%%  agums.sty -- August 6, 1996 version
%
%%  revisions by Amy Hendrickson, TeXnology Inc, 1/5/96
%
%%  This file (agums.sty) creates pages for first-time
%   submission to AGU editors (i.e., for peer review
%   and copyediting).


\def\revtex@ver{4}
     \def\revtex@date{August 6, 1996}
     \def\revtex@org{AGU}
     \def\revtex@jnl{JGR}
     \def\revtex@genre{manuscript}
     \typeout{\revtex@org\space \revtex@genre\space substyle,
     v\revtex@ver\space <\revtex@date>.}
     \def\revtex@pageid{\xdef\@thefnmark{\null}
%\@footnotetext{This \revtex@genre\space 
% was prepared with the \revtex@org\space
% \LaTeX\ macros v\revtex@ver.}
}

\def\genre@MS{manuscript}
\def\genre@PP{preprint}
\ifx\revtex@genre\genre@MS
\ifnum\@ptsize<2
\typeout{Warning: Undersize \revtex@genre\space font (1\@ptsize\space 
pts).
Using 12pt documentstyle option.}
\@input{art12.sty}
\fi
\fi

\def\ps@plaintop{\let\@mkboth\@gobbletwo
\def\@oddfoot{}\def\@oddhead{\rm\hfil\thepage}
\def\@evenfoot{}\let\@evenhead\@oddhead}
\ps@plaintop
%\pretolerance=10000
\@rightskip=\z@ plus 4em\rightskip\@rightskip
\textwidth=6.25in
\textheight=8.6in
\topmargin=0in
\headheight=9pt
\headsep=.4in
\oddsidemargin=0in
\evensidemargin=0in
\parindent=2em
\parskip=\z@
\voffset=-0.25in
\let\footnotesize=\normalsize
\def\@tightleading{1.1}
\def\@doubleleading{1.6}
\def\baselinestretch{\@doubleleading}
\def\tighten{\def\baselinestretch{\@tightleading}}
\let\tightenlines=\tighten
\let\singlespace=\relax
\let\doublespace=\relax
\def\sec@upcase#1{\relax{#1}}
\def\eqsecnum{
\@newctr{equation}[section]
\def\theequation{\hbox{\normalsize\arabic{section}-\arabic{equation}}}
}
\def\@journalname{The Geopolitical Journal}
\def\cpr@holder{American Geophysical Union}
\def\received#1{\gdef\@recvdate{#1}} \received{}
\def\revised#1{\gdef\@revisedate{#1}} \revised{}
\def\accepted#1{\gdef\@accptdate{#1}} \accepted{}
\def\journalid#1#2{\gdef\@jourvol{#1}\gdef\@jourdate{#2}}
\def\articleid#1#2{\gdef\@startpage{#1}\gdef\@finishpage{#2}}
\def\paperid#1{\gdef\@paperid{#1}} \paperid{}
\def\ccc#1{\gdef\CCC@code{#1}} \ccc{}
\def\cpright#1#2{\@nameuse{cpr@#1} \gdef\cpr@year{#2}
\typeout{`#1' copyright \cpr@year.}}
\newcount\@cprtype \@cprtype=\@ne
\def\cpr@AGU{\@cprtype=1}
\def\cpr@PD{\@cprtype=2}
\def\cpr@Crown{\@cprtype=3}
\def\cpr@none{\@cprtype=4}
\def\cpr@year{\number\year}
\def\@slug{\par\noindent
\ifcase\@cprtype
\relax
\or
Copyright \cpr@year\space by the \cpr@holder.
\or
This paper is not subject to U.S. copyright.
Published in \cpr@year\space by the \cpr@holder.
\or
Published in \cpr@year\space by the \cpr@holder.
\or
No copyright is claimed for this article.
\fi
\par\noindent
Paper number \@paperid.\par\noindent
\CCC@code
}
\def\lefthead#1{\gdef\@versohead{#1}} \lefthead{\relax}
\def\righthead#1{\gdef\@rectohead{#1}} \righthead{\relax}
\newdimen\@rhdwidth \@rhdwidth=30pc
\def\@runheads{\@tempcnta\c@page\hsize\@rhdwidth\parindent\z@
\setbox\@tempboxa\hbox{%
\small\expandafter\uppercase\expandafter{\@versohead}:
\expandafter\uppercase\expandafter{\@rectohead}}
\@tempdima\wd\@tempboxa \advance\@tempdima by-\@rhdwidth
\ifdim \@tempdima >\z@
\typeout{Running head information too long by 
\the\@tempdima.}\fi
\@whilenum \@tempcnta >0\do{
\vskip 3ex
\hbox{\copy\@tempboxa\hfil}
\advance\@tempcnta by\m@ne}
}

\def\slugcomment#1{\gdef\slug@comment{#1}} \slugcomment{}
\newdimen\@slugcmmntwidth \@slugcmmntwidth \textwidth
\long\def\@makeslugcmmnt{\ifx\slug@comment\@empty\relax\else
\vskip 5ex
\setbox\@tempboxa\hbox{\slug@comment}
\ifdim \wd\@tempboxa >\@slugcmmntwidth
\hbox to\textwidth{\parbox\@slugcmmntwidth\slug@comment\hfil}
\else
\hbox to\textwidth{\box\@tempboxa\hfil}
\fi
\fi}
\def\@rcvaccrule{\vrule\@width1.75in\@height0.5pt\@depth\z@}

