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+% This is part of the book TeX for the Impatient.
+% Copyright (C) 2003 Paul W. Abrahams, Kathryn A. Hargreaves, Karl Berry.
+% See file fdl.tex for copying conditions.
+
+\input macros
+\chapter {Commands for \linebreak horizontal and \linebreak vertical modes}
+
+\chapterdef{hvmodes}
+
+This section covers commands that have corresponding or identical
+forms for both horizontal and vertical modes.
+These commands provide boxes, spaces, rules, leaders,
+and alignments.
+For an explanation of the conventions used in this section,
+see \headcit{Descriptions of the commands}{cmddesc}.
+
+\begindescriptions
+
+%==========================================================================
+\section {Producing space}
+
+%==========================================================================
+
+\subsection {Fixed-width horizontal space}
+
+\begindesc
+\bix^^{space//producing}
+\bix^^{horizontal space}
+\cts thinspace {}
+\explain
+This command produces a positive \minref{kern}
+whose width is one-sixth of an em
+(\xref{dimdefs})
+i.e., it causes \TeX\ to move its position right by that amount.
+It is useful
+when you have a nested quotation, for example,
+and you want to separate the levels of quotes.
+\TeX\ won't break a line at
+a |\thinspace|.\minrefs{line break}
+
+\example
+``\thinspace`A quote.'\thinspace''\par
+24,\thinspace 29--31,\thinspace 45,\thinspace 102
+|
+\produces
+``\thinspace`A quote.'\thinspace''\par
+24,\thinspace 29--31,\thinspace 45,\thinspace 102
+\endexample
+\enddesc
+
+\begindesc
+\cts negthinspace {}
+\explain
+This command
+produces a negative kern whose width is one-sixth of an em
+(\xref{dimdefs}),
+i.e., it causes \TeX\ to move its position left by that amount.
+It is useful for bringing together characters that are a little too
+far apart.
+\TeX\ won't break a line at a |\negthinspace|.\minrefs{line break}
+\example
+The horror, the horror\negthinspace, the horror of it all!!
+|
+\produces
+The horror, the horror\negthinspace, the horror of it all!
+\endexample
+\enddesc
+
+\begindesc
+\cts enspace {}
+\explain
+This command produces a \minref{kern} whose width is one ^{en}
+(half of an em, see \xrefpg{dimdefs}).
+\TeX\ won't break a line
+at an |\enspace| unless it's followed by glue.
+In a bulleted list, the bullets are usually separated from the following
+text by an |\enspace|.
+\example
+Lemma 1.\enspace There exists a white rabbit.
+|
+\produces
+Lemma 1.\enspace There exists a white rabbit.
+\endexample
+% the enspace here follows the \proclaim convention (Knuth p. 355).
+\enddesc
+
+\begindesc
+\easy\cts enskip {}
+\cts quad {}
+\cts qquad {}
+\explain
+^^{en}
+Each of these commands
+produces a glob of horizontal \minref{glue}
+that can neither stretch nor shrink.
+\TeX\ can break a line \minrefs{line break} at such glue.
+The width of these glues (which are relative to the current font)
+are as follows for |cmr10|, the default \plainTeX\ font:
+\medskip
+
+\def\distance#1{\hbox{\strut $\rightarrow$\vrule\hskip #1\vrule$\leftarrow$}}
+
+{\def\l#1{\hfil$#1$\thinspace em}
+\tabskip 3pc \halign{#&#&\hfil#\hfil\cr
+{\it Command}&{\it Space}&{\it Illustration}\cr
+\noalign{\vskip 4pt}
+|\enskip|&\l{\frac 1/2}&\distance{.5em}\cr
+|\quad|&\l1&\distance{1em}\cr
+|\qquad|&\l2&\distance{2em}\cr
+}}
+\example
+en\enskip skip; quad\quad skip; qquad\qquad skip
+|
+\produces
+en\enskip skip; quad\quad skip; qquad\qquad skip
+\endexample
+\eix^^{horizontal space}
+\enddesc
+
+%==========================================================================
+\subsection {Fixed-length vertical space}
+
+\begindesc
+\bix^^{vertical space}
+\easy\cts smallskip {}
+\cts medskip {}
+\cts bigskip {}
+\explain
+These commands produce successively larger
+amounts of vertical space:
+\display{{\def\bar{\kern 2pt\hrule width 5pc}
+\def\lbl#1{\hbox to 5pc{\hfil #1skip\hfil}}
+\leavevmode
+\vtop{\lbl{small}\bar\smallskip\bar}\quad
+\vtop{\lbl{med}\bar\medskip\bar}\quad\vtop{\lbl{big}\bar\bigskip\bar}}}
+\noindent
+|\smallskip| skips by $3$ points and can stretch or
+shrink by $1$ point. |\med!-skip| is equivalent to two |\smallskip|s
+and |\bigskip| is equivalent to two |\medskip|s.
+
+These commands end a paragraph since they are inherently vertical.
+The skips that they produce
+are in addition to the normal interparagraph skip.
+\example
+Hop \smallskip skip \medskip and \bigskip jump.
+|
+\produces
+Hop \smallskip skip \medskip and \bigskip jump.
+\endexample
+\enddesc
+
+\begindesc
+\cts smallskipamount {\param{glue}}
+\cts medskipamount {\param{glue}}
+\cts bigskipamount {\param{glue}}
+\explain
+These parameters specify the amounts of glue produced by
+the |\small!-skip|, |\med!-skip|, and |\big!-skip| commands.
+By changing these parameters you change the effect of the commands.
+The default values (for \plainTeX)
+correspond to a quarter of a linespace, half a linespace,
+and a full linespace.
+We recommend that you maintain this ratio by changing
+these values whenever
+you change |\baselineskip| (\xref\baselineskip).
+^^|\baselineskip//and {\tt\\smallskipamount}, etc.|
+\eix^^{vertical space}
+
+\enddesc
+
+%==========================================================================
+\subsection {Variable-size space}
+
+\begindesc
+\easy\cts hskip {\<dimen$_1$> {\bt plus} \<dimen$_2$> {\bt minus} \<dimen$_3$>}
+\cts vskip {\<dimen$_1$> {\bt plus} \<dimen$_2$> {\bt minus} \<dimen$_3$>}
+^^{vertical skip}^^{vertical glue}
+^^{horizontal skip}^^{horizontal glue}
+\bix^^{horizontal space}
+\bix^^{vertical space}
+\explain
+These commands produce horizontal and vertical glue respectively.
+In the simplest and most common case when only \<dimen$_1$> is present,
+|\hskip| skips to the right by \<dimen$_1$>
+and |\vskip| skips down the page by \<dimen$_1$>.
+More generally, these commands
+produce \minref{glue} whose natural size is
+\<dimen$_1$>, whose stretch is \<dimen$_2$>, and whose shrink is \<dimen$_3$>.
+Either the |plus| \<dimen$_2$>, the |minus |\<dimen$_3$>,
+or both can be omitted.
+If both are present, the |plus| must come before the |minus|.
+An omitted value
+is taken to be zero. Any of the \<dimen>s can be negative.
+
+You can use |\hskip| in math mode, but you can't use |mu| units
+\seeconcept{mathematical unit}
+for any of the dimensions. If you want |mu| units, use |\mskip|
+(\xref\mskip) instead.
+
+\example
+\hbox to 2in{one\hskip 0pt plus .5in two}
+|
+\produces
+\hbox to 2in{one\hskip 0pt plus 2in two}
+
+\doruler{\8\8}2{in}
+\nextexample
+\hbox to 2in{Help me!! I can't fit
+{\hskip 0pt minus 2in} inside this box!!}
+|
+\produces
+\hbox to 2in{Help me! I can't fit
+{\hskip 0pt minus 2in} inside this box!}
+
+\doruler{\8\8}2{in}
+\nextexample
+\vbox to 4pc{\offinterlineskip% Just show effects of \vskip.
+ \hbox{one}\vskip 0pc plus 1pc \hbox{two}
+ \vskip .5pc \hbox{three}}
+|
+\produces
+\smallskip
+\vbox to 4pc{\offinterlineskip% Just show effects of \vskip.
+ \hbox{one}\vskip 0pc plus 1pc \hbox{two}
+ \vskip .5pc \hbox{three}}
+\endexample
+\enddesc
+
+\begindesc
+\cts hglue {\<glue>}
+\cts vglue {\<glue>}
+^^{vertical glue}
+^^{horizontal glue}
+\explain
+The |\hglue| command produces horizontal \minref{glue} that won't disappear at
+a line break; the |\vglue| command
+produces vertical \minref{glue} that won't disappear at a page break.
+In other respects these commands are just like |\hskip| and |\vskip|.
+You can use |\vglue| to produce blank space at the top of a page,
+e.g., above a title on the first page of a document, but
+^|\topglue| (next) is usually better for this purpose.
+\enddesc
+
+\begindesc
+\cts topglue {\<glue>}
+\explain
+\margin{Command added; recent addition to \TeX}
+This command\footnote{|\topglue| was added to \TeX\ in version 3.0,
+later than the other enhancements introduced by ^{\newTeX}
+(\xref{newtex}). It is first described in the \emph{eighteenth\/}
+edition of \texbook.} causes the space from the top of the page to the
+top of the first box on the page to be \<glue> precisely.
+The top of the page is considered to be at the baseline of an
+imaginary line of text just above the top line of the page.
+More precisely, it's a distance |\topskip| above the origin as given by
+|\hoffset| and |\voffset|.
+
+This command is useful because \TeX\ ordinarily adjusts the glue
+produced by |\topskip| in a complex way. By using |\topglue| you can
+control the position of the first box on the page without worrying about
+those adjustments.
+
+\enddesc
+
+\begindesc
+\cts kern {\<dimen>}
+\explain
+The effect of this command depends on the mode that \TeX\ is in when
+it encounters it:
+\ulist
+
+\li In a horizontal mode, \TeX\ moves its position to the right (for a positive
+kern) or to the left (for a negative kern).
