\batchmode
 % ɽ��: ��̩�١���Ū�����٤η׻���ˡ


\documentclass[a4j,12pt]{jarticle}
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\usepackage{Dennou6}
\usepackage{ascmac}



\setlength{\parindent}{0mm} 

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\Dtitle{��̩�١���Ū�����٤η׻���ˡ}
\Dauthor[�����̰�ϯ]
{
 {\bf �����̰�ϯ(������������)} \\
sugiyama@gfd-dennou.org
}


\Ddate{2005/08/21}




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$T$%
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$M$%
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$T^{*}$%
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$M^{*}$%
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$z+dz$%
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$T = 300$%
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$\displaystyle \frac{\left(\rho - \rho^{*}\right) g}{\rho^{*}}$%
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$M_{v}$%
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$X$%
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$\displaystyle c_{v} dT.$%
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$\displaystyle 0.$%
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$\displaystyle \delta W$%
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$\displaystyle - p dV,$%
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\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3558}%
$\displaystyle - R dT + V \left( \frac{- M p g}{R T} \right) dz,
\; (�� �ſ尵ʿ�դμ�)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3560}%
$\displaystyle - R dT - M g  dz .$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3561}%
$\displaystyle \delta Z$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3563}%
$\displaystyle - \lambda dX.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1203}%
$c_{v}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1207}%
$p$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1209}%
$V$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1211}%
$R$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1217}%
$\lambda$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1219}%
$dX$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3574}%
$\displaystyle c_{v}dT + R dT + M g dz   +  \lambda dX = 0 ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3575}%
$\displaystyle c_{p}dT + M g dz   + \lambda dX = 0 ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1221}%
$c_{p}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1223}%
$c_{p} = c_{v} + R$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3580}%
$\displaystyle c_{p}dT + M g dz = 0,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3581}%
$\displaystyle \DD{T}{z} = - \frac{ M g }{c_{p}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3583}%
$\displaystyle \DD{T}{z} =
- \frac{ M_{v} g }{ {c_{p}}_{d}}
\left\{
\frac{  1  + \frac{(M_{v} - M_{d})X}{M_{d}} }
{ 1 + \frac{( {c_{p}}_{v} - {c_{p}}_{d} ) X}{{c_{p}}_{d}}}
\right\}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3585}%
$\displaystyle \DD{T}{p} =  \frac{ R T }{ c_{p} p },$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3586}%
$\displaystyle \DD{T}{p} =  \frac{ R T }{ {c_{p}}_{d} p }
\left\{
\Dinv{ 1 + \frac{( {c_{p}}_{v} - {c_{p}}_{d} ) X}{{c_{p}}_{d}}}
\right\}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3590}%
$\displaystyle M \approx M_{d}, \;\;\;
c_{p} \approx {c_{p}}_{d}, \;\;\;$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3592}%
$\displaystyle \DD{T}{z}
\approx - \frac{M_{d} g}{{c_{p}}_{d}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3594}%
$\displaystyle M \approx M_{v}, \;\;\;
c_{p} \approx {c_{p}}_{v},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3596}%
$\displaystyle \DD{T}{z}
\approx - \frac{M_{v} g}{{c_{p}}_{v}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3600}%
$\displaystyle dX = \Dinv{p} de - \left( \frac{e}{p^{2}} \right) dp.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1227}%