\def\@dates{{\rm Received}\space%
\ifx\@recvdate\@empty\@rcvaccrule\else\@recvdate\fi%
\ifx\@revisedate\@empty\relax\else%
; \space{\rm revised}\space\@revisedate\fi%
\ifx\@accptdate\@empty\else
; \space{\rm accepted}\space%
\@accptdate.\fi%
}

%=======
\def\@authaddrs{\ifx\authaddr@list\@empty\relax
\else
\noindent\minipage{20pc}\parindent=1em
\small\authaddr@list\endminipage
\gdef\authaddr@list{}
\fi}

\def\@sluginfo{{\parindent\z@\vskip 9\p@
\footnoterule
\vspace{2ex}
\@authaddrs\par
\vspace{2ex}
\@dates
\hsize\@fmwidth
%\@runheads
}}
%=======
\def\@authaddrs{\ifx\authaddr@list\@empty\relax
\else
{\footnotesize\authaddr@list}
\gdef\authaddr@list{}
\fi}

\def\@sluginfo{{\vspace{4ex}
\@dates
\vskip1pt
\@makeslugcmmnt}}

\let\dates=\relax
\let\sluginfo=\relax
\let\forcesluginfo=\relax

\def\abstract{%
\vspace{\fill}
{\flushleft Short title:\small\quad
  \expandafter\uppercase\expandafter{\@rectohead}
\endflushleft}
\vspace{\fill}
\clearpage
\normalsize{\bf Abstract.}
}
\def\endabstract{\par\clearpage}
\def\title#1{{\def\baselinestretch{\@tightleading}
\flushleft\large\bf{#1}\endflushleft}
%\thispagestyle{empty}
}
\def\author#1{{\topsep\z@\flushleft\normalsize#1\endflushleft}}
\def\affil#1{\vspace*{-2.5ex}{\topsep\z@\flushleft#1\endflushleft}}
\def\altaffilmark#1{$^{#1}$}
\def\and{\vspace*{-0.5ex}{\topsep\z@\flushleft and\endflushleft}}
\newtoks\@temptokenb
\def\authaddr@list{}
\def\authoraddress#1{
\@temptokena={\vskip1sp\noindent\hskip1em\relax#1}
\@temptokenb=\expandafter{\authaddr@list}
\xdef\authaddr@list{\the\@temptokenb\the\@temptokena}}
\let\authoraddr=\authoraddress
\def\@keywordtext{Subject headings}
\def\@keyworddelim{---}
\let\keywords=\@gobble
\let\subjectheadings=\keywords
\def\@kwds#1{#1\relax}
\skip\footins 4ex plus 1ex minus .5ex
\footnotesep 3ex

% Make Section heads with numbers 
% and text wraps flush left.

\setcounter{secnumdepth}{0}

\def\@sect#1#2#3#4#5#6[#7]#8{\ifnum #2>\c@secnumdepth
  \let\@svsec\@empty\else
  \refstepcounter{#1}\edef\@svsec{\csname  the#1\endcsname.\ \ }\fi%
     %
\@tempskipa #5\relax
\ifdim \@tempskipa>\z@
  \begingroup #6\relax
% \@hangfrom{
  \hskip #3\relax%
  \@svsec%}%
  {\hyphenpenalty10000\relax\interlinepenalty \@M #8\par}%
  \endgroup%
\csname #1mark\endcsname{#7}\addcontentsline
  {toc}{#1}{\ifnum #2>\c@secnumdepth \else
  \protect\numberline{\csname the#1\endcsname}\fi
  #7}\else%***
     \def\@svsechd{#6\hskip #3\relax
%% \relax added 2 May 90
  \@svsec #8\ifnum#2=4:\else\ifnum#2=3.\fi\fi\csname 
  #1mark\endcsname%
  {#7}\addcontentsline
  {toc}{#1}{\ifnum #2>\c@secnumdepth\else
  \protect\numberline{\csname 
  the#1\endcsname}\fi
  #7}}\fi
  \@xsect{#5}}

% \@startsection 
% {NAME}{LEVEL}{INDENT}{BEFORESKIP}{AFTERSKIP}{STYLE}
%            optional * [ALTHEADING]{HEADING}
%    Generic command to start a section.
%    NAME       : e.g., `subsection'
%    LEVEL      : a number, denoting depth of 
%                 section -- e.g., chapter=1,
%                 section = 2, etc.
%    INDENT     : Indentation of heading from 
%                 left margin
%    BEFORESKIP : Absolute value = skip to leave 
%                 above the heading.  If negative, 
%                 then paragraph indent of text 
%                 following heading is suppressed.
%    AFTERSKIP  : if positive, then skip to leave 
%                 below heading, else negative of 
%                 skip to leave to right of run-in 
%                 heading.
%    STYLE      : commands to set style
%  If `*' missing, then increments the counter.  
%  If it is present, then there should be no 
%  [ALTHEADING] argument.  Uses the counter 
%  `secnumdepth' whose value is the highest 
%  section level that is to be numbered.