+
+\li In a vertical mode, \TeX\ moves its position down the page (for a positive
+kern) or up the page (for a negative kern).
+
+\endulist
+\noindent
+Thus a positive kern produces empty space while a negative kern
+causes \TeX\ to back up over something that it's already produced.
+This notion of a kern ^^{kerns}
+is different from the notion of a kern in some computerized
+typesetting systems---in \TeX, positive kerns push two letters \emph{apart}
+instead of bringing them closer together.
+
+A kern is similar to
+\minref{glue}, except that (a)~a kern can neither stretch nor shrink,
+and (b)~\TeX\ will only break a line or a page at a kern if the kern
+is followed by glue and is not part of a math formula.
+If \TeX\ finds a kern at the
+end of a line or a page, it discards the kern.
+If you want to get the effect of a kern that never disappears,
+use ^|\hglue| or ^|\vglue|.
+
+You can use |\kern| in math mode, but you can't use |mu| units
+\seeconcept{mathematical unit}
+for \<dimen>. If you want |mu| units, use |\mkern|
+(\xref\mkern) instead.
+^^{line breaks//kerns at}
+^^{page breaks//kerns at}
+
+\example
+\centerline{$\Downarrow$}\kern 3pt % a vertical kern
+\centerline{$\Longrightarrow$\kern 6pt % a horizontal kern
+ {\bf Heed my warning!!}\kern 6pt % another horizontal kern
+ $\Longleftarrow$}
+\kern 3pt % another vertical kern
+\centerline{$\Uparrow$}
+|
+\produces
+\centerline{$\Downarrow$}\kern 3pt % a vertical kern
+\centerline{$\Longrightarrow$\kern 6pt % a horizontal kern
+ {\bf Heed my warning!}\kern 6pt % another horizontal kern
+ $\Longleftarrow$}
+\kern 3pt % another vertical kern
+\centerline{$\Uparrow$}
+\endexample
+\enddesc
+
+\begindesc
+\makecolumns 4/2:
+\cts hfil {}
+\cts hfill {}
+\cts vfil {}
+\cts vfill {}
+\explain
+\bix^^{glue//infinitely stretchable}
+These commands produce infinitely stretchable horizontal
+and vertical glue that
+overwhelms any finite stretch that may be present.
+|\hfil| and |\hfill| produce horizontal glue, while
+|\vfil| and |\vfill| produce vertical glue.
+
+|\hfill| is infinitely larger than |\hfil|.
+If both |\hfill| and |\hfil| appear in the same \minref{box},
+the |\hfill| will consume all the available extra space
+and the |\hfil| will be effectively ignored.
+|\hfill| can in turn be overwhelmed by |\hskip 0pt plus 1filll|.
+The glue produced by
+|\hfil| and |\hfill| never shrinks.
+
+The behavior of |\vfil| and |\vfill| is analogous.
+
+\example
+\hbox to 2in{Left\hfil Middle \hfil Right}
+|
+\produces
+\hbox to 2in{Left\hfil Middle \hfil Right}
+
+\doruler{\8\8}2{in}
+\nextexample
+\hbox to 2in{Left\hfil Middle \hfill Right}
+|
+\produces
+\hbox to 2in{Left\hfil Middle \hfill Right}
+
+\doruler{\8\8}2{in}
+\nextexample
+\leftline{%
+\vbox to 4pc{%
+ \hbox{Top}\vfil\hbox{Middle}\vfil \hbox{Bottom}}\quad
+\vbox to 4pc{%
+ \hbox{Top}\vfil\hbox{Middle}\vfill\hbox{Bottom}}}
+|
+\produces
+\smallskip
+\leftline{%
+\vbox to 4pc{%
+ \hbox{Top}\vfil\hbox{Middle}\vfil \hbox{Bottom}}\quad
+\vbox to 4pc{%
+ \hbox{Top}\vfil\hbox{Middle}\vfill\hbox{Bottom}}}
+\endexample
+
+\eix^^{glue//infinitely stretchable}
+\enddesc
+
+\begindesc
+\cts hss {}
+\cts vss {}
+\explain
+These commands produce horizontal and vertical glue
+that is both infinitely stretchable and
+infinitely shrinkable. The glue can shrink
+to a negative distance, producing the effect of backspacing along a line
+(for |\hss|) or moving back up a page (for |\vss|).
+
+\example
+\line{text\hfil\hbox to 0pt{margin\hss}}
+% `margin\hss' shrinks to the zero width of the hbox.
+|
+\produces
+\line{text\hfil\hbox to 0pt{margin\hss}}
+\nextexample
+\vbox to 1pc{\hrule width 6pc % Top of box.
+ \hbox{1} \vskip 1pc\hbox to 2pc{\hfil 2}
+ % The \vss absorbs the extra distance produced by \vskip.
+ \vss \hbox to 3pc{\hfil 3}
+ \hrule width 6pc}% Bottom of box.
+|
+\produces
+\medskip
+\vbox to 1pc{\hrule width 6pc % top of box
+ \hbox{1} \vskip 1pc\hbox to 2pc{\hfil 2}
+ \vss \hbox to 3pc{\hfil 3}
+ \hrule width 6pc}% bottom of box
+\vskip 2.5pc
+\endexample
+\enddesc
+
+\begindesc
+\cts hfilneg {}
+\cts vfilneg {}
+\explain
+^^{glue//negative}
+These commands cancel the effect of a preceding |\hfil|
+or |\vfil|. While |\hfil| and |\vfil|
+produce infinitely stretchable positive \minref{glue}, |\hfilneg|
+and |\vfilneg| produce infinitely stretchable negative glue.
+(Thus, $n$ |\hfilneg|s cancel $n$ ^|\hfil|s, and similarly for
+|\vfilneg|.)
+The main use of |\hfilneg| and |\vfilneg|
+is to counteract the effect of an |\hfil| or |\vfil|
+inserted by a \minref{macro}.
+
+|\hfilneg| and |\vfilneg| have
+the curious property that if they are the only infinitely stretchable
+glue in a box, they produce exactly the same effect as |\hfil|
+and |\vfil|.
+
+\example
+\leftline{\hfil on the right\hfilneg}
+% Cancel the \hfil that \leftline produces to the right
+% of its argument.
+|
+\produces
+\leftline{\hfil on the right \hfilneg}
+% Cancel the \hfil that \leftline produces to the right
+% of its argument.
+%
+\nextexample
+\def\a{\hbox to 1pc{\hfil 2}\vfil}
+\vbox to 4pc{\hbox{1} \vfil \a
+ \vfilneg \hbox to 2pc{\hfil 3}}
+|
+\produces
+\smallskip
+\def\a{\hbox to 1pc{\hfil 2}\vfil}
+\vbox to 4pc{\hbox{1} \vfil \a
+ \vfilneg \hbox to 2pc{\hfil 3}}
+\endexample\enddesc
+
+{\emergencystretch=2em
+\see |\hbadness| and |\vbadness| (\xref \vbadness),
+|\hfuzz| and |\vfuzz| (\xref \vfuzz),
+\conceptcit{leaders}.\par}
+\eix^^{space//producing}
+\eix^^{horizontal space}
+\eix^^{vertical space}
+
+%==========================================================================
+\section {Manipulating boxes}
+
+%==========================================================================
+\subsection {Constructing hboxes and vboxes}
+
+\begindesc
+\bix^^{box commands}
+^^{hboxes//constructing with \b\tt\\hbox\e}
+%
+\cts hbox {\rqbraces{\<horizontal mode material>}}
+\aux\cts hbox {{\bt to} \<dimen> \rqbraces{\<horizontal mode material>}}
+\aux\cts hbox {{\bt spread} \<dimen> \rqbraces{\<horizontal mode material>}}
+\explain
+This command produces an hbox
+(horizontal \minref{box}) containing \<horizontal mode material>.
+The braces around \<horizontal mode material> define a group.
+\TeX\ doesn't break the \<horizontal mode material> into lines,
+since it's in restricted horizontal mode when it's assembling the box.
+\TeX\ won't change the size of the box once it's been produced.
+
+|\hbox| is often useful when you want to keep some text all on one line.
+If your use of |\hbox| prevents \TeX\ from breaking lines in an acceptable
+way, \TeX\ will complain about an overfull hbox.
+
+The width of the hbox depends on the arguments to |\hbox|:
+\ulist\compact
+\li If you specify only \<horizontal mode material>,
+the hbox will have its natural \minref{width}.
+\li If you specify |to| \<dimen>, the width of the hbox will be \<dimen>.
+\li If you specify |spread| \<dimen>, the width of the hbox will be
+its natural width plus \<dimen>, i.e., the hbox will be spread out by
+\<dimen>.
+\endulist
+
+The ^|\hfil| command (\xref\hfil) is useful for filling out an
+hbox with empty space when the material in the box isn't as wide as
+the width of the box.
+\example
+\hbox{ugly suburban sprawl}
+\hbox to 2in{ugly \hfil suburban \hfil sprawl}
+\hbox spread 1in {ugly \hfil suburban \hfil sprawl}
+% Without \hfil in the two preceding lines,
+% you'd get `underfull hbox'es.
+|
+\produces
+\hbox{ugly suburban sprawl}
+\hbox to 2in{ugly \hfil suburban \hfil sprawl}
+\hbox spread 1in {ugly \hfil suburban \hfil sprawl}
+% Without \hfil in the two preceding lines,
+% you'd get `underfull hbox'es.
+
+\doruler{\8\8\8}3{in}
+\endexample
+\enddesc
+
+\begindesc
+\cts vtop {\<vertical mode material>}
+\aux\cts vtop {{\bt to} \<dimen> \rqbraces{\<vertical mode material>}}
+\aux\cts vtop {{\bt spread} \<dimen> \rqbraces{\<vertical mode material>}}
+\cts vbox {\rqbraces{\<vertical mode material>}}
+\aux\cts vbox {{\bt to} \<dimen> \rqbraces{\<vertical mode material>}}
+\aux\cts vbox {{\bt spread} \<dimen> \rqbraces{\<vertical mode material>}}
+\explain
+^^{hbox//constructing with \b\tt\\hbox\e}
+These commands
+produce a \minref{vbox} (vertical \minref{box})
+containing \<vertical mode material>.
