circ$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline22642}%
$75^\circ$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline22656}%
$-10^\circ$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline22658}%
$+20^\circ$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline22660}%
$280^\circ$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline22666}%
$2\mu{\rm m}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline22678}%
$6.5^\circ K km^{-1}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline22690}%
$7^\circ$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline22698}%
$\tan^5$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline22702}%
$\beta~(=H_0/r_0)$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline22706}%
$\beta$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline22933}%
$70^\circ$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline22935}%
$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.05$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline22947}%
$93^\circ$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline22949}%
$=93^\circ$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline22955}%
$1\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.0$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline22957}%
$80^\circ$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline22959}%
$\nu=p_w/p_s$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline22961}%
$\nu=\rho_w/\rho_s$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23162}%
$30^\circ$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23164}%
$\zeta=70^\circ$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23168}%
$\zeta_{obs}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23172}%
$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.4$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23174}%
$81^\circ$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23176}%
$0\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.8$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23178}%
$82^\circ$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23180}%
$1\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.6$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23182}%
$83^\circ$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23186}%
$84^\circ$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23188}%
$7\hspace{-0.05em}^{'\hspace{-0.1em}'}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23190}%
$85^\circ$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23194}%
$86^\circ$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23196}%
$45\hspace{-0.05em}^{'\hspace{-0.1em}'}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23198}%
$87^\circ$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23200}%
$150\hspace{-0.05em}^{'\hspace{-0.1em}'}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23202}%
$88^\circ$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23204}%
$340\hspace{-0.05em}^{'\hspace{-0.1em}'}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23206}%
$89^\circ$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23208}%
$620\hspace{-0.05em}^{'\hspace{-0.1em}'}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23212}%
$1100\hspace{-0.05em}^{'\hspace{-0.1em}'}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23214}%
$91^\circ$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23216}%
$1900\hspace{-0.05em}^{'\hspace{-0.1em}'}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23220}%
$92^\circ$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23222}%
$3200\hspace{-0.05em}^{'\hspace{-0.1em}'}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23228}%
$\zeta=84^\circ$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23469}%
$\zeta=80^\circ$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23471}%
$\zeta=83^\circ$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath23457}%
\begin{displaymath}\Delta \zeta = F \left(
  \frac{0^\circ\hspace{-0.37em}.\hspace{0.02em}55445
                - 0^\circ\hspace{-0.37em}.\hspace{0.02em}01133 E
                          + 0^\circ\hspace{-0.37em}.\hspace{0.02em}00202 E^2}
             {1 + 0.28385 E +0.02390 E^2} \right) \end{displaymath}%
\lthtmldisplayZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23475}%
$E=90^\circ-\zeta_{true}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23495}%
$1\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.5$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23499}%
$3\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.2$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23503}%
$4\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.9$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23507}%
$5\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.8$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23511}%
$6\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.1$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23515}%
$7\hspace{-0.05em}^{'\hspace{-0.1em}'}\hspace{-0.4em}.1$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23523}%
$21\hspace{-0.05em}^{'\hspace{-0.1em}'}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23527}%
$43\hspace{-0.05em}^{'\hspace{-0.1em}'}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23531}%
$92\hspace{-0.05em}^{'\hspace{-0.1em}'}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23537}%
$220\hspace{-0.05em}^{'\hspace{-0.1em}'}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23720}%
$l^{I\!I}=90^{\circ}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23722}%
$b^{I\!I}=0$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23896}%
$l^{I\!I}=53^{\circ},b^{I\!I}=+25^{\circ}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline23995}%
$\alpha=18^{\rm h},\delta=+30^{\circ}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline24798}%
$\times n$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline24800}%
$m \geq n$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline24802}%
$m \times n$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline24806}%
$w_{ii} \geq 0$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25275}%
$\cdot~[diag(1/$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline25277}%
$_{j})]
           \cdot ($%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}