$e$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3603}%
$\displaystyle de = \frac{e \lambda dT}{R T^{2}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3605}%
$\displaystyle dX$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3607}%
$\displaystyle \Dinv{p} de - \frac{e}{p^{2}} dp,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3609}%
$\displaystyle \Dinv{p} \left( \frac{e \lambda dT}{R T^{2}} \right)
- \frac{e}{p^{2}} \left( - \frac{ M p g}{R T} dz \right) ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3611}%
$\displaystyle \frac{e}{p} \frac{\lambda}{ R_{v} T^{2}} dT
+  \frac{e}{p} \frac{M g}{ R T} dz ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3613}%
$\displaystyle \frac{ \lambda X }{ R T^{2}} dT
+  \frac{M g X}{ R T} dz .$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3616}%
$\displaystyle c_{p} dT + M g dz +
\lambda
\left(\frac{\lambda X }{ R T^{2}} dT
+  \frac{M g X}{ R T} dz \right)  = 0,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3617}%
$\displaystyle c_{p}
\left( 1+ \frac{ \lambda^{2} X}{ c_{p} R T^{2}} \right) dT
+ M g \left( 1 +  \frac{ \lambda X}{R T} \right) dz
= 0,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3618}%
$\displaystyle \DD{T}{z} = - \frac{M g}{c_{p}}
\left(
\frac{ 1 +  \frac{ \lambda X}{R T}}
{ 1 + \frac{ \lambda^{2} X}{ c_{p} R T^{2}} }
\right).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3620}%
$\displaystyle \DD{T}{z} = - \frac{M_{d} g}{{c_{p}}_{d}}
\left\{
\frac{  1  + \frac{(M_{v} - M_{d})X}{M_{d}} }
{ 1 + \frac{( {c_{p}}_{v} - {c_{p}}_{d} ) X}{{c_{p}}_{d}}}
\right\}
\left(
\frac{ 1 +  \frac{ \lambda X}{R T}}
{ 1 + \frac{ \lambda^{2} X}{ c_{p} R T^{2}} }
\right)
.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3622}%
$\displaystyle \DD{T}{p} =  \frac{R T}{c_{p} p}
\left(
\frac{ 1 +  \frac{ \lambda X}{R T}}
{ 1 + \frac{ \lambda^{2} X}{ c_{p} R T^{2}} }
\right),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3623}%
$\displaystyle \DD{T}{p} =  \frac{R T}{{c_{p}}_{d} p}
\left\{
\Dinv{ 1 + \frac{( {c_{p}}_{v} - {c_{p}}_{d} ) X}{{c_{p}}_{d}}}
\right\}
\left(
\frac{ 1 +  \frac{ \lambda X}{R T}}
{ 1 + \frac{ \lambda^{2} X}{ c_{p} R T^{2}} }
\right).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3627}%
$\displaystyle M \approx M_{d}, \;\;\;
c_{p} \approx {c_{p}}_{d}, \;\;\;
\frac{ \lambda X }{R T } \ll 1, \;\;\;
\frac{ \lambda^{2} X }{ c_{p} R T^{2} } \ll 1,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3629}%
$\displaystyle \DD{T}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3630}%
$\textstyle \approx$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3631}%
$\displaystyle - \frac{M_{d} g}{{c_{p}}_{d}}
\left( 1 +  \frac{ \lambda X}{R T} \right)
\left( 1 - \frac{ \lambda^{2} X}{ {c_{p}}_{d} R
T^{2}} \right) ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3633}%
$\displaystyle - \frac{M_{d} g}{{c_{p}}_{d}}
\left\{  1 -  \frac{\lambda X}{ {c_{p}}_{d} T}
\left( \frac{ \lambda}{ R T}
- \frac{{c_{p}}_{d}}{R} \right) \right\},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3636}%
$\displaystyle M \approx M_{v}, \;\;\;
c_{p} \approx {c_{p}}_{v}, \;\;\;
\frac{ \lambda X }{R T } \gg 1, \;\;\;
\frac{ \lambda^{2} X }{ c_{p} R T^{2} } \gg 1,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3640}%
$\displaystyle - \frac{M_{v} g}{{c_{p}}_{v}}
\frac{\frac{ \lambda X}{R T}}
{\frac{ \lambda^{2} X}{ {c_{p}}_{v} R
T^{2}} } ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3642}%
$\displaystyle -
\frac{M_{v} g T}{\lambda}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3645}%
$\displaystyle N^{2}
=
\frac{g}{T}
\left(
\DD{T}{z}
+ \frac{M g}{c_{p}}
\right)
-
\frac{ g (M_{v} - M_{d})}{M} \DD{X}{z},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3647}%
$\displaystyle \DD{X}{z}
= \frac{ \lambda X }{ R T^{2}} \DD{T}{z} +  \frac{M g X}{ R T}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3649}%