+The braces around \<vertical mode material> define a group.
+\TeX\ is in internal vertical mode when it's assembling the box.
+\TeX\ won't change the size of the box once it's been produced.
+
+The difference between |\vtop| and |\vbox| lies in where \TeX\ puts
+the reference point of the constructed vbox.
+Ordinarily, the reference point gotten from |\vtop| tends to be at or near
+the top of the constructed vbox,
+while
+the reference point gotten from |\vbox| tends to be at or near
+the bottom of the constructed vbox.
+Thus a row of vboxes all constructed with |\vtop|
+will tend to have their tops nearly in a line,
+while a row of vboxes all constructed with |\vbox|
+will tend to have their bottoms nearly in a line.
+
+|\vtop| and |\vbox| are often useful
+when you want to keep some text together on a single page.
+(For this purpose, it usually doesn't matter which command you use.)
+If your use of these commands
+prevents \TeX\ from breaking pages in an acceptable
+way, \TeX\ will complain that it's found an overfull or underfull vbox while
+|\output| is active.
+
+The height of a vbox depends on
+the arguments to |\vtop| or |\vbox|.
+For |\vbox|, \TeX\ determines the height as follows:
+\ulist\compact
+\li If you specify only \<vertical mode material>,
+the vbox will have its natural height.
+\li If you specify |to| \<dimen>,
+the height of the vbox will be \<dimen>.
+\li If you specify |spread| \<dimen>, the height of the vbox will be
+its natural height plus \<dimen>, i.e.,
+the height of the vbox will be stretched vertically by \<dimen>.
+\endulist
+\noindent
+For |\vtop|,
+\TeX\ constructs the box using its rules for |\vbox| and then
+apportions the vertical extent between the height and the depth as
+described below.
+
+Ordinarily, the width of a constructed vbox is the width of the widest
+item inside it.\footnote
+{More precisely, it's the distance from the reference point to the rightmost
+edge of the constructed vbox. Therefore,
+if you move any of the items right using ^|\moveright| or
+^|\moveleft| (with a negative distance),
+the constructed vbox might be wider.}
+The rules for apportioning the vertical extent between the
+height and the depth are more complicated:
+\ulist
+\li For |\vtop|,
+the height is the height of its first item, if that item is a box or rule.
+Otherwise the height is zero. The depth is whatever vertical
+extent remains after the height is subtracted.
+\li For |\vbox|,
+the depth is the depth of its last item, if that item is a box or rule.
+Otherwise the depth is zero. The height is whatever vertical
+extent remains after the depth is subtracted.%
+\footnote{In fact, there's a further complication.
+Suppose that after the depth has been determined
+using the two rules just given, the depth turns out to be greater than
+^|\boxmaxdepth|.
+Then the depth is reduced to |\boxmaxdepth| and the height is adjusted
+accordingly.}
+\endulist
+
+The |\vfil| command (\xref\vfil) is useful for filling out a vbox
+^^|\vfil//filling a vbox|
+with empty space when the material in the box isn't as tall as
+the vertical extent of the box.
+\example
+\hbox{\hsize = 10pc \raggedright\parindent = 1em
+\vtop{In this example, we see how to use vboxes to
+produce the effect of double columns. Each vbox
+contains two paragraphs, typeset according to \TeX's
+usual rules except that it's ragged right.\par
+This isn't really the best way to get true double
+columns because the columns}
+\hskip 2pc
+\vtop{\noindent
+aren't balanced and we haven't done anything to choose
+the column break automatically or even to fix up the
+last line of the first column.\par
+However, the technique of putting running text into a
+vbox is very useful for placing that text where you
+want it on the page.}}
+|
+\produces
+\hbox{\hsize = 10pc \raggedright\parindent = 1em
+\vtop{In this example, we see how to use vboxes to
+produce the effect of double columns. Each vbox
+contains two paragraphs, typeset according to \TeX's
+usual rules except that it's ragged right.\par
+This isn't really the best way to get true double
+columns because the columns}
+\hskip 2pc
+\vtop{\noindent
+aren't balanced and we haven't done anything to choose
+the column break automatically or even to fix up the
+last line of the first column.\par
+However, the technique of putting running text into a
+vbox is very useful for placing that text where you
+want it on the page.}}
+\nextexample
+\hbox{\hsize = 1in \raggedright\parindent = 0pt
+\vtop to .75in{\hrule This box is .75in deep. \vfil\hrule}
+\qquad
+\vtop{\hrule This box is at its natural depth. \vfil\hrule}
+\qquad
+\vtop spread .2in{\hrule This box is .2in deeper than
+ its natural depth.\vfil\hrule}}
+|
+\produces
+\hbox{\hsize = 1in \raggedright\parindent=0pt
+\vtop to .75in{\hrule This box is .75in deep. \vfil\hrule}
+\qquad
+\vtop{\hrule This box is at its natural depth. \vfil\hrule}
+\qquad
+\vtop spread .2in{\hrule This box is .2in deeper than
+ its natural depth.\vfil\hrule}}
+\nextexample
+% See how \vbox lines up boxes at their bottoms
+% instead of at their tops.
+\hbox{\hsize = 1in \raggedright
+\vbox to .5in{\hrule This box is .5in deep.\vfil\hrule}
+\qquad
+\vbox to .75in{\hrule This box is .75in deep.\vfil\hrule}}
+|
+\produces
+\hbox{\hsize = 1in \raggedright
+\vbox to .5in{\hrule This box is .5in deep.\vfil\hrule}
+\qquad
+\vbox to .75in{\hrule This box is .75in deep.\vfil\hrule}}
+\vskip 16pt % to avoid running into the next command description
+\endexample
+\enddesc
+
+\begindesc
+\margin{Two commands interchanged here.}
+\cts boxmaxdepth {\param{dimen}}
+\explain
+This parameter contains a dimension $D$.
+\TeX\ will not construct a box whose depth exceeds $D$.
+If you produce a box whose depth $d$ would exceed $D$,
+\TeX\ will transfer the
+excess depth to the height of the box, effectively moving the
+\minref{reference point} of the box down by $d-D$.
+If you set |\boxmaxdepth| to zero, \TeX\ will line up a row of vboxes
+so that their bottom boundaries all lie on the same horizontal line.
+\PlainTeX\ sets |\boxmaxdepth| to |\maxdimen| \ctsref{\maxdimen},
+so |\boxmaxdepth| won't affect your boxes unless you change it.
+\enddesc
+
+\begindesc
+\cts underbar {\<argument>}
+\explain
+This command puts \<argument> into an \minref{hbox}
+and underlines it without regard to anything that protrudes below the
+\minref{baseline} of the box.
+\example
+\underbar{Why not learn \TeX?}
+|
+\produces
+\underbar{Why not learn \TeX?}
+\endexample
+\enddesc
+
+\begindesc
+\cts everyhbox {\param{token list}}
+\cts everyvbox {\param{token list}}
+\explain
+These parameters contain token lists that \TeX\ expands at the start of
+every \minref{hbox} or \minref{vbox} that it constructs.
+Any items resulting from the expansion then become
+the beginning of the list of items for the box.
+By default these token lists are empty.
+\enddesc
+
+%==========================================================================
+\subsection {Setting and retrieving the contents of boxes}
+
+\begindesc
+\bix^^{box registers}
+%
+\cts setbox {\<register>\thinspace{\bt =}\thinspace\<box>}
+\cts box {\<register>}
+\explain
+^^{assignments//of boxes}
+These commands respectively set and retrieve the contents
+of the box register
+whose number is \<register>.
+Note that you set a box register a little differently than
+you set the other kinds of registers: you use
+|\setbox|$\,n$~|=| rather than |\box|$\,n$~|=|.
+
+\emph{Retrieving the contents of a box register
+with these commands has the side effect of emptying it,
+so that the box register become void.} If you don't want that to happen,
+you can use |\copy| (see below) to retrieve the contents.
+You should use |\box| in preference to |\copy|
+when you don't care about what's in a box register after you've used it,
+so as not to exhaust \TeX's memory by filling it with obsolete boxes.
+\example
+\setbox0 = \hbox{mushroom}
+\setbox1 = \vbox{\copy0\box0\box0}
+\box1
+|
+\produces
+\setbox0 = \hbox{mushroom}
+\setbox1 = \vbox{\copy0\box0\box0}
+\box1
+\endexample
+\enddesc
+
+\begindesc
+\cts copy {\<register>}
+\explain
+^^{boxes//copying}\minrefs{box}
+This command
+produces a copy of box register \<register>.
+This command is useful when you want to retrieve the contents of a box
+register but don't want to destroy the contents.
+(Retrieving the register contents with ^|\box| makes the register void.)
+\example
+\setbox0 = \hbox{good }
+Have a \copy0 \box0 \box0 day!!
+|
+\produces
+\setbox0 = \hbox{good }
+Have a \copy0 \box0 \box0 day!
+\endexample
+\enddesc
+
+\begindesc
+\cts unhbox {\<register>}
+\cts unvbox {\<register>}
+^^{boxes//extracting contents of}
+\explain
+These commands produce the list contained in box register \<register> and make
+that box register void.
+|\unhbox| applies to box registers containing
+hboxes and |\unvbox| applies to box registers containing vboxes.
+You should use these commands in preference to |\unhcopy| and |\unvcopy|
+(see below)
+when you don't care about what's in the box register after you've used it,
+so as not to exhaust \TeX's memory by filling it with obsolete boxes.
+\example
+\setbox0=\hbox{The Mock Turtle sighed deeply, and
+drew the back of one flapper across his eyes. }
+\setbox1=\hbox{He tried to speak, but sobs choked
+ his voice. }
+\unhbox0 \unhbox1
+% \box0 \box1 would set two hboxes side by side
+% (and produce a badly overfull line).
