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+
+%% agupp.sty -- March 29, 1999 version
+%% revisions by Jennifer Harvey, AGU, 3/29/99:
+%% Table breaking problem corrected.
+%%
+% revisions by Jennifer Harvey, AGU, 8/3/98
+% Changed \gras journal command to \gji
+%
+%% revisions by Amy Hendrickson, TeXnology Inc, 1/5/96
+%
+%% This file (agupp.sty) creates two-column preprint
+% pages suitable for distribution among colleagues.
+% Do not submit two-column output to AGU.
+
+
+\def\revtex@ver{5.01}
+\def\revtex@date{August 3, 1998}
+\def\revtex@org{AGU}
+\def\revtex@jnl{AGU}
+\def\revtex@genre{preprint}
+\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
+\revtex@org{'s}\space \LaTeX\ macros v\revtex@ver. \fmtdate@id}}
+\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).
+Use 12pt documentstyle option.}
+\fi
+\fi
+\def\ps@plaintop{\let\@mkboth\@gobbletwo
+\def\@oddfoot{}\def\@oddhead{\rm\hfil--\space\thepage\space--\hfil}
+\def\@evenfoot{}\let\@evenhead\@oddhead}
+%\ps@plain
+\textwidth=6.9in
+\textheight=8.6in
+\topmargin=0in
+\headheight=9pt
+\headsep=12pt
+\oddsidemargin=0in
+\evensidemargin=0in
+\parindent=1.2em
+
+\newdimen\saveparindent
+\saveparindent=\parindent
+
+\parskip=0.5ex
+\columnsep=0.5in
+\hoffset=-0.2in
+\def\@tolerant{600}
+\def\@verytolerant{10000}
+\tolerance\@tolerant
+\def\@tightleading{1.1}
+\def\@doubleleading{1.6}
+\let\tighten=\relax
+\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 by \cpr@year\space
+by the \cpr@holder.
+\or
+Published by \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}
+\def\@runheads{\@tempcnta\c@page
+\@whilenum \@tempcnta >0\do{
+\vskip 3ex
+\hbox to30pc{\small\expandafter\uppercase\expandafter{\@versohead}:
+\expandafter\uppercase\expandafter{\@rectohead}\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
+\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
+\vskip 2ex
+\fi}
+
+\def\@dates{
+\ifx\@recvdate\@empty\relax\else
+{\rm Received}\space\@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
+{\normalsize\authaddr@list\vskip1sp} \gdef\authaddr@list{}
+\fi}
+\def\@sluginfo{{\flushleft
+\@dates
+\endflushleft}}
+\let\dates=\relax
+\let\sluginfo=\relax
+\let\forcesluginfo=\relax
+\def\abstract{\if@twocolumn
+\section*{Abstract}
+\else \large \vspace{3em}
+\flushleft{\bf{Abstract}\vspace{-.5em}\vspace{0pt}}\endflushleft
+\parindent\z@
+\fi}
+\def\title#1{%\thispagestyle{plain}
+\@makeslugcmmnt
+{\flushleft\if@twocolumn\large\else\Large\fi\bf#1\endflushleft}}
+\def\author#1{{\topsep 0pt\flushleft
+\if@twocolumn\normalsize\else\vspace{4ex}\large\fi#1\endflushleft}}
+\def\affil#1{\vspace*{-0.8ex}{\topsep 0pt\flushleft
+\if@twocolumn\small\else\normalsize\fi\rm#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={\vskip-\parskip\noindent\hskip1em#1}
+\@temptokenb=\expandafter{\authaddr@list}
+\xdef\authaddr@list{\the\@temptokenb\the\@temptokena}}
+\let\authoraddr=\authoraddress
+\def\@keywordtext{Subject headings}
+\def\@keyworddelim{---}
+\def\keywords#1{\vspace*{-.7ex}
+\if@twocolumn\noindent{\small{\it\@keywordtext:\/}\space\@kwds{#1}}
+\else{\quote\if@twocolumn\small\else\large\fi
+{\it\@keywordtext:\/}\space\@kwds{#1}\endquote}