$\displaystyle N^{2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3651}%
$\displaystyle \frac{g}{T}
\left(
\DD{T}{z}
+ \frac{M g}{c_{p}}
\right)
-
\frac{ g (M_{v} - M_{d})}{M}
\left( \frac{ \lambda X }{ R T^{2}} \DD{T}{z} +  \frac{M g X}{ R T} \right),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3653}%
$\displaystyle \frac{g}{T}
\left[
\frac{M g}{c_{p}}  +
\DD{T}{z} \left\{
1 -  \frac{ (M_{v} - M_{d})}{M}  \frac{ \lambda X }{ R T}
\right\}
\right]
-
\frac{g}{T} \frac{  (M_{v} - M_{d})}{M} \frac{M g X}{ R }$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3657}%
$\displaystyle \frac{g}{T}
\left[
\frac{M_{d} g}{{c_{p}}_{d}}
\left\{
\frac{  1  + \frac{(M_{v} - M_{d})X}{M_{d}} }
{ 1 + \frac{( {c_{p}}_{v} - {c_{p}}_{d} ) X}{{c_{p}}_{d}}}
\right\}
+
\DD{T}{z} \left\{
1 -  \frac{ (M_{v} - M_{d}) \frac{ \lambda X }{ R T}}
{M_{d} \left\{ 1 + \frac{(M_{v} - M_{d})X}{M_{d}} \right\}}
\right\}
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3658}%
$\displaystyle -
\frac{g}{T} \frac{  (M_{v} - M_{d}) g X}{ R }.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3664}%
$\displaystyle \frac{g}{T}
\left[
\frac{M_{d} g}{{c_{p}}_{d}}
- \frac{M_{d} g}{{c_{p}}_{d}}
\left\{  1 -  \frac{\lambda X}{{c_{p}}_{d} T}
\left( \frac{ \lambda}{ R T}
- \frac{{c_{p}}_{d}}{R} \right) \right\}
\left\{
1 -  \frac{ (M_{v} - M_{d})}{M_{d}}  \frac{ \lambda X }{ R T}
\right\}
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3665}%
$\displaystyle -
\frac{g}{T} \frac{  (M_{v} - M_{d})}{M_{d}} \frac{M_{d} g X}{ R }$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3667}%
$\displaystyle \frac{M_{d} g^{2}}{{c_{p}}_{d} T}
\left\{
\frac{\lambda X}{{c_{p}}_{d} T}
\left( \frac{ \lambda}{ R T}
- \frac{{c_{p}}_{d}}{R} \right)
+
\frac{ (M_{v} - M_{d})}{M_{d}}  \frac{ \lambda X }{ R T}
\right\}
-
\frac{M_{d} g^{2}}{{c_{p}}_{d} T}
\frac{  (M_{v} - M_{d})}{M_{d}} \frac{ {c_{p}}_{d} X}{ R }$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3669}%
$\displaystyle \frac{M_{d} g^{2}}{{c_{p}}_{d} T}
\left(
\frac{ \lambda}{ R T}
- \frac{{c_{p}}_{d}}{R} \right)
\left\{
\frac{\lambda}{{c_{p}}_{d} T}
+ \frac{ (M_{v} - M_{d})}{M_{d}}
\left( 1 - \frac{\lambda^{2} X}{{c_{p}}_{d} R T^{2}} \right)
\right\} X$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3671}%
$\displaystyle \frac{M_{d} g^{2}}{{c_{p}}_{d} T}
\left(
\frac{ \lambda}{ R T}
- \frac{{c_{p}}_{d}}{R} \right)
\left(
\frac{\lambda}{{c_{p}}_{d} T}
+ \frac{ (M_{v} - M_{d})}{M_{d}}
\right) X.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3675}%
$\displaystyle \frac{g}{T}
\left[
\frac{M_{v} g}{{c_{p}}_{v}}
- \frac{M_{v} g T}{\lambda}
\left\{
1 -  \frac{ (M_{v} - M_{v})}{M_{v}}  \frac{ \lambda X }{ R T}
\right\}
-
\frac{  (M_{v} - M_{v})}{M_{v}} \frac{M_{v} g X}{ R }
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3677}%
$\displaystyle \frac{g}{T}
\left[
\frac{M_{v} g}{{c_{p}}_{v}}
\left( 1 - \frac{{c_{p}}_{v} T}{\lambda} \right)
+ \frac{M_{v} g T}{\lambda}
\frac{ (M_{v} - M_{d})}{M_{v}}  \frac{ \lambda X }{ R T}
-
\frac{  (M_{v} - M_{d})}{M_{v}} \frac{M_{v} g X}{ R }
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3679}%
$\displaystyle \frac{M_{v} g^{2}}{{c_{p}}_{v} T}
\left( 1 - \frac{{c_{p}}_{v} T}{\lambda} \right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3682}%
$\displaystyle \ln{e}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3684}%
$\displaystyle A - \frac{B}{C + T},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3685}%
$\displaystyle ������$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3686}%
$\displaystyle A = 7.9186968d0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3687}%
$\displaystyle B = 1636.909d0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3688}%
$\displaystyle C = 224.92d0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1623}%
$^{\circ}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3693}%
$\displaystyle \ln{e} = \left(
A - \frac{B}{C + T - 273.15 }