\def\section{\@startsection {section}{1}{-\parindent}
{3ex plus .5ex}{1ex plus .2ex}{\large\bf\raggedright}}
\def\subsection{\@startsection{subsection}{2}{-\parindent}
{3ex plus .5ex}{1ex plus .2ex}{\normalsize\bf\raggedright}}
\def\subsubsection{\@startsection{subsubsection}{3}{\parindent}
{1sp}{-1em}{\normalsize\bf}}
\def\subsubsubsection{\@startsection{paragraph}{4}{\parindent}
{1sp}{-1em}{\normalsize\bf}}
\let\paragraph\subsubsubsection

\def\thesection{\@arabic{\c@section}}
\def\thesubsection{\thesection.\@arabic{\c@subsection}}
\def\thesubsubsection{\thesubsection.\@arabic{\c@subsubsection}}
\def\theparagraph{\thesubsubsection.\@arabic{\c@paragraph}}

\def\appendix{\par
\global\c@section=0
\global\c@equation=0
\def\theequation{\hbox{\Alph{section}\arabic{equation}}}
\let\body@section=\section
\def\section{\global\c@equation=0\relax
\setcounter{table}{0}\refstepcounter{section}%
\def\@currentlabel{\Alph{section}}%
\body@section*}}

\newcounter{cureqno}
\newenvironment{mathletters}{\refstepcounter{equation}%
\setcounter{cureqno}{\value{equation}}%
\let\@curtheeqn\theequation%
\edef\cur@eqn{\csname theequation\endcsname}%
\def\theequation{\cur@eqn\alph{equation}}%
\setcounter{equation}{0}}%
{\let\theequation\@curtheeqn%
\setcounter{equation}{\value{cureqno}}\hskip-4pt\relax}
\def\eqnum#1{\def\theequation{#1}\let\@currentlabel\theequation
\addtocounter{equation}{\m@ne}}
\def\references{\clearpage\@startsection{section}{1}{\z@}
{3ex plus .5ex}{1ex plus .2ex}{\large\bf}*{References}
\bgroup\parindent=\z@\parskip=\z@
\def\refpar{\par\hangindent=3em\hangafter=1}}
\def\endreferences{\refpar\egroup
%% new ==>>
\vskip\baselineskip
\footnoterule
\parindent=0pt
\leftskip=0pt
\@authaddrs
\vskip1pt
\@dates
\doaltaffils
\vspace{4ex}
\@makeslugcmmnt
%% <==
\revtex@pageid\normalsize}

\def\forcesluginfo{\vskip\baselineskip
\footnoterule
\parindent=0pt
\leftskip=0pt
\@authaddrs
\vskip1pt
\@dates
\doaltaffils
\vspace{4ex}
\@makeslugcmmnt
\revtex@pageid\normalsize}

\def\thebibliography#1{\clearpage\@startsection{section}{1}{\z@}
{3ex plus .5ex}{1ex plus .2ex}{\large\bf}*{References}
\list{\null}{\leftmargin 3em\labelwidth\z@\labelsep\z@\itemindent -3em
\itemsep=\z@\usecounter{enumi}}
\def\refpar{\relax}
\def\newblock{\hskip .11em plus .33em minus .07em}
\sloppy\clubpenalty4000\widowpenalty4000
\sfcode`\.=1000\relax}

\def\endthebibliography{\endlist
%% new ==>>
{\vskip\baselineskip
\leftskip-3em
\footnoterule
{\parindent=1em
\@authaddrs}
\vskip1pt
\@dates
\doaltaffils
\vspace{4ex}
\@makeslugcmmnt
%% <==
\revtex@pageid}\normalsize}

\def\@biblabel#1{\relax}

\def\reference{\relax\refpar}
\def\markcite#1{#1\relax}


\def\figurenum#1{\def\thefigure{#1}\let\@currentlabel\thefigure
\addtocounter{figure}{\m@ne}}

\def\sidehead#1{\noalign{\vskip 1.5ex}
\multicolumn{\pt@ncol}{@{\hskip\z@}l}{#1}\pt@nl
\noalign{\vskip .5ex}}
\def\set@tblnotetext{\def\tablenotetext##1##2{{%
\@temptokena={\vspace*{.5ex}{%
%\parbox{\pt@width}
{\hsize=\pt@width\hskip1em\strut$^{\rm ##1}$##2}\par}}%
\@temptokenb=\expandafter{\tblnote@list}
\xdef\tblnote@list{\the\@temptokenb\the\@temptokena}}}}

\def\spew@tblnotes{\ifx\tblnote@list\@empty\relax
\else\vskip1sp
{\small\tblnote@list}
\gdef\tblnote@list{}\fi}