+\box1 % produces nothing
+|
+\produces
+\setbox0=\hbox{The Mock Turtle sighed deeply, and
+drew the back of one flapper across his eyes. }
+\setbox1=\hbox{He tried to speak, but sobs choked
+ his voice. }
+\unhbox0 \unhbox1
+% \hbox0 \hbox1 would set two hboxes side by side
+% (and produce a badly overfull line).
+\box1 % Produces nothing.
+\endexample
+\enddesc
+
+\begindesc
+\cts unhcopy {\<register>}
+\cts unvcopy {\<register>}
+^^{boxes//extracting contents of}
+^^{boxes//copying }\minrefs{box}
+\explain
+These commands produce the list contained in box register \<register> and
+leave the contents of the register undisturbed.
+|\unhcopy| applies to box registers containing hboxes
+and |\unvcopy| applies to box registers containing vboxes.
+\example
+\setbox0=\hbox{The Mock Turtle sighed deeply, and
+drew the back of one flapper across his eyes. }
+\setbox1=\hbox{He tried to speak, but sobs choked his
+ voice. }
+\unhcopy0 \unhcopy1\par\noindent
+% \box0 \box1 would set two hboxes side by side
+% (and produce a badly overfull line).
+\box1 % Produces an hbox (which can't be broken).
+|
+\produces
+\setbox0=\hbox{The Mock Turtle sighed deeply, and
+drew the back of one flapper across his eyes. }
+\setbox1=\hbox{He tried to speak, but sobs choked his
+ voice. }
+\unhcopy0 \unhcopy1\par\noindent
+% \hbox0 \hbox1 would set two hboxes side by side
+% (and produce a badly overfull line).
+\box1 % produces an hbox (which can't be broken)
+\endexample
+\enddesc
+
+\see |\wd|, |\dp|, |\ht| (\xref\ht).
+\eix^^{box registers}
+
+%==========================================================================
+\subsection {Shifting boxes}
+
+\begindesc
+\cts moveleft {\<dimen> \<box>}
+\cts moveright {\<dimen> \<box>}
+\bix^^{boxes//shifting}
+\minrefs{box}
+\explain
+These commands move \<box> left or right by \<dimen> (which can be
+negative). You can only apply |\moveleft| and |\moveright| to a box
+that's in a \minref{vertical list}.
+\example
+\vbox{\vbox{Phoebe}\vbox{walked}%
+\moveleft 20pt\vbox{a}\moveright 20pt\vbox{crooked}%
+\vbox{mile.}}
+|
+\produces
+\hfuzz = \maxdimen
+\vbox{\vbox{Phoebe}\vbox{walked}%
+\moveleft 20pt\vbox{a}\moveright 20pt\vbox{crooked}%
+\vbox{mile.}}
+\endexample
+\enddesc
+
+\begindesc
+\cts lower {\<dimen> \<box>}
+\cts raise {\<dimen> \<box>}
+\explain
+These commands move \<box> up or down by \<dimen>
+(which can be negative).
+You can only apply |\raise| and |\lower| to a box
+that's in a \minref{horizontal list}.
+\example
+Are you feeling \lower 6pt \hbox{depressed} about the
+ \raise 6pt \hbox{bump} on your nose?
+|
+\produces
+Are you feeling \lower 6pt \hbox{depressed} about the
+ \raise 6pt \hbox{bump} on your nose?
+\endexample
+
+\eix^^{boxes//shifting}
+\enddesc
+
+%==========================================================================
+\subsection {Dimensions of box registers}
+
+\begindesc
+\bix^^{box registers}
+\bix^^{dimensions//of box registers}
+\cts ht {\<register>\param{dimen}}
+\cts dp {\<register>\param{dimen}}
+\cts wd {\<register>\param{dimen}}
+\explain
+These parameters refer to the ^{height}, ^{depth}, and ^{width}
+respectively of \minref{box} \minref{register} \<register>.
+You can use them to find out the dimensions of a box.
+You can also change the dimensions of a box, but it's a tricky business;
+if you want to be adventurous you can
+learn all about it from \knuth{pages~388--389}.
+\example
+\setbox0 = \vtop{\hbox{a}\hbox{beige}\hbox{bunny}}%
+The box has width \the\wd0, height \the\ht0,
+and depth \the\dp0.
+|
+\produces
+\setbox0 = \vtop{\hbox{a}\hbox{beige}\hbox{bunny}}%
+The box has width \the\wd0, height \the\ht0,
+and depth \the\dp0.
+\endexample
+\eix^^{box registers}
+\eix^^{dimensions//of box registers}
+\enddesc
+
+%==========================================================================
+\subsection {Struts, phantoms, and empty boxes}
+
+\begindesc
+\margin{This subsection is a merger of two previous subsections.
+The commands have also been reordered.}
+\bix^^{struts}
+\cts strut {}
+\explain
+This command produces a box whose width is zero
+and whose height (|8.5pt|) and depth (|3.5pt|)
+are those of a more or less typical line of type in |cmr10|,
+the default \plainTeX\ font.
+Its main use is in forcing lines to have the same height
+when you've disabled \TeX's interline glue with
+|\offinter!-lineskip| ^^|\offinterlineskip| or a similar command,
+e.g., when you're constructing an alignment.
+If the natural height of a line is
+too short, you can bring it up to standard by including a |\strut|
+in the line. The strut will force the height and depth of the line
+to be larger, but it won't print anything or consume any horizontal
+space.
+
+If you're setting type in a font that's bigger or smaller than |cmr10|,
+you should redefine |\strut| for that context.
+\example
+\noindent % So we're in horizontal mode.
+\offinterlineskip % So we get the inherent spacing.
+% The periods in this vbox are not vertically equidistant.
+\vtop{\hbox{.}\hbox{.(}\hbox{.x}
+ \hbox{.\vrule height 4pt depth 0pt}}\qquad
+% The periods in this vbox are vertically equidistant
+% because of the struts.
+\vtop{\hbox{.\strut}\hbox{.(\strut}\hbox{.x\strut}
+ \hbox{.\vrule height 4pt depth 0pt\strut}}
+|
+
+\produces
+\noindent % So we're in horizontal mode.
+\offinterlineskip % So we get the inherent spacing.
+% The periods in this vbox are not vertically equidistant.
+\vtop{\hbox{.}\hbox{.(}\hbox{.x}
+ \hbox{.\vrule height 4pt depth 0pt}}\qquad
+% The periods in this vbox are vertically equidistant
+% because of the struts.
+\vtop{\hbox{.\strut}\hbox{.(\strut}\hbox{.x\strut}
+ \hbox{.\vrule height 4pt depth 0pt\strut}}
+\endexample
+\enddesc
+
+\begindesc
+\cts mathstrut {}
+\explain
+This command produces a phantom formula whose width is zero
+and whose height and depth are the same as those of a left parenthesis.
+|\mathstrut| is in fact defined as `|\vphantom(|'.
+Its main use is for getting radicals, underbars, and overbars to line
+up with other radicals, underbars, and overbars in a formula.
+It is much like ^|\strut| (\xref \strut),
+except that it adjusts itself to the different \minref{style}s
+that can occur in math formulas.
+\example
+$$\displaylines{
+\overline{a_1a_2} \land \overline{b_1b_2}
+\quad{\rm versus}\quad \overline{a_1a_2\mathstrut}
+ \land \overline{b_1b_2\mathstrut}\cr
+\sqrt{\epsilon} + \sqrt{\xi} \quad{\rm versus}\quad
+\sqrt{\epsilon\mathstrut} + \sqrt{\xi\mathstrut}\cr}$$
+|
+\dproduces
+\kern 4pt
+$$\displaylines{
+\overline{a_1a_2} \land \overline{b_1b_2}
+\quad{\rm versus}\quad \overline{a_1a_2\mathstrut}
+ \land \overline{b_1b_2\mathstrut}\cr
+\sqrt{\epsilon} + \sqrt{\xi} \quad{\rm versus}\quad
+\sqrt{\epsilon\mathstrut} + \sqrt{\xi\mathstrut}\cr}$$
+\endexample
+\eix^^{struts}
+\enddesc
+
+\begindesc
+\cts phantom {\<argument>}
+\explain
+\bix^^{boxes//phantom}
+\bix^^{phantoms}
+This command produces an empty \minref{box}
+having the same size and placement
+that \<argument> would have were it typeset.
+One use of |\phantom| is for reserving space for a symbol that for some
+reason needs to be drawn in by hand.
+\example
+$1\phantom{9}2$
+|
+\produces
+$1\phantom{9}2$
+\endexample
+\enddesc
+
+\begindesc
+\cts hphantom {\<argument>}
+\cts vphantom {\<argument>}
+\explain
+These commands produce phantom boxes\minrefs{box}\ that
+don't print anything:
+\ulist\compact
+\li |\hphantom| produces a box with the same width as \<argument>
+but zero height and depth.
+\li |\vphantom| produces a box with the same height and depth as \<argu\-ment>
+but zero width.
+\endulist
+\noindent
+Their main purpose is to force a subformula to have a certain minimum
+horizontal or vertical dimension.
+\example
+$$\left[\vphantom{u\over v}t\right] \star
+ \left[{u\over v}\right]\quad
+ \{\hphantom{xx}\}$$
+|
+\dproduces
+\kern 4pt
+$$\left[\vphantom{u\over v}t\right] \star
+ \left[{u\over v}\right]\quad
+ \{\hphantom{xx}\}$$
+\endexample
+\enddesc
+
+\begindesc
+\cts smash {\<argument>}
+\explain
+This command typesets \<argument>,
+but forces the height and depth of its containing \minref{box} to be zero.
+You can use |\smash| and |\vphantom| in combination to give a subformula
+any height and depth that you wish.