\right)  \ln{10} + \ln{133.322}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3695}%
$\displaystyle \lambda$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3697}%
$\displaystyle R T^{2} \DD{\ln{e}}{T}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3699}%
$\displaystyle R T^{2}  \frac{B * \ln{10}}{ ( C + T - 273.15 )^2 }$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1625}%
$18 \times 10^{-3}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1627}%
$2.323 \times 10^{-3}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1629}%
$^2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1631}%
$40.66 \times 10^{3}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1633}%
$23.35 \times 10^{3}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1635}%
$8.180 \times 10^{3}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1637}%
$373.15$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1639}%
$195.40$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1641}%
$90.68$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1643}%
$\Deqref{lapserate:Cond_LapseRate_low}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1645}%
$M \approx M_{d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3761}%
$\displaystyle \frac{(M_{v} - M_{d}) X}{M_{d}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3763}%
$\displaystyle \frac{(18.0 - 2.323) \times 10^{-3}}{ 2.323 \times 10^{-3} },$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3765}%
$\displaystyle 6.7486 X
\ll 1.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3766}%
$\displaystyle X$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3767}%
$\textstyle \ll$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3768}%
$\displaystyle 1.5 \times 10^{-1}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1647}%
$c_{p} \approx {c_{p}}_{d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3771}%
$\displaystyle \frac{( {c_{p}}_{v} - {c_{p}}_{d} ) X}{ {c_{p}}_{d}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3773}%
$\displaystyle \frac{23.5 - 27.66}{27.66}X,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3775}%
$\displaystyle 0.21 X  \ll 1.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3778}%
$\displaystyle 4.76.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1649}%
$\frac{ \lambda X}{R T} \ll 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3781}%
$\displaystyle \frac{ \lambda X}{R T}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3783}%
$\displaystyle \frac{44492}{8.31 \times 300} X$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3785}%
$\displaystyle 17.8 X \ll 1.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3788}%
$\displaystyle 5.6 \times 10^{-2}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1651}%
$\frac{ \lambda^{2} X}{ c_{p} R T^{2} } \ll 1 $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3791}%
$\displaystyle \frac{ \lambda^{2} X}{ c_{p} R T^{2} }$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3793}%
$\displaystyle \frac{(44492)^{2}}{30 \times 8.31 \times (300)^{2}} X$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3795}%
$\displaystyle 88 X \ll 1.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3798}%
$\displaystyle 1.1 \times 10^{-2}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1653}%
$X \ll 1.1 \times 10^{-2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1655}%
$\Deqref{lapserate:Cond_LapseRate_high}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1657}%
$M \approx M_{v}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3807}%
$\displaystyle X \approx 1.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1659}%
$c_{p} \approx {c_{p}}_{v}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1661}%
$\frac{ \lambda X}{R T} \gg 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3817}%
$\displaystyle 17.8 X \gg 1.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3819}%
$\textstyle \gg$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1663}%