\newcounter{plate}
\def\theplate{\@arabic\c@plate}
\def\fps@plate{bp}
\def\ftype@plate{4}
\def\ext@plate{lof}
\def\fnum@plate{{\bf Plate \theplate.}}
\def\plate{\@float{plate}}
\let\endplate\end@float
\@namedef{plate*}{\@dblfloat{plate}}
\@namedef{endplate*}{\end@dblfloat}
\def\platenum#1{\def\theplate{#1}\let\@currentlabel\theplate
\addtocounter{plate}{\m@ne}}
\def\thefigure{\@arabic\c@figure}
\def\fnum@figure{{\bf Figure \thefigure.}}
\def\fnum@table{{\bf Table \thetable.}}
\def\fps@figure{bp}
\def\fps@table{bp}
\def\plotone#1{\centering \leavevmode
\epsfxsize=\columnwidth \epsfbox{#1}}
\def\plottwo#1#2{\centering \leavevmode
\epsfxsize=.45\columnwidth \epsfbox{#1} \hfil
\epsfxsize=.45\columnwidth \epsfbox{#2}}
\def\plotfiddle#1#2#3#4#5#6#7{\centering \leavevmode
\vbox to#2{\rule{0pt}{#2}}
\special{psfile=#1 voffset=#7 hoffset=#6 vscale=#5 hscale=#4 
angle=#3}}
\let\jnl@style=\it
\def\ref@jnl#1{{\jnl@style#1}}
\def\aj{\ref@jnl{Astron.\ J., }}
\def\apj{\ref@jnl{Astrophys.\ J., }}
\def\apjl{\ref@jnl{Astrophys.\ J., }} 
\def\apjs{\ref@jnl{Astrophys.\ J.\ (Supp.), }}
\def\aap{\ref@jnl{Astron.\ Astrophys., }}
\def\bams{\ref@jnl{Bull.\ Am.\ Meteorol.\ Soc., }}
\def\bssa{\ref@jnl{Bull.\ Seismol.\ Soc.\ Am., }}
\def\eos{\ref@jnl{Eos Trans.\ AGU, }} 
\def\epsl{\ref@jnl{Earth Planet.\ Sci.\ Lett., }}
\def\gca{\ref@jnl{Geochim.\ Cosmochim.\ Acta, }}
\def\gjras{\ref@jnl{Geophys.\ J.\ R.\ Astron.\ Soc., }}
\def\grl{\ref@jnl{Geophys.\ Res.\ Lett., }}
\def\gsab{\ref@jnl{Geol.\ Soc.\ Am.\ Bull., }}
\def\jatp{\ref@jnl{J.\ Atmos.\ Terr.\ Phys., }}
\def\jgr{\ref@jnl{J.\ Geophys.\ Res., }}
\def\jpo{\ref@jnl{J.\ Phys.\ Oceanogr., }} 
\def\mnras{\ref@jnl{Mon.\ Not.\ R.\ Astron.\ Soc., }} 
\def\mwr{\ref@jnl{Mon.\ Weather Rev., }}
\def\pepi{\ref@jnl{Phys.\ Earth Planet.\ Inter., }}
\def\pra{\ref@jnl{Phys.\ Rev.\ A, }}
\def\prl{\ref@jnl{Phys.\ Rev.\ Lett., }}
\def\pasp{\ref@jnl{Publ.\ A.\ S.\ P., }}
\def\qjrms{\ref@jnl{Q.\ J.\ R.\ Meteorol.\ Soc., }}
\def\rg{\ref@jnl{Rev.\ Geophys., }}
\def\rs{\ref@jnl{Radio Sci., }}
\def\usgsof{\ref@jnl{U.S.\ Geol.\ Surv.\ Open File Rep., }}
\def\usgspp{\ref@jnl{U.S.\ Geol.\ Surv.\ Prof.\ Pap., }}
\let\astap=\aap
\let\apjlett=\apjl
\let\apjsupp=\apjs

%% Add on, Aug 24, 1995
\def\lookforpunct{\ifcat\next]\else, \fi}
\def\dsr#1{\ifcase#1\or{\it Deep Sea Res.\ Part I}\or%
{\it Deep Sea Res.\ Part II}\fi\futurelet\next\lookforpunct}

\def\gras{{\frenchspacing\it Geophys. J. 
Int.}\futurelet\next\lookforpunct}

\def\prb{{\frenchspacing\it Phys. Rev. B Condens. Matter}%
\futurelet\next\lookforpunct}

\def\prc{{\frenchspacing\it Phys. Rev. C Nucl. Phys.}%
\futurelet\next\lookforpunct}

\def\prd{{\frenchspacing\it Phys. Rev. D Part. Fields}%
\futurelet\next\lookforpunct}