+\example
+$${\smash{r_m \brace r_n}\vphantom{r}} \Longrightarrow r$$
+|
+\dproduces
+\kern 4pt
+$${\smash{r_m \brace r_n}\vphantom{r}} \Longrightarrow r$$
+\endexample
+\eix^^{boxes//phantom}
+\eix^^{phantoms}
+\enddesc
+
+\begindesc
+^^{boxes//empty}
+\cts null {}
+\explain
+This command produces an empty \minref{hbox}.
+\example
+\setbox0 = \null
+The null box \null has width \the\wd0, height \the\ht0,
+and depth \the\dp0.
+|
+\produces
+\setbox0 = \null
+The null box \null has width \the\wd0, height \the\ht0,
+and depth \the\dp0.
+\endexample
+\enddesc
+
+
+%==========================================================================
+\subsection {Parameters pertaining to malformed boxes}
+
+\begindesc
+\bix^^{boxes//overfull}
+\bix^^{boxes//underfull}
+\cts overfullrule {\param{dimen}}
+\explain
+This parameter specifies the width of the rule
+that \TeX\ appends to an overfull \minref{hbox}.
+\PlainTeX\ sets it to |5pt|.
+\enddesc
+
+\begindesc
+\cts hbadness {\param{number}}
+\cts vbadness {\param{number}}
+\explain
+These parameters specify the thresholds of horizontal and vertical
+\minref{badness} for reporting underfull or overfull boxes.
+|\hbadness| applies to hboxes and |\vbadness| applies to vboxes.
+If the badness of a constructed box exceeds the threshold,
+\TeX\ will report an error. If you raise the thresholds
+(the \plainTeX\ defaults are both $1000$),
+\TeX\ will be less likely to complain.
+Note that the settings of |\hbadness| and |\vbadness| have no effect on
+the appearance of your typeset document; they only affect the error
+messages that you get.
+See \knuth{page~302} for a precise description
+of how \TeX\ decides when to complain about an overfull or underfull
+box.
+
+\margin{The material on tolerance was inappropriate here and has been
+removed. A new example replaces it.}
+\example
+\hbadness = 10000 % Suppress any hbadness complaints.
+\hbox to 2in{a b}\par
+\hbadness = 500 % Report hbadness exceeding 500.
+\hbox to 2in{a\hskip 0pt plus .5in b}
+|
+\logproduces
+Underfull \hbox (badness 5091) detected at line 4
+\tenrm a b
+
+\hbox(6.94444+0.0)x144.54, glue set 3.70787
+.\tenrm a
+.\glue 0.0 plus 36.135
+.\tenrm b
+|
+\endexample
+\enddesc
+
+\begindesc
+\cts badness {}
+\explain
+This command yields the numerical value of the badness of the \minref{box}
+(either horizontal or vertical) that \TeX\ has most recently produced.
+If the box was overfull, |\badness| will be $1000000$; in all other cases
+it will be between $0$ and $10000$.
+\enddesc
+
+\begindesc
+\cts hfuzz {\param{dimen}}
+\cts vfuzz {\param{dimen}}
+\explain
+These parameters specify the amount that
+a \minref{box} can exceed its natural size before \TeX\ considers it to be
+overfull. ^^{boxes//overfull}
+|\hfuzz| applies to hboxes and |\vfuzz| applies to vboxes.
+\PlainTeX\ sets both parameters to |0.1pt|.
+\example
+\hfuzz = .5in
+\hbox to 2in{This box is longer than two inches.}
+% No error results
+|
+\produces
+\hfuzz = .5in
+\hbox to 2in{This box is longer than two inches.}
+% No error results
+\doruler{\8\8\8}3{in}
+\endexample
+
+\eix^^{boxes//overfull}
+\eix^^{boxes//underfull}
+\eix^^{box commands}
+\enddesc
+
+\see |\tolerance| \ctsref{\tolerance}.
+%==========================================================================
+\section {Retrieving the last item from a list}
+
+\begindesc
+^^{boxes//last box in a list}
+^^{kerns//last kern in a list}
+^^{penalties//last penalty in a list}
+^^{glue//last glue item in a list}
+\margin{This section has been moved in its entirety from the chapter
+(`Commands for general operations')}
+\cts lastkern {}
+\cts lastskip {}
+\cts lastpenalty {}
+\cts lastbox {}
+\explain
+These control sequences yield the value of the last item on the current
+list. They aren't true commands because they can only appear as
+part of an argument.
+If the last item on the list isn't of the indicated type,
+they yield a zero value (or an empty box, in the case of |\lastbox|).
+For example,
+if the last item on the current list is a \minref{kern},
+|\lastkern| yields the dimension of that kern; if it
+isn't a kern, it yields a dimension of $0$.
+
+Using |\lastbox| has the additional effect of removing the last box from
+the list.
+If you want the original |\last!-box| to remain on the list, you
+have to add a copy of it to the list.
+|\last!-box| is not permitted in a math list or in the main
+vertical~list.
+
+These control sequences are
+most useful after macro calls that might have inserted entities of
+the indicated kinds.
+
+\example
+\def\a{two\kern 15pt}
+one \a\a\hskip 2\lastkern three\par
+% Get three times as much space before `three'.
+\def\a{\hbox{two}}
+one \a
+\setbox0 = \lastbox % Removes `two'.
+three \box0.
+|
+\produces
+\def\a{two\kern 15pt}
+one \a\a\hskip 2\lastkern three\par
+% get three times as much space before `three'
+\def\a{\hbox{two}}
+one \a
+\setbox0 = \lastbox % removes `two'
+three \box0.
+\endexample
+\enddesc
+
+\begindesc
+\cts unkern {}
+\cts unskip {}
+\cts unpenalty {}
+\explain
+If the last item on the current list is of type \minref{kern},
+\minref{glue}, or \minref{penalty} respectively, these commands remove it
+from that list. If the item isn't of the right type, these commands have
+no effect. Like ^|\lastbox|, you can't apply them to lists in math mode or to
+the main vertical list.
+These commands
+are most useful after a macro call that is known to have inserted
+a specific item that you don't want there.
+\TeX\ doesn't provide an ^|\unbox| command because |\lastbox| produces
+nearly the same effect.
+\enddesc
+
+
+%==========================================================================
+\section {Rules and leaders}
+
+\begindesc
+\bix^^{rules}
+\bix^^{horizontal rules}
+\bix^^{vertical rules}
+%
+\cts hrule {}
+\aux\cts hrule {\bt height \<dimen> width \<dimen> depth \<dimen>}
+\cts vrule {}
+\aux\cts vrule {{\bt width \<dimen> height \<dimen> depth \<dimen>}}
+\explain
+The |\hrule| command produces a horizontal rule; the |\vrule| command
+produces a vertical rule. You can specify any or all of the width,
+height, and depth of the rule---\TeX\ supplies default values for those
+that you omit. You can give the dimensions of the rule in any order;
+the forms listed above show just two of the possible combinations. You
+can even give a dimension of a given kind more than once---if you do,
+the last one is the one that counts.
+
+If you don't specify the width of a horizontal rule, the rule is
+extended horizontally to the boundaries of the innermost \minref{box} or
+\minref{alignment} that contains the rule. If you don't specify the
+height of a horizontal rule, it defaults to |0.4pt|; if you don't
+specify the depth of a horizontal rule, it defaults to |0pt|.
+
+If you don't specify the width of a vertical rule, it defaults to
+|0.4pt|. If you don't specify the height or the depth of a vertical
+rule, the rule is extended to the boundary of the innermost \minref{box}
+or \minref{alignment} that contains the rule.
+
+\TeX\ treats a horizontal rule as an inherently vertical item
+and a vertical rule as an inherently horizontal item.
+Thus a horizontal rule is legal only in a \minref{vertical mode},
+while a vertical rule is legal only in a \minref{horizontal mode}.
+^^{horizontal mode//rules in}
+^^{vertical mode//rules in}
+If this seems surprising, visualize it---a horizontal rule runs
+from left to right and separates vertical items in a sequence, while
+a vertical rule runs up and down and
+separates horizontal items in a sequence.
+
+\example
+\hrule\smallskip
+\hrule width 2in \smallskip
+\hrule width 3in height 2pt \smallskip
+\hrule width 3in depth 2pt
+|
+\produces
+\medskip
+\hrule\smallskip
+\hrule width 2in \smallskip
+\hrule width 3in height 2pt \smallskip
+\hrule width 3in depth 2pt
+\nextexample
+% Here you can see how the baseline relates to the
+% height and depth of an \hrule.
+\leftline{
+ \vbox{\hrule width .6in height 5pt depth 0pt}
+ \vbox{\hrule width .6in height 0pt depth 8pt}
+ \vbox{\hrule width .6in height 5pt depth 8pt}
+ \vbox{\hbox{ baseline}\kern 3pt \hrule width .6in}
+}
+|
+\produces
+\medskip
+\leftline{
+ \vbox{\hrule width .6in height 5pt depth 0pt}
+ \vbox{\hrule width .6in height 0pt depth 8pt}
+ \vbox{\hrule width .6in height 5pt depth 8pt}
+ \vbox{\hbox{ baseline}\kern 3pt \hrule width .6in}
+}
+\nextexample
+\hbox{( {\vrule} {\vrule width 8pt} )}
+\hbox {( {\vrule height 13pt depth 0pt}
+ {\vrule height 13pt depth 7pt} x)}
+% the parentheses define the height and depth of each of the
+% two preceding boxes; the `x' sits on the baseline
+|
+\produces
+\medskip
+\hbox{( {\vrule} {\vrule width 8pt} )}
+\hbox {( {\vrule height 13pt depth 0pt}
+ {\vrule height 13pt depth 7pt} x)}
+\endexample
+
+\eix^^{rules}
+\eix^^{horizontal rules}
+\eix^^{vertical rules}
+\enddesc
+
+\begindesc
+\bix^^{leaders}
+\easy\cts leaders {\<box or rule> \<skip command>}
+\cts cleaders {\<box or rule> \<skip command>}
+\cts xleaders {\<box or rule> \<skip command>}
+\explain
+These commands produce \minref{leaders}, i.e., they fill a
+horizontal or vertical space with
+copies of a pattern \seeconcept{leaders}.