$\frac{ \lambda^{2} X}{ c_{p} R T^{2} } \gg 1 $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3827}%
$\displaystyle 88 X \gg 1.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1665}%
$X \le 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1667}%
$X = 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlfigureA{figure1405}%
\begin{figure} \begin{center}
  \Depsf[120mm]{ps/MolWtMean.ps}
 \end{center}
\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1412}%
\begin{figure} \begin{center}
  \Depsf[120mm]{ps/CpMean.ps}
 \end{center}
\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlfigureA{figure1421}%
\begin{figure} \begin{center}
  \Depsf[120mm]{ps/LapseRateDry.ps}
 \end{center}
\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1679}%
$1.0 \times 10^{-1} \le X \le 1 $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3853}%
$\displaystyle \DD{T}{z} \approx - \frac{M_{d} g R T^{2} }{\lambda^{2}}
\left\{
\Dinv{X}
+ \frac{(M_{v} - M_{d})}{M_{d}}
+  \frac{ \lambda }{R T}
+ \frac{(M_{v} - M_{d}) \lambda X }{M_{d} R T}
\right\}
,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1467}%
\begin{figure} \begin{center}
  \Depsf[120mm]{ps/LapseRate.ps}
 \end{center}
\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1480}%
\begin{figure} \begin{center}
  \Depsf[120mm]{ps/EffLatentHeat.ps}
 \end{center}
\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1492}%
\begin{figure} \begin{center}
  \Depsf[120mm]{ps/LapseRate2.ps}
 \end{center}
\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1500}%
\begin{figure} \begin{center}
  \Depsf[120mm]{ps/LapseRateList.ps}
 \end{center}
\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlfigureA{figure1514}%
\begin{figure} \begin{center}
  \Depsf[120mm]{ps/Stab.ps}
 \end{center}
\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1528}%
\begin{figure} \begin{center}
  \Depsf[120mm]{ps/StabList.ps}
 \end{center}
\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1735}%
$_4$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1737}%
$_3$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1555}%
\begin{figure} \begin{center}
  \Depsf[120mm]{ps/Jupiter.ps}
 \end{center}
\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1563}%
\begin{figure} \begin{center}
  \Depsf[120mm]{ps/Jupiter2.ps}
 \end{center}
\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlfigureA{figure1573}%
\begin{figure}\begin{center}
\Depsf[120mm]{ps/jupiter.ps}
\end{center}
\end{figure}%
\lthtmlfigureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2662}%
$r$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2664}%
$M = (1 - rX^{sat}) M_{d} + rX^{sat} M_{v}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2666}%
$dT(z)/dz$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2668}%
$M = M_{d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2670}%
$dT^{*}(z)/dz$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2672}%
$dT^{*}/dz = - M_{d} g/ {c_{p}}_{d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2674}%
$M = M^{*}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2676}%
$M^{*} = M_{d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3998}%
$\displaystyle N^{2} =
\frac{g}{T}
\left(
\DD{T}{z} + \frac{M g}{{c_{p}}_{d}}
\right)
-
g
\left(
\Dinv{M} \DD{M}{z}
\right).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4001}%
$\displaystyle N^{2}
=
\frac{g}{T}
\left(
\DD{T}{z} + \frac{M g}{{c_{p}}_{d}}
\right)
-
g \left(
\frac{r (M_{v} - M_{d})}{M} \DD{X^{sat}}{z}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2680}%
$T_{v} = M_{d} T/ M $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4004}%
$\displaystyle N^{2} =
\frac{g}{T_{v}}
\left(
\DD{T_{v}}{z} + \frac{M_{d} g}{{c_{p}}_{d}}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4009}%
$\displaystyle N^{2} =
\frac{g}{T_{v}}
\left(
\DD{T_{v}}{z} + \frac{g}{{c_{p}^{\dagger}}_{d}}