\def\pag{{\frenchspacing\it Pure Appl. Geophys.}%
\futurelet\next\lookforpunct}

%
\def\deg{\hbox{$^\circ$}}
\def\sun{\hbox{$\odot$}}
\def\earth{\hbox{$\oplus$}}
\def\lesssim{\mathrel{\hbox{\rlap{\hbox{\lower4pt\hbox{$\sim$}}}\hbox{
$<$}}}}
\def\gtrsim{\mathrel{\hbox{\rlap{\hbox{\lower4pt\hbox{$\sim$}}}\hbox{$
>$}}}}
\def\sq{\hbox{\rlap{$\sqcap$}$\sqcup$}}
\def\arcmin{\hbox{$^\prime$}}
\def\arcsec{\hbox{$^{\prime\prime}$}}
\def\fd{\hbox{$.\!\!^{\rm d}$}}
\def\fh{\hbox{$.\!\!^{\rm h}$}}
\def\fm{\hbox{$.\!\!^{\rm m}$}}
\def\fs{\hbox{$.\!\!^{\rm s}$}}
\def\fdg{\hbox{$.\!\!^\circ$}}
\def\farcm{\hbox{$.\mkern-4mu^\prime$}}
\def\farcs{\hbox{$.\!\!^{\prime\prime}$}}
\def\fp{\hbox{$.\!\!^{\scriptscriptstyle\rm p}$}}
\def\micron{\hbox{$\mu$m}}
\let\la=\lesssim
\let\ga=\gtrsim
\def\case#1#2{\hbox{$\frac{#1}{#2}$}}
\def\slantfrac#1#2{\hbox{$\,^#1\!/_#2$}}
\def\onehalf{\slantfrac{1}{2}}
\def\onethird{\slantfrac{1}{3}}
\def\twothirds{\slantfrac{2}{3}}
\def\onequarter{\slantfrac{1}{4}}
\def\threequarters{\slantfrac{3}{4}}
\def\ubvr{\hbox{$U\!BV\!R$}}
\def\ub{\hbox{$U\!-\!B$}} 
\def\bv{\hbox{$B\!-\!V$}} 
\def\vr{\hbox{$V\!-\!R$}} 
\def\ur{\hbox{$U\!-\!R$}} 
\def\ion#1#2{#1$\;${\small\rm\@Roman{#2}}\relax}
\def\nodata{\multicolumn{1}{c}{$\cdots$}}
\newcount\lecurrentfam
\def\LaTeX{\lecurrentfam=\the\fam \leavevmode L\raise.42ex
\hbox{$\fam\lecurrentfam\scriptstyle\kern-.3em A$}\kern-.15em\TeX}
\def\sizrpt{
(\fontname\the\font): em=\the\fontdimen6\font, ex=\the\fontdimen5\font
\typeout{
(\fontname\the\font): em=\the\fontdimen6\font, ex=\the\fontdimen5\font
}}
\def\format@date{\number\year\space\ifcase\month\or
January\or February\or March\or April\or May\or June\or
July\or August\or September\or October\or November\or December\fi
\space\number\day}
\def\fmtdate@id{File \jobname\space formatted \format@date.}

% Changes needed for all styles

% Alternate affiliations appearing 
% at the end of the article:

\def\altaffiltext#1#2{%
\global\advance\totalaffils by 1
\expandafter\xdef\csname altaffil#1\endcsname{\noindent%
\hskip1em$^{#1}${#2}}}

\def\doaltaffils{{\parindent=0pt
\loop\ifnum\affilnum<\totalaffils
\ifnum\affilnum=0
\vskip14pt
\footnoterule
\vspace{1sp}\fi
\csname altaffil\the\affilnum\endcsname
\vskip3pt
\global\advance\affilnum by 1
\repeat
\expandafter\ifx\csname altaffil\the\affilnum\endcsname\relax
\else
\csname altaffil\the\affilnum\endcsname\fi
\global\affilnum=0
\global\totalaffils=0
\vskip12pt
}}
\let\doaffils\doaltaffils

\newcount\affilnum
\affilnum=0
\newcount\totalaffils 

% Changes to citations

\def\newcite{\@ifnextchar
[{\@tempswatrue\@citex}{\@tempswafalse\x@citex[]}}

\def\x@citex[#1]#2{\if@filesw\immediate\write\@auxout{\string\citation{#2}}
\fi
  \let\@citea\@empty
  \@cite{\@for\@citeb:=#2\do
    {\@citea\def\@citea{;\penalty\@m\ }%
     \def\@tempa##1##2\@nil{\edef\@citeb{\if##1\space##2\else##1##2\fi}}%
     \expandafter\@tempa\@citeb\@nil
     \@ifundefined{b@\@citeb}{{\reset@font\bf ?}\@warning
       {Citation `\@citeb' on page \thepage \space undefined}}%
\expandafter\csname b@\@citeb\endcsname
}}{#1}}

\def\cite{\futurelet\next\lookforbrac}

\def\dobrac[#1]#2{\newcite[#1]{#2}}

\def\donobrac#1{\newcite{#1}}

\def\lookforbrac{\if\next[\let\go\dobrac\else\let\go\donobrac\fi\go}

% second part

% Begin and end article.  
% (In here to match other styles.)

\def\article{\relax}
\def\endarticle{\@normalsize
\clearpage}

%

\def\footnoterule{\kern-3\p@
\hrule width 4pc
\kern 2.6\p@}

% Make \eqnum work in \eqnarray:

\def\arrayeqnum#1{\gdef\xtheequation{#1}%
\let\@currentlabel\xtheequation
\addtocounter{equation}{\m@ne}}


\def\eqnarray{\let\eqnum\arrayeqnum
% (to make eqnum work in eqnarray)
\stepcounter{equation}%
\let\@currentlabel\theequation
\global\@eqnswtrue\m@th
\global\@eqcnt\z@\tabskip\@centering\let\\\@eqncr
$$\halign to\displaywidth\bgroup\@eqnsel\hskip\@centering
  $\displaystyle\tabskip\z@{##}$&\global\@eqcnt\@ne
  \hskip 2\arraycolsep \hfil${##}$\hfil
  &\global\@eqcnt\tw@ \hskip 2\arraycolsep 
$\displaystyle\tabskip\z@{##}$\hfil
  \tabskip\@centering&\llap{##}\tabskip\z@\cr}
 