+The \<box> or \<rule> specifies a leader,
+i.e., a single copy of the pattern,
+while the \<skip command> specifies a
+window to be filled with a
+row or a column of the leaders.
+The pattern is repeated as many times as will fit into the window.
+If \<skip command> is a horizontal skip, the window
+contains a row of leaders and \TeX\ must be in a horizontal mode;
+if \<skip command> is a vertical skip, the window
+contains a column of leaders and \TeX\ must be in a vertical mode.
+
+The commands differ in how they arrange the repeated pattern in the space
+and where they put any leftover space:
+
+\ulist\compact
+\li For |\leaders|, \TeX\ aligns a row of leaders with the left end of
+the innermost \minref{box} $B$ that is to contain the result of the
+|\leaders| command.
+It aligns a column of leaders with the top of $B$.
+Those leaders that fall entirely within the window are retained.
+Any leftover space at the top and bottom of the window is left empty.
+\li For |\cleaders|, the leaders are centered within the window.
+\li For |\xleaders| the pattern is uniformly distributed throughout the window.
+If the leftover space is $l$ and the leader is repeated $n$ times,
+\TeX\ puts space of width or height $l/(n+1)$ between adjacent leaders and
+at the two ends (left and right or top and bottom) of the leaders.
+\endulist
+
+\example
+\def\pattern{\hbox to 15pt{\hfil.\hfil}}
+\line{Down the Rabbit-Hole {\leaders\pattern\hfil} 1}
+\line{The Pool of Tears {\leaders\pattern\hfil} 9}
+\line{A Caucus-Race and a Long Tale {\cleaders\pattern
+ \hfil} 19}
+\line{Pig and Pepper {\xleaders\pattern\hfil} 27}
+|
+\produces
+\def\pattern{\hbox to 15pt{\hfil.\hfil}}\par
+\line{Down the Rabbit-Hole {\leaders\pattern\hfil} 1}
+\line{The Pool of Tears {\leaders\pattern\hfil} 9}
+\line{A Caucus-Race and a Long Tale {\cleaders\pattern
+ \hfil} 19}
+\line{Pig and Pepper {\xleaders\pattern\hfil} 27}
+\nextexample
+\def\bulletfill{\vbox to 3ex{\vfil\hbox{$\bullet$}\vfil}}%
+\def\mybox{\vbox to 1in}
+\def\myrule{\hrule width 4pt}\hsize=2in
+\hrule \line{%
+ \mybox{\myrule depth 8pt \leaders\bulletfill\vfill}
+ \hfil
+ \mybox{\myrule depth 15pt \leaders\bulletfill\vfill}
+ \hfil
+ \mybox{\myrule depth 18pt \cleaders\bulletfill\vfill}
+ \hfil
+ \mybox{\myrule depth 12pt \xleaders\bulletfill\vfill}%
+}\hrule
+|
+\produces
+\medskip
+\def\bulletfill{\vbox to 3ex{\vfil\hbox{$\bullet$}\vfil}}%
+\def\mybox{\vbox to 1in}\def\myrule{\hrule width 4pt}\hsize=2in
+\hrule \line{%
+ \mybox{\myrule depth 8pt \leaders\bulletfill\vfill}
+ \hfil
+ \mybox{\myrule depth 15pt \leaders\bulletfill\vfill}
+ \hfil
+ \mybox{\myrule depth 18pt \cleaders\bulletfill\vfill}
+ \hfil
+ \mybox{\myrule depth 12pt \xleaders\bulletfill\vfill}%
+}\hrule
+\endexample\enddesc
+
+\begindesc
+\cts dotfill {}
+\cts hrulefill {}
+\explain
+^^{fill}
+These commands respectively fill the enclosing horizontal space with
+a row of dots on the baseline and with
+a horizontal line on the baseline.
+It's usually a good idea to leave a space between
+|\dotfill| or |\hrulefill|
+and any text that precedes or follows it (see the example below).
+\example
+\hbox to 3in{Start {\dotfill} Finish}
+\hbox to 3in{Swedish {\hrulefill} Finnish}
+|
+\produces
+\par\hbox to 3in{Start {\dotfill} Finish}
+\hbox to 3in{Swedish {\hrulefill} Finnish}
+\endexample\enddesc
+
+\begindesc
+\cts leftarrowfill {}
+\cts rightarrowfill {}
+\explain
+^^{fill}
+These commands fill the enclosing horizontal space with
+left-pointing or right-pointing ^{arrows}.
+\example
+\hbox to 3in{\vrule \rightarrowfill \ 3 in
+ \leftarrowfill\vrule}
+|
+\produces
+\medskip
+\hbox to 3in{\vrule \rightarrowfill \ 3 in
+ \leftarrowfill\vrule}
+\endexample
+
+\eix^^{leaders}
+\enddesc
+
+%==========================================================================
+\section {Alignments}
+
+%==========================================================================
+\subsection {Tabbing alignments}
+
+\begindesc
+\bix^^{tabbing alignments}
+\bix^^{alignments//commands for}
+%
+\ctspecial + {{\bt \<text>\thinspace\&\thinspace\<text>%
+ \thinspace\& $\cdots$ \\cr}}
+\ctsxrdef{@plus}
+\cts tabalign {}
+\explain
+These commands begin a single line in a tabbed \minref{alignment}.
+The only difference between |\+| and |\tabalign| is that
+|\+| is an outer macro---you can't use it when \TeX\ is reading tokens at
+high speed \seeconcept{outer}.
+
+If you place an `|&|' at a position
+to the right of all existing tabs in a tabbing alignment,
+the `|&|' establishes a new tab at that position.
+\example
+\cleartabs % Nullify any previous \settabs.
+\+ {\bf if }$a[i] < a[i+1]$ &{\bf then}&\cr
+\+&&$a[i] := a[i+1]$;\cr
+\+&&{\it found }$:=$ {\bf true};\cr
+\+&{\bf else}\cr
+\+&&{\it found }$:=$ {\bf false};\cr
+\+&{\bf end if};\cr
+|
+\produces
+\cleartabs % Nullify any previous \settabs.
+\+ {\bf if }$a[i] < a[i+1]$ &{\bf then}&\cr
+\+&&$a[i] := a[i+1]$;\cr
+\+&&{\it found }$:=$ {\bf true};\cr
+\+&{\bf else}\cr
+\+&&{\it found }$:=$ {\bf false};\cr
+\+&{\bf end if};\cr
+\endexample
+\enddesc
+
+\begindesc
+\cts settabs {\<number> {\bt \\columns}}
+\aux\cts settabs {{\bt \\+} \<sample line> {\bt \\cr}}
+\explain
+The first form of
+this command defines a set of tab stops ^^{tabs}
+for a tabbing \minref{alignment}.
+It tells \TeX\ to set the tab stops so as to divide each line into
+\<number> equal parts. \TeX\ takes the length of a line to be
+|\hsize|, as usual. You can make the alignment narrower by decreasing
+|\hsize|.
+\margin{paragraph ``The tab settings $\ldots$'' moved to below.}
+\example
+{\hsize = 3in \settabs 3 \columns
+\+$1$&one&first\cr
+\+$2$&two&second\cr
+\+$3$&three&third\cr}
+|
+\produces
+{\hsize = 3in \settabs 3 \columns
+\+$1$ & one & first\cr
+\+$2$ & two & second\cr
+\+$3$ & three & third\cr}
+
+\noindent\doruler{\8\8\8}3{in}
+\smallskip
+\endexample
+
+The second form of this command defines tab stops by setting the tab stops
+at the positions indicated by the `|&|'s in the sample line.
+The sample line itself does not appear in the output. When you
+use this form you'll usually want to put material into the sample line that is
+somewhat wider than the widest corresponding material in the alignment,
+in order to produce space between the columns.
+That's what we've done in the
+example below. The material following the last tab
+stop is irrelevant, since \TeX\ does not need to position
+anything at the place where the |\cr|~appears.
+
+The tab settings established by |\settabs| remain in effect until
+you issue a new |\settabs| command or end a group containing
+the |\settabs| command.
+This is true for both forms of the command.
+
+\example
+% The first line establishes the template.
+\settabs \+$1$\qquad & three\quad & seventh\cr
+\+$1$&one&first\cr
+\+$2$&two&second\cr
+\+$3$&three&third\cr
+|
+\produces
+\settabs \+$1$\qquad & three\quad & seventh\cr % the sample line
+\+$1$&one&first\cr
+\+$2$&two&second\cr
+\+$3$&three&third\cr
+\smallskip
+\endexample
+\enddesc
+
+\begindesc
+
+\cts cleartabs {}
+\explain
+This command clears all the tabs to the right of the current column.
+Its main use is in applications such as typesetting computer programs
+in which the tab positions change from line to line.
+\enddesc
+
+\see |\cr|, |\endline|, |\crcr| (\xref \endline).
+\eix^^{tabbing alignments}
+
+%==========================================================================
+\subsection {General alignments}
+
+\begindesc
+\cts halign {{\bt \rqbraces{\<preamble> \\cr \<row> \\cr $\ldots$ \<row> \\cr}}}
+ \xrdef{@and}\xrdef{@pound}
+\aux\cts halign {{\bt to \<dimen>%
+ \rqbraces{\<preamble> \\cr \<row> \\cr $\ldots$ \<row> \\cr}}}
+\aux\cts halign {{\bt spread \<dimen>%
+ \rqbraces{\<preamble> \\cr \<row> \\cr $\ldots$ \<row> \\cr}}}
+\explain
+This command produces a horizontal \minref{alignment} consisting of a
+sequence of rows, where each row in turn contains a sequence of column
+entries. \TeX\ adjusts the widths of the column entries to accommodate
+the widest one in each column.
+
+A horizontal alignment can only appear when \TeX\ is in a vertical
+\minref{mode}. We recommend that you first study alignments in general
+(\xref{alignment}) before you attempt to use this command.