\right),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4010}%
$\displaystyle T_{v} =
\frac{T }{1 + (\varepsilon - 1) e /p },$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4011}%
$\displaystyle \DD{T}{z} = - \frac{g}{c_{p}^{\dagger}}
\left(
\frac{ 1 + \frac{\lambda^{\dagger} q}{R^{\dagger} T}  }
{ 1 + \frac{{\lambda^{\dagger}}^{2} \varepsilon q}{R^{\dagger} c_{p}^{\dagger} T^{2}}  }
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2682}%
$\dagger$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2684}%
$R^{\dagger} =
R/M$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2686}%
$c_{p}^{\dagger} = c_{p}/M$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2688}%
${c_{p}^{\dagger}}_{d}=c_{p}/M_{d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2690}%
$\lambda^{\dagger}=\lambda/M_{v}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2692}%
$\varepsilon = M_{v}/M_{d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2696}%
$q$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2698}%
$r = 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4024}%
$\displaystyle \frac{g}{T_{v}}
\left(
\DD{T_{v}}{z} + \frac{M_{d} g}{{c_{p}}_{d}}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4026}%
$\displaystyle \frac{g}{T_{v}}
\left(
\DD{T_{v}}{z} + \frac{g}{{c_{p}^{\dagger}}_{d}}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4028}%
$\displaystyle T_{v}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4030}%
$\displaystyle T \frac{M_{d}}{M} ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4032}%
$\displaystyle T \frac{M_{d}}{M_d (1 - X) + M_{v} X} ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4034}%
$\displaystyle T \frac{M_{d}}{M_d (p - e)/p + M_{v} e/p } ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4036}%
$\displaystyle T \frac{M_{d} p}{M_d p +  (M_{v} - M_{d}) e } ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4038}%
$\displaystyle T \frac{1}{1 +  (M_{v} - M_{d})/M_{d} e/p } ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4040}%
$\displaystyle \frac{T}{1 +  (\varepsilon - 1) e/p }.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4042}%
$\displaystyle q
= \frac{M_{v} X}{M_{d} (1 - X) + M_{v} X}
\approx \frac{M_{v}}{M_{d}} X.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4043}%
$\displaystyle M \approx M_{d}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4047}%
$\displaystyle - \frac{M g}{c_{p}}
\left(
\frac{ 1 +  \frac{ \lambda X}{R T}}
{ 1 + \frac{ \lambda^{2} X}{ c_{p} R T^{2}} }
\right),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4049}%
$\displaystyle - \frac{M g}{( M  c_{p}^{\dagger}  ) }
\left(
{ 1 +  \frac{ (M_{v} \lambda^{\dagger}) (q M_{d} / M_{v})}{(M_{d} R^{\dagger}) T}}
\right)
/
\left(
{ 1 + \frac{ (M_{v} \lambda^{\dagger})^{2} (q M_{d} / M_{v})}
{ (M_{d} c_{p}^{\dagger}) (M_{d} R^{\dagger})  T^{2}} }
\right),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4051}%
$\displaystyle - \frac{g}{c_{p}^{\dagger}}
\left(
\frac{ 1 + \frac{\lambda^{\dagger} q}{R^{\dagger} T} }
{ 1 + \frac{{\lambda^{\dagger}}^{2} \varepsilon q}{R^{\dagger}
c_{p}^{\dagger} T^{2}} }
\right) .$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4057}%
$\displaystyle - \frac{g}{{c_{p}^{\dagger}}_{d}}
\left(
\frac{ 1 + \frac{\lambda^{\dagger} q}{R_{d}^{\dagger} T}  }
{ 1 + \frac{{\lambda^{\dagger}}^{2}  q}{R_{v}^{\dagger} {c_{p}^{\dagger}}_{d} T^{2}}  }
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4059}%
$\displaystyle - \frac{g}{{c_{p}^{\dagger}}_{d}}
\left\{ 1 -  \left(
\frac{\lambda^{\dagger}}{R^{\dagger}_{v} T} - \frac{{c_{p}^{\dagger}}_{d}}{R_{d}^{\dagger}}
\right)
\frac{\lambda^{\dagger} q^{\dagger}}{{c_{p}^{\dagger}}_{d} T}
\right\}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4062}%
$\displaystyle \frac{g}{T}
\left(
\DD{T}{z} + \frac{g}{{c_{p}^{\dagger}}_{d}}
\right)
+ g \left(\frac{M_{d}}{M_{v}} - 1 \right) \DP{ (rq)}{z},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4064}%