 
\def\@@eqncr{\let\@tempa\relax
  \ifcase\@eqcnt \def\@tempa{& & &}\or \def\@tempa{& &}%
  \else \def\@tempa{&}\fi
  \@tempa \if@eqnsw\expandafter\ifx\csname 
xtheequation\endcsname\relax
  \@eqnnum\else(\xtheequation)\global\let\xtheequation\relax\fi
% <===
\stepcounter{equation}\fi
  \global\@eqnswtrue\global\@eqcnt\z@\cr}

%
\def\broadside{\bgroup
\global\dimen0=\the\textheight
\global\dimen1=\the\textwidth
\global\textheight = \dimen1
\global\textwidth= \dimen0
\clearpage
%
%\thispagestyle{empty}
%

\figurewidth{\textwidth}
\tablewidth{\textwidth}}

\def\endbroadside{\egroup
\global\textheight\dimen0
\global\textwidth\dimen1\clearpage}

% Reworked Table Macros

\let\tableline=\hline
\newtoks\@temptokena
\newtoks\@temptokenb

\def\tablenotemark#1{\rlap{$^{\rm #1}$}}
\def\nodata{\multicolumn{1}{c}{$\cdots$}}
\newcount\pt@ncol
\def\tblnote@list{}

\newdimen\pt@width
\pt@width=\textwidth

\def\tablecaption#1{\gdef\pt@caption{#1}} 

\def\pt@caption{\relax}


\newcount\ampcount
\def\saveamp{&}
\def\saveandcountamps{\global\advance\ampcount by1\saveamp}
\catcode`\&=\active

\def\htabular #1{\def\@halignto{to#1}\@tabular[t]}

\def\xendtabular{\crcr\egroup\egroup}

\let\endhtabular\xendtabular

\def\x@tabular{\let\@acol\@tabacol
  \let\@classz\@tabclassz
  \let\@classiv\@tabclassiv \let\\\@tabularcr\@tabarray}

  \def\multicolumn#1#2#3{\multispan{#1}\begingroup
  \@mkpream{#2}%
  \def\@sharp{#3}\let\protect\relax
  \let\@startpbox\@@startpbox\let\@endpbox\@@endpbox
  \@arstrut \@preamble\hbox{}\endgroup\ignorespaces}


\def\tablecomments#1{\@temptokena={\hskip1em\rm #1\par}%
\@temptokenb=\expandafter{\tblnote@list}
\xdef\tblnote@list{\the\@temptokenb\the\@temptokena}}

\def\tablenotetext#1#2{{%
\@temptokena={\vspace{0.0ex}{%
\vskip1pt\noindent\strut\hskip1em$^{\rm #1}$#2}\par}%
\@temptokenb=\expandafter{\tblnote@list}
\xdef\tblnote@list{\the\@temptokenb\the\@temptokena}}}

\def\spew@ptblnotes{\ifx\tblnote@list\@empty\relax
\else
\par
\vspace{2ex}
{\small\tblnote@list}
\gdef\tblnote@list{}
\fi}

\def\continuedcaption{{\bf Table \thetable.} 
({\rm continued})}

\newbox\tabbox
\newdimen\totaltabdp

\def\xplanotable{planotable}

\def\HasNoWidth#1{\cr\noalign{\vskip-4ex}%
\multicolumn{\the\finalcolcount}{c}{$\vcenter{\parindent=0pt
\center\baselineskip=14pt\relax%
\hsize=.5\hsize%
\it\relax#1
\endcenter\vskip1sp}$}\cr%
\noalign{\vskip-4ex}}

\def\haswidth#1{\cr\noalign{\center\baselineskip=14pt\relax%
\hsize=\pt@width
\it\relax\vskip-28pt#1}}

\def\cutinhead#1{\ifdim\pt@width=0pt\let\go\HasNoWidth\else%
\let\go\haswidth\fi\go{#1}}

\def\xend{\end}
\def\lookforending{\ifx\next\end
\global\let\xgo\pickuparg\else
\global\let\xgo\xendline\fi\xgo}

\def\pickuparg#1#2{\def\two{#2}\ifx\two\xplanotable
\gdef\ygo{\end{planotable}}\else\gdef\ygo{#1#2\endline}\fi\ygo}

\def\endline{\futurelet\next\lookforending}

\long\def\xendline#1\nl{\let&\saveandcountamps
\setbox0=\vbox{\hbox{\tabular[t]{\pt@format}
#1\cr\doendtabular}}%
\ifnum\ampcount>\finalcolcount \global\finalcolcount=\ampcount\fi
\global\ampcount=0
\ifdim\wd0>\insidetablewd
\global\insidetablewd=\wd0\fi
\global\advance\totaltabdp by\ht0
\global\advance\totaltabdp by\dp0
\ifdim\totaltabdp >.85\textheight\global\let\zgo\endpage\else
\global\let\zgo\endline\fi#1\cr\let&\relax\zgo}%% 