+
+An alignment consists of a ^{preamble}
+followed by the text to be aligned. The preamble,
+which describes the layout of the rows that follow, consists of a
+sequence of column templates, separated by `|&|' and ended
+by |\cr|.
+\bix^^{template}
+\bix^^{entry (column or row)}
+Each row consists of a sequence of column
+entries, also separated by `|&|' and ended by |\cr|. Within
+a template, `|#|' indicates where \TeX\ should insert the
+corresponding text of a column entry.
+In contrast, |\settabs| uses a fixed implicit template of `|#|',
+i.e., it just inserts the text as is.
+
+\TeX\ typesets each column entry in restricted horizontal mode,
+i.e., as the contents of an \minref{hbox},
+and implicitly encloses it in a group.
+
+The |to| form of this command instructs \TeX\
+to make the width of the alignment be \<dimen>,
+adjusting the space between columns as necessary.
+The |spread| form of this command instructs \TeX\
+to make the alignment wider by \<dimen> than its natural width.
+These forms are like the corresponding forms of |\hbox| \ctsref\hbox.
+
+See |\tabskip| \ctsref\tabskip{} for an example using the
+|to| form.
+
+\example
+\tabskip = 1em \halign{%
+ \hfil\it#\hfil&\hfil#\hfil&#&\hfil\$#\cr
+ United States&Washington&dollar&1.00\cr
+ France&Paris&franc&0.174\cr
+ Israel&Jerusalem&shekel&0.507\cr
+ Japan&Tokyo&yen&0.0829\cr}
+|
+\produces
+\tabskip = 1em \halign{%
+ \hfil\it#\hfil&\hfil#\hfil&#&\hfil\$#\cr
+ United States&Washington&dollar&1.00\cr
+ France&Paris&franc&0.174\cr
+ Israel&Jerusalem&shekel&0.507\cr
+ Japan&Tokyo&yen&0.0829\cr}
+\endexample
+\enddesc
+
+\begindesc
+{\tighten
+\cts valign {{\bt \rqbraces{\<preamble>\\cr \<column>\\cr $\ldots$
+ \<column>\\cr}}}
+\aux\cts valign {{\bt to \<dimen>%
+ \rqbraces{\<preamble>\\cr \<column>\\cr $\ldots$ \<column>\\cr}}}
+\aux\cts valign {{\bt spread \<dimen>%
+ \rqbraces{\<preamble>\\cr \<column>\\cr $\ldots$ \<column>\\cr}}}
+\par}
+\explain
+This command produces a vertical \minref{alignment}
+consisting of
+a sequence of columns, where each column in turn contains a sequence
+of row entries.
+\TeX\ adjusts the heights of the row entries to accommodate the tallest one
+in each row.
+
+A vertical alignment
+can only appear when \TeX\ is in a horizontal \minref{mode}.
+Because vertical alignments are (a)~conceptually somewhat difficult and
+(b)~not often used, we recommend that you learn about
+alignments in general
+(\xref{alignment}) and the |\halign| command (see above) before
+you attempt to use the |\valign| command.
+
+An alignment consists of a ^{preamble}
+followed by the text to be aligned. The preamble,
+which describes the layout of the columns that follow,
+consists of a
+sequence of row templates, separated by `|&|' and ended
+by |\cr|.
+\bix^^{template}
+Each column consists of a sequence of ^{row}
+entries, also separated by `|&|' and ended by |\cr|. Within
+a template, `|#|' indicates where \TeX\ should insert the
+corresponding text of a row entry.
+
+\TeX\ typesets each row entry in internal vertical
+mode, i.e., as the contents of a \minref{vbox},
+and implicitly encloses the entry in a group.
+It always gives the vbox zero depth.
+Any text or other horizontal mode material in a row entry then puts \TeX\
+into ordinary horizontal mode.
+(This is just an application of the general rules for \TeX's behavior
+in internal vertical mode.)
+The usual paragraphing parameters apply in this case:
+the row entry has an initial
+indentation of |\parindent| (\xref\parindent) and
+its lines have the
+|\leftskip| and |\rightskip| (\xref\leftskip) \minref{glue}
+appended to~them.
+
+Note in particular that a row entry containing text has
+a width of |\hsize| (\xref\hsize). Unless you reset
+|\hsize| to the row width that you want, you're likely to
+encounter overfull \minref{hbox}es, or find that
+the first column takes up the width of the entire page, or both.
+\eix^^{entry (column or row)}
+
+Normally, you need to include a \minref{strut}
+^^{struts//in vertical alignments}
+in each
+template so that the rows don't come out crooked as a result
+of the varying heights of the entries in the alignment. You
+can produce a strut with the |\strut| command.
+
+The |to| form of this command instructs \TeX\
+to make the vertical extent of the alignment be \<dimen>,
+adjusting the space between rows as necessary.
+The |spread| form of this command instructs \TeX\
+to make the alignment taller by \<dimen> than its natural height.
+These forms are like the corresponding forms of |\vbox| \ctsref\vbox.
+
+\example
+{\hsize=1in \parindent=0pt
+\valign{#\strut&#\strut&#\strut&#\strut\cr
+ bernaise&curry&hoisin&hollandaise\cr
+ ketchup&marinara&mayonnaise&mustard\cr
+ rarebit&tartar\cr}}
+|
+\produces
+{\hsize=1in \parindent=0pt \leftskip=0pt
+\valign{#\strut&#\strut&#\strut&#\strut\cr
+ bernaise&curry&hoisin&hollandaise\cr
+ ketchup&marinara&mayonnaise&mustard\cr
+ rarebit&tartar\cr}}
+\nextexample
+% same thing but without struts (shows why you need them)
+{\hsize=1in \parindent=0pt
+\valign{#&#&#&#\cr
+ bernaise&curry&hoisin&hollandaise\cr
+ ketchup&marinara&mayonnaise&mustard\cr
+ rarebit&tartar\cr}}
+|
+\produces
+{\hsize=1in \parindent=0pt \leftskip=0pt
+\valign{#&#&#&#\cr
+ bernaise&curry&hoisin&hollandaise\cr
+ ketchup&marinara&mayonnaise&mustard\cr
+ rarebit&tartar\cr}}
+\endexample
+\enddesc
+
+\begindesc
+\cts ialign {}
+\explain
+This command behaves just like ^|\halign|,
+except that it first sets the |\tabskip| glue to zero and
+sets |\everycr| empty.
+\enddesc
+
+\begindesc
+\cts cr {}
+\explain
+This command ends the preamble of a horizontal or vertical
+alignment, a row of a horizontal or tabbing alignment,
+or a column of a vertical alignment.
+You can cause \TeX\ to take certain actions whenever it sees a |\cr|
+by setting the value of the ^|\everycr| parameter \ctsref\everycr.
+\enddesc
+
+\begindesc
+\cts endline {}
+\explain
+This command is a synonym for the ^|\cr| command. It is useful when
+you've redefined |\cr| but still need access to the original definition.
+\enddesc
+
+\begindesc
+\cts crcr {}
+\explain
+This command behaves just like ^|\cr|, except that \TeX\ ignores it if
+it comes immediately after a |\cr| or a ^|\noalign|.
+Its main application is as a safety measure to avoid a misleading error
+message caused by a \minref{macro} that expects an argument ending in |\cr|.
+If you put |\crcr| after the `|#|$n$' that denotes such an argument
+in the macro's definition, the
+macro will work properly whether or not the argument ends with |\cr|.
+\enddesc
+
+\begindesc
+\cts omit {}
+\explain
+This command tells \TeX\ to ignore a template in a horizontal or vertical
+\minref{alignment} while processing a particular column or row entry
+respectively.
+|\omit| must appear as the first item in a column or row entry; in effect,
+it overrides the template from the preamble with the simple
+template `|#|'.
+
+
+\example
+\tabskip = 2em\halign{%
+ \hfil\it#\hfil&\hfil#\hfil&#&\hfil\$#\cr
+ United States&Washington&dollar&1.00\cr
+ \omit \dotfill France\dotfill&Paris&franc&0.174\cr
+ Israel&Jerusalem&shekel&0.507\cr
+ Japan&Tokyo&yen&0.0829\cr}
+|
+\produces
+\tabskip = 2em\halign{%
+ \hfil\it#\hfil&\hfil#\hfil&#&\hfil\$#\cr
+ United States&Washington&dollar&1.00\cr
+ \omit \dotfill France\dotfill&Paris&franc&0.174\cr
+ Israel&Jerusalem&shekel&0.507\cr
+ Japan&Tokyo&yen&0.0829\cr}
+\nextexample
+{\hsize=1.2in \parindent=0pt
+\valign{(#)\strut&(#)\strut&(#)\strut&(#)\strut\cr
+ bernaise&curry&hoisin&hollandaise\cr
+ ketchup&\omit\strut{\bf MARINARA!!}&mayonnaise&mustard\cr
+ rarebit&tartar\cr}}
+|
+\produces
+{\hsize=1.2in \parindent=0pt \leftskip=0pt
+\valign{(#)\strut&(#)\strut&(#)\strut&(#)\strut\cr
+ bernaise&curry&hoisin&hollandaise\cr
+ ketchup&\omit\strut{\bf MARINARA!}&mayonnaise&mustard\cr
+ rarebit&tartar\cr}}
+\endexample
+\enddesc
+
+\begindesc
+\cts span {}
+\explain
+The meaning of this command depends on whether it appears in a preamble
+or in an alignment entry.
+\ulist
+\li Normally, \TeX\ does not expand tokens in the preamble
+when it reads them.
+Putting |\span| in front of a token in the preamble causes
+that token to be expanded immediately according to \TeX's usual rules
+of \minref{macro} expansion.
+\li Putting |\span| instead of `|&|' between two column or row entries
+causes those columns or rows to be combined.
+For a horizontal alignment,
+the width of the combined column is the sum of the
+widths of the component columns.
+For a vertical alignment,
+the height of the combined row is the sum of the
+heights of the component rows.
+The template of the combined column or combined row forms a single group,
+so font-setting commands preceding a |\span| affect everything up to
+the next `|&|'.