+\fi}
+\let\subjectheadings=\keywords
+\def\@kwds#1{#1\relax}
+\skip\footins 3ex plus 1ex minus .5ex \footnotesep 2ex
+\newif\if@firstsection \@firstsectiontrue
+
+% 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} {2.3ex plus 1ex minus
+.2ex}{1.5ex plus .2ex}{\large\raggedright\bf}}
+\def\subsection{\@startsection{subsection}{2}{-\parindent} {2ex plus 1ex
+minus .2ex}{1ex plus .2ex}{\normalsize\raggedright\bf}}
+\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
+\setcounter{section}{0}
+\setcounter{equation}{0}
+\def\theequation{\hbox{\Alph{section}\arabic{equation}}}
+\let\body@section=\section
+\def\section{\setcounter{equation}{0}
+\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{\@startsection{section}{1}{\z@}
+{2.3ex plus 1ex minus .2ex}{1.5ex plus .2ex}{\large\bf}*{References}
+\bgroup\parindent=\z@\parskip=\itemsep
+\def\refpar{\vskip-\parskip\hangindent=1.2em\hangafter=1}}
+
+\def\endreferences{\refpar\egroup
+% new ==>>
+\vskip12pt
+\footnoterule
+\footnotesize
+\@authaddrs
+\vskip1pt
+\@dates
+\doaltaffils
+% <==
+\revtex@pageid\normalsize}
+
+\def\forcesluginfo{\vskip12pt
+\footnoterule
+\footnotesize
+\@authaddrs
+\vskip1pt
+\@dates
+\doaltaffils
+\revtex@pageid\normalsize}
+
+\def\thebibliography#1{\@startsection{section}{1}{\z@}
+{2.3ex plus 1ex minus .2ex}{1.5ex plus .2ex}{\large\bf}*{References}
+\list{\null}{\leftmargin 1.2em\labelwidth\z@\labelsep\z@\itemindent -1.2em
+\usecounter{enumi}}
+\def\refpar{\relax}
+\def\newblock{\hskip .11em plus .33em minus .07em}
+\sloppy\clubpenalty4000\widowpenalty4000 \itemsep=-2.5pt
+\sfcode`\.=1000\relax}
+\def\endthebibliography{\endlist{
+% new ==>> \vskip3pt
+\leftskip-1.2em
+\footnoterule
+\footnotesize
+\@authaddrs
+\vskip1pt
+\@dates
+\doaltaffils
+% <==
+\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}}
+
+\let\set@mkcaption=\relax
+\def\set@mkcaptioncont{\long\def\@makecaption##1##2{ \hbox
+to\pt@width{##1\hfil}\vskip -0.8ex}}
+
+\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\thetable{\@arabic\c@table}
+\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\gji{{\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$}\kern-.15em\TeX}
+\def\sizrpt{
+(\fontname\the\font): em=\the\fontdimen6\font, ex=\the\fontdimen5\font
+\typeout{
+(\fontname\the\font): em=\the\fontdimen6\font, ex=\the\fontdimen5\font }}
+\def\format@date{\ifcase\month\or January\or February\or
+March\or April\or May\or June\or
+July\or August\or September\or October\or November\or December\fi
+\space\number\day, \number\year}
+\def\fmtdate@id{File \jobname\space formatted \format@date.}
+
+% Captions
+
+\let\saveAA\AA
+\def\captionAA{\protect{\footnotesize\saveAA}}
+
+\long\def\@makecaption#1#2{{\let\AA\captionAA \vskip
+2ex\noindent\parbox{\pt@width}{#1 #2}\par}}
+\long\def\@caption#1[#2]#3{\par\addcontentsline{\csname
+ext@#1\endcsname}{#1}{\protect\numberline{\csname
+the#1\endcsname}{\ignorespaces #2}}\begingroup \@makecaption{\csname
+fnum@#1\endcsname}{\ignorespaces #3}\par \endgroup}
+
+% Changes needed for all styles
+
+% Alternate affiliations appearing
+% at the end of the article:
+
+\def\altaffiltext#1#2{{\small