\def\endpage{\crcr\noalign{\vskip-\the\baselineskip\hrule\vskip4pt}
\doendtabular\egroup%
\expandafter\ifx\csname pt@caption\endcsname\relax
\else
\noindent%
{\bf Table \thetable.} \pt@caption 
\vskip10pt\global\let\pt@caption\relax
\fi
\noindent\unvbox\tabbox
\newpage
\global\totaltabdp=0pt
\startcontinueddata}

\def\dofirstpreamble{\htabular{\the\pt@width}{@{\extracolsep{\fill}}
\pt@format}}
\def\dofirstend{\endhtabular}

\def\dosecondpreamble{\tabular[t]{\pt@format}}

\def\dosecondend{\endtabular}

\newdimen\insidetablewd

\def\startdata{%
%
\let\endtabular\xendtabular
\let\@tabular\x@tabular
\global\advance\totaltabdp by 48pt
\setbox\tabbox=\vbox\bgroup%
%
\ifdim\pt@width=0pt\relax%
\gdef\dopreamble{\dosecondpreamble}%
\gdef\doendtabular{\dosecondend}%
\else%
\gdef\dopreamble{\dofirstpreamble}%
\gdef\doendtabular{\dofirstend}\fi%
\let&\saveamp
\advance\totaltabdp by\the\baselineskip
\dopreamble\pt@head\cr%
\noalign{\vskip-\the\baselineskip
\global\finalcolcount=\the\pt@ncol\relax}
\let&\relax
\xendline}

\def\xrelax{\relax}

\def\startcontinueddata{\let&\saveamp
\let\endtabular\xendtabular
\let\@tabular\x@tabular
\setbox\tabbox=\vbox\bgroup%
%
\ifx\pt@caption\xrelax\else
\hbox{\continuedcaption}\fi
\vskip-10pt %
\let&\saveamp
\setbox0=\vbox{\tabular[t]{\pt@format}\pt@head\cr\doendtabular}%
\global\advance\totaltabdp by\ht0
\global\advance\totaltabdp by\dp0
\advance\totaltabdp by\the\baselineskip
\ifdim\wd0>\insidetablewd
\global\insidetablewd=\wd0\fi
%
\dopreamble\pt@head\cr%
\noalign{\vskip-\the\baselineskip}%
\let&\relax\xendline}

\let\nl\relax

\long\def\pickupend#1\end#2{\def\two{#2}\ifx\two\xplanotable
\gdef\ago{#1\nl\end{planotable}}\else
\gdef\ago{#1\end{#2}\pickupend}\fi\ago}

\def\planotable#1{\clearpage%
\global\pt@width=0pt
\catcode`\&=\active
\let\ltx@label=\label\gdef\pt@label{\let\label=\ltx@label}%
\def\label##1{\gdef\pt@labeltag{##1}%
\gdef\pt@label{\ltx@label{\pt@labeltag}\let\label=\ltx@label}}
\global\advance\c@table by 1\relax
\def\@captype{table}\def\pt@format{#1}\pickupend}

\def\endplanotable{\crcr
\noalign{\vskip-\the\baselineskip\hrule}
\doendtabular
\egroup%
\hsize=\wd\tabbox
\expandafter\ifx\csname pt@caption\endcsname\relax
\else
\noindent%
{\bf Table \thetable.} \pt@caption 
\vskip10pt\global\let\pt@caption\relax
\fi
\noindent\unvbox\tabbox
\pt@label
\vskip1sp
%
\spew@ptblnotes
\vskip1sp
\hsize=\textwidth
\catcode`\&=4
\global\pt@ncol=0
\gdef\pt@caption{\relax}
\global\pt@width=\textwidth\relax\gdef\thespnum{}}

\edef\tablewidth#1{\global\pt@width=#1}
\def\figurewidth#1{\hsize=#1}

\let\platewidth=\tablewidth

\def\tablehead#1{\gdef\pt@head{\noalign{\hrule\vskip3pt}
#1\strut\cr\noalign{\vskip3pt\hrule}}}

\def\colhead#1{\hfill\relax #1\global\advance\pt@ncol 
by\@ne\hfill\relax}

\newcount\finalcolcount

% Tablenum
%
% If a letter is given preceding the number, 
% that letter is assumed to be an appendix 
% letter and is repeated onfollowing tables 
% until a new appendix letter is given.  If 
% a letter follows the table number, it is 
% used for that table number only.

\let\thespnum\relax
\def\saveapos{'}
\def\savedoll{$}
\def\dodollars#1${\xdef\thespnum{$#1$}}

\def\gotokazowee#1\kazowee{\xdef\thespnum{\x#1}}
\def\xkazowee{\kazowee}
\def\kazowee{\relax}
\def\xrelax{\relax}

\def\loopthru#1{\def\x{#1}\ifx\x\xkazowee\let\go\relax\else
\ifx\x\savedoll\let\go\dodollars\else
\ifx\x\xrelax\let\go\relax\else
\let\go\loopthru
\expandafter\ifcat\x 8\ifx\x\saveapos\xdef\thespnum{'}\fi\else%
\let\go\gotokazowee\fi\fi\fi\fi\go}