$\displaystyle \frac{g^{2}}{{c_{p}^{\dagger}}_{d} T}
\left(
\frac{\lambda^{\dagger}}{R^{\dagger}_{v} T} - \frac{{c_{p}^{\dagger}}_{d}}{R^{\dagger}_{d}}
\right)
\left\{
\frac{\lambda^{\dagger}}{{c_{p}^{\dagger}}_{d} T}
+ \left(1 - \frac{M_{d}}{M_{v}} \right)
\right\} q$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2702}%
$R_{d}^{\dagger} = R/M_{d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2704}%
$R_{v}^{\dagger} = R/M_{v}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2714}%
$r q$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2716}%
$M \approx M_{d},
R^{\dagger}_{v} = R^{\dagger} / \varepsilon$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2718}%
$ 1 \gg
\frac{{\lambda^{\dagger}}^{2} q}{R_{v}^{\dagger} {c_{p}^{\dagger}}_{d}
T^{2}} $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4078}%
$\displaystyle - \frac{g}{{c_{p}^{\dagger}}_{d}}
\left(
\frac{ 1 + \frac{\lambda^{\dagger} q}{R_{d}^{\dagger} T}  }
{ 1 + \frac{{\lambda^{\dagger}}^{2}  q}{R_{v}^{\dagger} {c_{p}^{\dagger}}_{d} T^{2}}  }
\right) ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4080}%
$\displaystyle - \frac{g}{{c_{p}^{\dagger}}_{d}}
\left( 1 + \frac{\lambda^{\dagger} q}{R_{d}^{\dagger} T}  \right)
\left(
1 - \frac{{\lambda^{\dagger}}^{2}  q}{R_{v}^{\dagger} {c_{p}^{\dagger}}_{d} T^{2}}
\right),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2722}%
$q
\ll 2.0 \times 10^{-2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4088}%
$\displaystyle \frac{g}{T}
\left(
\Gamma_{m} + \frac{M g}{{c_{p}^{\dagger}}_{d} M}
\right)
-
g \left(
\frac{r (M_{v} - M_{d})}{M} \DD{X}{z}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4090}%
$\displaystyle \frac{g}{T}
\left(
\Gamma_{m} + \frac{ g}{{c_{p}^{\dagger}}_{d}}
\right)
-
g \left(
\frac{r (M_{v} - M_{d})}{M_{d}} \frac{M_{d}}{M_{v}} \DD{q}{z}
\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4092}%
$\displaystyle \frac{g}{T}
\left(
\Gamma_{m} + \frac{ g}{{c_{p}^{\dagger}}_{d}}
\right)
+
g \left(
\frac{M_{d}}{M_{v}} - 1
\right) \DD{(r q)}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2724}%
$dT/dz = \Gamma_{m}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2726}%
$dq/dz$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4096}%
$\displaystyle \DD{ ( r q )}{z}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4098}%
$\displaystyle \left(
\frac{ \lambda^{\dagger} M_{v} }{ R^{\dagger}_{d} M_{d} T^{2}} \DD{T}{z}
+  \frac{M g }{ R^{\dagger}_{d} M T}
\right) (r q) ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4100}%
$\displaystyle \left(
-  \frac{ \lambda^{\dagger} }{ R^{\dagger}_{v} T^{2}} \frac{g}{{c_{p}^{\dagger}}_{d}}
+  \frac{g }{ R^{\dagger}_{d} T}
\right) (r q) ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4102}%
$\displaystyle \frac{g}{{c_{p}^{\dagger}}_{d} T}
\left(
\frac{ {c_{p}^{\dagger}}_{d} }{ R^{\dagger}_{d} }
-  \frac{ \lambda^{\dagger} }{ R^{\dagger}_{v} T}
\right) (r q) .$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2730}%
$dT/dz \approx - g /{c_{p}^{\dagger}}_{d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4110}%
$\displaystyle \frac{g}{T}
\left[
\frac{g}{{c_{p}^{\dagger}}_{d}}
\left\{ \left(
\frac{\lambda^{\dagger}}{R^{\dagger}_{v} T} - \frac{{c_{p}^{\dagger}}_{d}}{R_{d}^{\dagger}}
\right)
\frac{\lambda^{\dagger} q^{\dagger}}{{c_{p}^{\dagger}}_{d} T}
\right\}
\right]
+
g \left(
\frac{M_{d}}{M_{v}} - 1
\right)
\left\{
\frac{g}{{c_{p}^{\dagger}}_{d} T}
\left(
\frac{ {c_{p}^{\dagger}}_{d} }{ R^{\dagger}_{d} }
-  \frac{ \lambda^{\dagger} }{ R^{\dagger}_{v} T}
\right) (r q)
\right\} ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4112}%
$\displaystyle \frac{g^{2}}{{c_{p}^{\dagger}}_{d} T}
\left(
\frac{\lambda^{\dagger}}{R^{\dagger}_{v} T} - \frac{{c_{p}^{\dagger}}_{d}}{R_{d}^{\dagger}}
\right)
\left\{
\frac{\lambda^{\dagger} }{{c_{p}^{\dagger}}_{d} T}
+
r \left(
1 -  \frac{M_{d}}{M_{v}}
\right)
\right\} q.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}


\end{document}