+\global\advance\totalaffils by 1
+\expandafter\xdef\csname altaffil#1\endcsname{\noindent\hskip1em$^{#1}${#2}}}}
+
+
+\def\doaltaffils{{\parskip=0pt
+\parindent=0pt
+\loop\ifnum\affilnum<\totalaffils
+\ifnum\affilnum=0
+\goodbreak
+\vskip12pt
+\footnoterule
+\vspace{1sp}\fi
+\csname altaffil\the\affilnum\endcsname \vskip1pt
+\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}}%
+% \hbox{ commented out to
+% let citation break over lines
+\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}
+
+%
+
+\def\article{\if@twocolumn\relax\else\twocolumn\fi\vskip28pt}
+\def\endarticle{\@normalsize\onecolumn}
+
+
+\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}
+
+\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}}
+
+\let\tablerefs\tablecomments
+
+\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@tblnotes{
+\ifx\tblnote@list\@empty\relax
+\else
+\vspace{.4ex}
+{\small\tblnote@list}
+\gdef\tblnote@list{}
+\fi}
+
+\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-2ex}%
+\multicolumn{\the\finalcolcount}{c}{$\vcenter{\parindent=0pt
+\hsize=.5\hsize
+\center\baselineskip=14pt\relax%
+\it\relax#1
+\endcenter\vskip1sp}$}\cr%
+\noalign{\vskip-2ex}}
+
+\def\haswidth#1{\cr\noalign{\center\baselineskip=14pt\relax%
+\hsize=\pt@width
+\it\relax\vskip-14pt#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{\advance\totaltabdp by \the\baselineskip
+\let\endtabular\xendtabular
+\let\@tabular\x@tabular
+\let&\saveamp
+\setbox\tabbox=\vbox\bgroup%
+%
+\ifdim\pt@width=0pt\relax%
+\gdef\dopreamble{\dosecondpreamble}%
+\gdef\doendtabular{\dosecondend}%
+\else%
+\gdef\dopreamble{\dofirstpreamble}%
+\gdef\doendtabular{\dofirstend}%
+\fi\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
+\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\totaltabdp=0pt
+\global\pt@width=\textwidth\relax\gdef\thespnum{}}
+
+\edef\tablewidth#1{\global\pt@width=#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 on
+% following 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
+
+\def\endtable{\spew@tblnotes\end@float}
+
+\def\tablevspace#1{\noalign{\vskip{#1}}}
+
+\def\tablebreak{\global\totaltabdp=2\textheight\relax}
+
+\catcode`\&=4
+
+%
+
+\def\ps@plaintop{\let\@mkboth\@gobbletwo
+\def\@oddfoot{}\def\@oddhead{\rm\hfil\thepage}
+\def\@evenfoot{}\let\@evenhead\@oddhead}
+\ps@plaintop
+
+\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{{\hsize=\wd\tabbox
+\ifx\currcaption\relax\else
+\savecaption{\hsize=\wd\tabbox\currcaption}\fi
+\global\tabwidth=\wd\tabbox
+\vskip9pt
+\noindent\unhbox\tabbox
+\vskip-6pt
+\spew@tblnotes}\egroup
+\vbox{\unvbox\tablebox}
+\dolabel\gdef\thespnum{}}
+
+\def\addtotabnum#1{\gdef\thespnum{#1}}
+\let\thespnum\relax
+
+%
+\def\acknowledgments{\vskip-\lastskip\vskip12pt\indent{\small\bf
+Acknowledgments.}\quad\small}
+
+\def\acknowledgment{\vskip-\lastskip\vskip12pt\indent{\small\bf
+Acknowledgment.}%
+\quad\small}
+
+\let\acknowledgements=\acknowledgments
+ \let\acknowledgement=\acknowledgment
+
+ \def\figurewidth#1{\hsize=#1}
+
+%
+
+ \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
+
+ \def\lefthead#1{\relax}
+ \def\righthead#1{\relax}
+
+ \let\@runheads\relax