\def\lookforletter#1#2#3\relax{\def\two{#2}
\ifx\two\empty\global\c@table=#1\relax\else
\def\x{#1}\def\y{#2}
\ifcat\x a
\ifcat\y a\gdef\theletter{#1#2}\def\test{#3}
% in case there are 2 letters
\else\def\test{#2#3}\gdef\theletter{#1}\fi
% in case there is one letter
%
\expandafter\loopthru\test\kazowee
\setbox0=\hbox{\global\c@table=\test}\else
\def\test{#1#2#3}\expandafter\loopthru\test\kazowee
\setbox0=\hbox{\global\c@table=\test}
\gdef\theletter{\relax}\fi\fi}


\def\tablenum#1{\def\xone{#1}\expandafter\lookforletter\xone\relax
\global\let\@currentlabel\thetable\relax\relax}
%

\def\thetable{\theletter\the\c@table\thespnum}

\let\theletter\relax
\let\thespnum\relax

\def\endtable{\spew@tblnotes\end@float}

\def\tablevspace#1{\noalign{\vskip{#1}}}

\def\tablebreak{\global\totaltabdp=2\textheight\relax}

\catcode`\&=4

\long\def\@makecaption#1#2{\vskip 2ex\parbox{\pt@width}{#1 #2}\par}
\long\def\@makecaptioncont#1#2{\parbox{\pt@width}{#1}\vskip -0.8ex}

\long\def\@caption#1[#2]#3{\par\addcontentsline{\csname
ext@#1\endcsname}{#1}{\protect\numberline{\csname
the#1\endcsname}{\ignorespaces #2}}\begingroup
\@makecaption{\csname fnum@#1\endcsname}{\ignorespaces #3}\par
\endgroup}

\let\saveenddocument\enddocument
\def\enddocument{\@runheads\saveenddocument}

\newif\ifprintcallout
\printcallouttrue
\def\nocallouts{\global\printcalloutfalse}
\def\callout#1{#1\ifprintcallout\marginpar{\fbox{\large#1}}\fi}

% Reset these to more generous values to 
% make it easier to position floats.

\setcounter{topnumber}{10}
\setcounter{bottomnumber}{10}

\def\topfraction{.99}
\def\bottomfraction{.99}
\def\textfraction{.01}
\def\floatpagefraction{.5}

\setcounter{totalnumber}{20}

\setcounter{dbltopnumber}{2}
\def\dbltopfraction{.7}
\def\dblfloatpagefraction{.5}

% Macros to make caption and tablenotes 
% be the width of the table in 
% \begin{table}\begin{tabular}...
% \end{tabular}\end{table}

\let\savetabular\tabular
\let\saveendtabular\endtabular

\newdimen\tabwidth

\def\ytabular{\global\setbox\tabbox=\hbox\bgroup\hsize=0pt\savetabular
}
\def\endytabular{\saveendtabular\egroup}

\let\savetable\table
\let\saveendtable\endtable

\let\savecaption\caption
\def\docaption#1{\gdef\currcaption{#1}}

\let\savetablenum\tablenum
\def\tabtablenum#1{\savetablenum{#1}\global\advance\c@table-1\relax}

\let\savelabel\label
\newcount\labnum
\newcount\labloopnum
\def\keeplabel#1{\global\advance\labnum by 1
\expandafter\gdef\csname label\the\labnum\endcsname{#1}}

\def\dolabel{\labloopnum=1\loop
\ifnum\labloopnum<\labnum
\savelabel{\csname label\the\labloopnum\endcsname}
\global\advance\labloopnum by 1
\repeat
\ifnum\labnum=0\else
\savelabel{\csname label\the\labloopnum\endcsname}\fi
\global\labloopnum=0
\global\labnum=0
\relax}

\newbox\tablebox
\def\table{\setbox\tablebox=\vbox\bgroup\let\tabular\ytabular
\let\endtabular\endytabular
\let\caption\docaption
\let\tablenum\tabtablenum
\let\label\keeplabel
\def\@captype{table}\tablook}

\newcount\tabnotecount
\newcount\loopnotecount

\def\endtable{{\parindent=0pt\hsize=\wd\tabbox
\ifx\currcaption\relax\else%
\savecaption{\hsize=\wd\tabbox\currcaption}\fi
\global\tabwidth=\wd\tabbox
\vskip9pt
\noindent\unhbox\tabbox 
\vskip-18pt
\spew@tblnotes}%
\egroup\vbox{\unvbox\tablebox}
\dolabel\gdef\thespnum{}}

\def\addtotabnum#1{\gdef\thespnum{#1}}
\let\spnum\relax

%
\def\acknowledgments{\vskip-\lastskip\vskip12pt\indent{\small\bf
Acknowledgments.}\ \ \small}

\def\acknowledgment{\vskip-\lastskip\vskip12pt\indent{\small\bf 
Acknowledgment.}%
\ \ \small}

\let\acknowledgements=\acknowledgments
\let\acknowledgement=\acknowledgment

%

\def\lookbrac{\if\next[\let\go\catchbrac\else\let\go\relax\fi\go}
\def\catchbrac[#1]{\relax}

\def\figure{\bgroup%
\def\@captype{figure}\futurelet\next\lookbrac}
\let\endfigure\egroup

\def\tablook{\futurelet\next\lookbrac}

% Jan. 4, 1996

\let\@runheads\relax