\setlength {\parskip}{\medskipamount}
%

\stepcounter{subsection}

\setlength {\parskip}{\medskipamount}
%

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline26731}%
$2^{\circ}
                        \hspace{-0.37em}.\hspace{0.02em}4$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline26733}%
$42^{\circ}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline27323}%
$0\!-\!\pi$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline27383}%
$61^\circ$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline27391}%
$+1^{\circ}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline27397}%
$24^{h}\,59^{m}\,59^{s}.999$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline27464}%
$[\,\theta,\phi~]$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline27478}%
$[\,\Delta x,\Delta y, \Delta z\,]$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline27484}%
${\bf D}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline27486}%
${\bf V1}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline27488}%
${\bf V2}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline27490}%
$<{\bf V1}+{\bf D}>$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline27492}%
$(1-{\bf D}\cdot{\bf V1})$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline27494}%
$\delta E$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline27498}%
${\tan \delta E\approx\delta E}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline27504}%
$\delta E \cos E$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline27506}%
$\delta E \sin E$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline27512}%
$\cos \delta E$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline27514}%
$(1-\delta E^2 /2)$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline27518}%
$\equiv$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline27524}%
$[\theta,\phi,\dot{\theta},\dot{\phi}]$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline27750}%
$\lambda,\beta$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline27752}%
$l^{I\!I},b^{I\!I}$%
\lthtmlinlinemathZ
\hfill\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure27550}%
\begin{figure}\begin{center}
\begin{tabular}{|cccccc|}   \hline
& & & & & \\\hspace{5em} & \hspace{5em} & \hspace{5em} &
   \hspace{5em} & \hspace{5em} & \hspace{5em}  \\\multicolumn{2}{|c}{\hspace{0em}
\fbox {\parbox{8.5em}{\center \vspace{-2ex}
                                                   mean $[\,\alpha,\delta\,]$, FK4, \\                                                   any equinox
                                                   \vspace{0.5ex}}}
} &
 \multicolumn{2}{c}{\hspace{0em}
\fbox {\parbox{8.5em}{\center \vspace{-2ex}
                                                   mean $[\,\alpha,\delta\,]$, FK4,
                                                   no $\mu$, any equinox
                                                   \vspace{0.5ex}}}
} &
\multicolumn{2}{c|}{\hspace{0em}
\fbox {\parbox{8.5em}{\center \vspace{-2ex}
                                                   mean $[\,\alpha,\delta\,]$, FK5, \\                                                   any equinox
                                                   \vspace{0.5ex}}}
} \\& \multicolumn{2}{|c|}{} & \multicolumn{2}{c|}{} & \\\multicolumn{2}{|c}{space motion} & \multicolumn{1}{c|}{} & &
   \multicolumn{2}{c|}{space motion} \\\multicolumn{2}{|c}{-- E-terms} &
   \multicolumn{2}{c}{-- E-terms} & \multicolumn{1}{c|}{} & \\\multicolumn{2}{|c}{precess to B1950} & \multicolumn{2}{c}{precess to B1950} &
   \multicolumn{2}{c|}{precess to J2000} \\\multicolumn{2}{|c}{+ E-terms} &
   \multicolumn{2}{c}{+ E-terms} & \multicolumn{1}{c|}{} & \\\multicolumn{2}{|c}{FK4 to FK5, no $\mu$} &
   \multicolumn{2}{c}{FK4 to FK5, no $\mu$} & \multicolumn{1}{c|}{} & \\\multicolumn{2}{|c}{parallax} & \multicolumn{1}{c|}{} & &
   \multicolumn{2}{c|}{parallax} \\& \multicolumn{2}{|c|}{} & \multicolumn{2}{c|}{} & \\ \cline{2-5}
\multicolumn{3}{|c|}{} & & & \\& \multicolumn{4}{c}{
\fbox {\parbox{18em}{\center \vspace{-2ex}
                                   FK5, J2000, current epoch, geocentric
                                          \vspace{0.5ex}}}
} & \\\multicolumn{3}{|c|}{} & & & \\& \multicolumn{4}{c}{light deflection} & \\& \multicolumn{4}{c}{annual aberration} & \\& \multicolumn{4}{c}{precession/nutation} & \\\multicolumn{3}{|c|}{} & & & \\& \multicolumn{4}{c}{
\fbox {Apparent $[\,\alpha,\delta\,]$}
} & \\\multicolumn{3}{|c|}{} & & & \\& \multicolumn{4}{c}{Earth rotation} & \\\multicolumn{3}{|c|}{} & & & \\& \multicolumn{4}{c}{
\fbox {Apparent $[\,h,\delta\,]$}
} & \\\multicolumn{3}{|c|}{} & & & \\& \multicolumn{4}{c}{diurnal aberration} & \\\multicolumn{3}{|c|}{} & & & \\& \multicolumn{4}{c}{
\fbox {Topocentric $[\,h,\delta\,]$}
} & \\\multicolumn{3}{|c|}{} & & & \\& \multicolumn{4}{c}{$[\,h,\delta\,]$\ to $[\,Az,El~]$} & \\\multicolumn{3}{|c|}{} & & & \\& \multicolumn{4}{c}{
\fbox {Topocentric $[\,Az,El~]$}
} & \\\multicolumn{3}{|c|}{} & & & \\& \multicolumn{4}{c}{refraction} & \\\multicolumn{3}{|c|}{} & & & \\& \multicolumn{4}{c}{
\fbox {Observed $[\,Az,El~]$}
} & \\& & & & & \\& & & & & \\ \hline
\end{tabular}
\end{center}
\vspace{-0.5ex}
Star positions are published or catalogued using
one of the mean $[\,\alpha,\delta\,]$\ systems shown at
the top.  The ``FK4'' systems
were used before about 1980 and are usually
equinox B1950.  The ``FK5'' system, equinox J2000, is now preferred,
or rather its modern equivalent, the International Celestial Reference
Frame (in the optical, the Hipparcos catalogue).
The figure relates a star's mean $[\,\alpha,\delta\,]$\ to the actual
line-of-sight to the star.
Note that for the conventional choices of equinox, namely
B1950 or J2000, all of the precession and E-terms corrections
are superfluous.
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