+\endulist
+\noindent
+|\span| is rarely useful by itself outside of a template,
+but it provides the basic mechanism
+for defining ^|\multispan|.
+\enddesc
+
+\begindesc
+\cts multispan {\<number>}
+\explain
+This command tells \TeX\ that the following
+\<number> columns in a row of a horizontal alignment,
+or
+\<number> rows in a column of a vertical alignment,
+should be combined into a single column or row (as with
+|\span|) and that their templates should be omitted (as with |\omit|).
+
+\example
+\tabskip = 13pt\halign{%
+ \hfil\it#\hfil&\hfil#\hfil&#&\hfil\$#\cr
+ United States&Washington&dollar&1.00\cr
+ France&Paris&franc&0.174\cr
+ Israel&Jerusalem &
+ \multispan 2 \hfil\it(no information)\hfil \cr
+ Japan&Tokyo&yen&0.0829\cr}
+|
+\produces
+\tabskip = 13pt\halign{%
+ \hfil\it#\hfil&\hfil#\hfil&#&\hfil\$#\cr
+ United States&Washington&dollar&1.00\cr
+ France&Paris&franc&0.174\cr
+ Israel&Jerusalem &
+ \multispan 2 \hfil\it(no information)\hfil \cr
+ Japan&Tokyo&yen&0.0829\cr}
+\nextexample
+{\hsize=1.2in \parindent=0pt
+\valign{(#)\strut&(#)\strut&(#)\strut&(#)\strut\cr
+ bernaise&curry&hoisin&hollandaise\cr
+ \multispan 3$$\left\{{{\rm ketchup}\atop{\rm marinara}}
+ \right\}$$&mustard\cr
+ rarebit&tartar\cr}}
+|
+\produces
+{\hsize=1.2in \parindent=0pt \leftskip=0pt
+\valign{(#)\strut&(#)\strut&(#)\strut&(#)\strut\cr
+ bernaise&curry&hoisin&hollandaise\cr
+ \multispan 3$$\left\{{{\rm ketchup}\atop{\rm marinara}}
+ \right\}$$&mustard\cr
+ rarebit&tartar\cr}}
+\endexample
+
+\eix^^{template}
+\enddesc
+
+\begindesc
+\cts noalign {\rqbraces{\<vertical mode material>}}
+\aux\cts noalign {\rqbraces{\<horizontal mode material>}}
+\explain
+This command inserts
+\<vertical mode material>
+after the current row of a horizontal \minref{alignment} or
+\<horizontal mode material> after the current column of a vertical
+\minref{alignment}.
+The material can be text, glue, a rule, or anything else.
+
+The most common use of |\noalign|
+is to put extra space after a row or column.
+If you want to put extra space after \emph{every\/} row of a horizontal
+alignment, use ^|\openup| (\xref\openup).
+
+\example
+\halign{%
+ \hfil\it#\hfil\tabskip=2em&\hfil#\hfil&#&
+ \hfil\$#\tabskip=0em\cr
+ % The \tabskip changes prevent the rule below
+ % from sticking out.
+ United States&Washington&dollar&1.00\cr
+ France&Paris&franc&0.174\cr
+ \noalign{\smallskip\hrule\smallskip}
+ Israel&Jerusalem&shekel&0.507\cr
+ Japan&Tokyo&yen&0.0829\cr}
+|
+\produces
+\halign{%
+ \hfil\it#\hfil\tabskip=2em&\hfil#\hfil&#&
+ \hfil\$#\tabskip=0em\cr
+ % The \tabskip changes prevent the rule below
+ % from sticking out.
+ United States&Washington&dollar&1.00\cr
+ France&Paris&franc&0.174\cr
+ \noalign{\smallskip\hrule\smallskip}
+ Israel&Jerusalem&shekel&0.507\cr
+ Japan&Tokyo&yen&0.0829\cr}
+\nextexample
+{\hsize=1in \parindent=0pt
+\valign{#\strut&#\strut&#\strut&#\strut\cr
+ \noalign{\vrule width 2pt\quad}
+ bernaise&curry&hoisin&hollandaise\cr
+ \noalign{\vrule width 2pt\quad}
+ ketchup&marinara&mayonnaise&mustard\cr
+ \noalign{\vrule width 2pt\quad}
+ rarebit&tartar\cr
+ \noalign{\vrule width 2pt\quad}}}
+|
+\produces
+\medskip
+{\hsize=1in \parindent=0pt
+\valign{#\strut&#\strut&#\strut&#\strut\cr
+ \noalign{\vrule width 2pt\quad}
+ bernaise&curry&hoisin&hollandaise\cr
+ \noalign{\vrule width 2pt\quad}
+ ketchup&marinara&mayonnaise&mustard\cr
+ \noalign{\vrule width 2pt\quad}
+ rarebit&tartar\cr
+ \noalign{\vrule width 2pt\quad}}}
+\endexample
+\enddesc
+
+\begindesc
+\cts tabskip {\param{glue}}
+\explain
+This parameter specifies the amount of horizontal or vertical glue
+that \TeX\ puts between the
+columns of a horizontal alignment or between the
+rows of a vertical alignment.
+\TeX\ also puts the |\tabskip| glue
+to the left of the first column and to the right of the last column
+of a horizontal alignment, and
+above the first row
+and below the last row of a vertical alignment.
+You can change |\tabskip| within a template---%
+the change will affect the glue associated with all the following
+|&|'s as well as the glue after the last row or column.
+\example
+\halign to 3.5in{%
+ \hfil\it#\tabskip = 2em plus 8pt
+ \hfil&\hfil#\hfil&#\tabskip = 1em
+ &\hfil\$#\tabskip = 0em\cr
+ United States&Washington&dollar&1.00\cr
+ France&Paris&franc&0.174\cr
+ Israel&Jerusalem&shekel&0.507\cr
+ Japan&Tokyo&yen&0.0829\cr}
+|
+\produces
+\halign to 3.5in{%
+ \hfil\it#\tabskip = 2em plus 8pt
+ \hfil&\hfil#\hfil&#\tabskip = 1em
+ &\hfil\$#\tabskip = 0em\cr
+ United States&Washington&dollar&1.00\cr
+ France&Paris&franc&0.174\cr
+ Israel&Jerusalem&shekel&0.507\cr
+ Japan&Tokyo&yen&0.0829\cr}
+\nextexample
+{\hsize = 1in \parindent=0pt \tabskip=5pt
+\valign{#\strut&#\strut\tabskip = 3pt
+ &#\strut&#\strut\cr
+ bernaise&curry&hoisin&hollandaise\cr
+ ketchup&marinara&mayonnaise&mustard\cr
+ rarebit&tartar\cr}}
+|
+\produces
+{\hsize = 1in \parindent=0pt \tabskip=5pt
+\valign{#\strut&#\strut\tabskip = 3pt
+ &#\strut&#\strut\cr
+ bernaise&curry&hoisin&hollandaise\cr
+ ketchup&marinara&mayonnaise&mustard\cr
+ rarebit&tartar\cr}}
+\endexample
+\enddesc
+
+\begindesc
+\cts hidewidth {}
+\explain
+This command tells \TeX\ to ignore the width of the next column entry in a
+horizontal alignment. It's useful when you have an entry that is longer
+than most of the others in the same column,
+and you'd rather have that entry stick out of the column than
+make all the entries
+in the column wider. If the |\hidewidth| is at the left of the
+entry, the entry sticks out to the left; if the |\hidewidth| is at the
+right of the entry, the entry sticks out to the~right.
+\example
+\tabskip = 25pt\halign{%
+ \hfil\it#\hfil&\hfil#\hfil&#&\hfil\$#\cr
+ United States&\hidewidth Washington&
+ dollar&1.00\cr
+ France&Paris&franc&0.174\cr
+ Israel&Jerusalem&shekel&0.507\cr
+ Japan&Tokyo&yen&0.0829\cr}
+|
+\produces
+\tabskip = 25pt\halign{%
+ \hfil\it#\hfil&\hfil#\hfil&#&\hfil\$#\cr
+ United States&\hidewidth Washington&
+ dollar&1.00\cr
+ France&Paris&franc&0.174\cr
+ Israel&Jerusalem&shekel&0.507\cr
+ Japan&Tokyo&yen&0.0829\cr}
+\endexample
+\enddesc
+
+\begindesc
+\cts everycr {\param{token list}}
+\explain
+\TeX\ expands \<token list> whenever it executes
+a |\cr|---at the end of every preamble,
+at the end of every row of a horizontal alignment,
+and at the end of every column of a vertical alignment.
+The |\everycr| commands are expanded just after the |\cr|.
+Thus you can cause \TeX\ to
+execute certain commands at the end of a preamble, row, or column by
+assigning a list of those commands to |\everycr|.
+
+The |\everycr| tokens shouldn't include any commands other than |\no!-align|.
+That's because
+the |\everycr| tokens will reappear after the last
+|\cr| of the alignment. A command other than
+|\noalign| will then make \TeX\ think that it's starting a new
+row or column.
+\TeX\ will complain about a missing |\cr|, insert
+a |\cr|, insert the |\everycr| tokens again, and repeat these actions
+indefinitely.
+\example
+\everycr={\noalign{\smallskip\hrule\smallskip}}
+\halign{#\tabskip = 11pt&\hfil#\hfil&\hfil#\hfil
+ \tabskip = 0pt\cr
+ $1$&one&first\cr
+ $2$&two&second\cr
+ $3$&three&third\cr}
+|
+\produces
+\medskip
+\everycr={\noalign{\smallskip\hrule\smallskip}}
+\halign{#\tabskip = 11pt&\hfil#\hfil&\hfil#\hfil
+ \tabskip = 0pt\cr
+ $1$&one&first\cr
+ $2$&two&second\cr
+ $3$&three&third\cr}
+\endexample
+
+\eix^^{alignments//commands for}
+\enddesc
+
+\enddescriptions
+
+
+\endchapter
+\byebye
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