# LaTeX2HTML 2002-2-1 (1.70)
# Associate images original text with physical files.


$key = q/displaystylefrac{(18.0-2.323)times10^{-3}}{2.323times10^{-3}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="187" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img157.png"
 ALT="$\displaystyle \frac{(18.0 - 2.323) \times 10^{-3}}{ 2.323 \times 10^{-3} },$">|; 

$key = q/frac{lambdaX}{RT}gg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img182.png"
 ALT="$\frac{ \lambda X}{R T} \gg 1$">|; 

$key = q/{c_{p}}_{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img56.png"
 ALT="${c_{p}}_{d}$">|; 

$key = q/dagger;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img220.png"
 ALT="$\dagger$">|; 

$key = q/M_{d}=18times10^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$M_{d} = 18 \times 10^{-3}$">|; 

$key = q/{figure}center{{Depsf[120mm]{psslashStab.ps}{center{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="543" HEIGHT="543" BORDER="0"
 SRC="|."$dir".q|img198.png"
 ALT="\begin{figure}\begin{center}
\Depsf[120mm]{ps/Stab.ps}
\end{center}\end{figure}">|; 

$key = q/displaystyle-frac{g}{T}frac{(M_{v}-M_{d})gX}{R}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img125.png"
 ALT="$\displaystyle -
\frac{g}{T} \frac{ (M_{v} - M_{d}) g X}{ R }.$">|; 

$key = q/dT(z)slashdz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img207.png"
 ALT="$dT(z)/dz$">|; 

$key = q/1ggfrac{{lambda^{dagger}}^{2}q}{R_{v}^{dagger}{c_{p}^{dagger}}_{d}T^{2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="52" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img250.png"
 ALT="$ 1 \gg
\frac{{\lambda^{\dagger}}^{2} q}{R_{v}^{\dagger} {c_{p}^{\dagger}}_{d}
T^{2}} $">|; 

$key = q/R_{d}^{dagger}=RslashM_{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img246.png"
 ALT="$R_{d}^{\dagger} = R/M_{d}$">|; 

$key = q/displaystylefrac{e}{p}frac{lambda}{R_{v}T^{2}}dT+frac{e}{p}frac{Mg}{RT}dz,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="182" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img103.png"
 ALT="$\displaystyle \frac{e}{p} \frac{\lambda}{ R_{v} T^{2}} dT
+ \frac{e}{p} \frac{M g}{ R T} dz ,$">|; 

$key = q/displaystyleDinv{p}left(frac{elambdadT}{RT^{2}}right)-frac{e}{p^{2}}left(-frac{Mpg}{RT}dzright),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="249" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img102.png"
 ALT="$\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) ,$">|; 

$key = q/g;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="$g$">|; 

$key = q/displaystylefrac{g}{{c_{p}^{dagger}}_{d}T}left(frac{{c_{p}^{dagger}}_{d}}{R^{dagger}_{d}}-frac{lambda^{dagger}}{R^{dagger}_{v}T}right)(rq).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="205" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img262.png"
 ALT="$\displaystyle \frac{g}{{c_{p}^{\dagger}}_{d} T}
\left(
\frac{ {c_{p}^{\dagger}}...
...\dagger}_{d} }
- \frac{ \lambda^{\dagger} }{ R^{\dagger}_{v} T}
\right) (r q) .$">|; 

$key = q/displaystyleDD{T^{*}}{z}=DD{T}{z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img51.png"
 ALT="$\displaystyle \DD{T^{*}}{z} = \DD{T}{z}$">|; 

$key = q/displaystylefrac{g}{T}left(DD{T}{z}+frac{Mg}{c_{p}}right)-frac{g(M_{v}-M_{d})}{M}left(frac{lambdaX}{RT^{2}}DD{T}{z}+frac{MgX}{RT}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="439" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img122.png"
 ALT="$\displaystyle \frac{g}{T}
\left(
\DD{T}{z}
+ \frac{M g}{c_{p}}
\right)
-
\frac{...
...{M}
\left( \frac{ \lambda X }{ R T^{2}} \DD{T}{z} + \frac{M g X}{ R T} \right),$">|; 

$key = q/displaystyleN^{2}=frac{g}{T}left(DD{T}{z}+frac{Mg}{c_{p}}right)-frac{g(M_{v}-M_{d})}{M}DD{X}{z},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="348" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img119.png"
 ALT="$\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},$">|; 

$key = q/displaystyledrho=rho^{*}-rho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="$\displaystyle d \rho = \rho^{*} - \rho$">|; 

$key = q/displaystyledeltaZ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img76.png"
 ALT="$\displaystyle \delta Z$">|; 

$key = q/displaystylefrac{g}{rho^{*}}left(DD{rho}{z}deltaz-DD{rho^{*}}{z}deltazright);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="170" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="$\displaystyle \frac{g}{\rho^{*}}
\left(
\DD{\rho}{z} \delta z - \DD{\rho^{*}}{z} \delta z
\right)$">|; 

$key = q/displaystyleN^{2}=frac{g}{T}left(DD{T}{z}+frac{Mg}{{c_{p}}_{d}}right)-gleft(Dinv{M}DD{M}{z}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="313" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img213.png"
 ALT="$\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).$">|; 

$key = q/e;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img98.png"
 ALT="$e$">|; 

$key = q/displaystylefrac{g^{2}}{{c_{p}^{dagger}}_{d}T}left(frac{lambda^{dagger}}{R^{dagg_{p}^{dagger}}_{d}T}+rleft(1-frac{M_{d}}{M_{v}}right)right}q.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="372" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img265.png"
 ALT="$\displaystyle \frac{g^{2}}{{c_{p}^{\dagger}}_{d} T}
\left(
\frac{\lambda^{\dagg...
...{c_{p}^{\dagger}}_{d} T}
+
r \left(
1 - \frac{M_{d}}{M_{v}}
\right)
\right\} q.$">|; 

$key = q/textstyle=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="$\textstyle =$">|; 

$key = q/_4;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img200.png"
 ALT="$_4$">|; 

$key = q/T=376.6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$T = 376.6$">|; 

$key = q/displaystyleRT^{2}DD{ln{e}}{T};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img143.png"
 ALT="$\displaystyle R T^{2} \DD{\ln{e}}{T}$">|; 

$key = q/displaystylefrac{lambda^{2}X}{c_{p}RT^{2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img173.png"
 ALT="$\displaystyle \frac{ \lambda^{2} X}{ c_{p} R T^{2} }$">|; 

$key = q/dT^{*}(z)slashdz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img209.png"
 ALT="$dT^{*}(z)/dz$">|; 

$key = q/displaystyle17.8Xll1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img170.png"
 ALT="$\displaystyle 17.8 X \ll 1.$">|; 

$key = q/T=500;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$T=500$">|; 

$key = q/dTslashdzapprox-gslash{c_{p}^{dagger}}_{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img263.png"
 ALT="$dT/dz \approx - g /{c_{p}^{\dagger}}_{d}$">|; 

$key = q/displaystyleRT^{2}frac{B*ln{10}}{(C+T-273.15)^2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="193" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img144.png"
 ALT="$\displaystyle R T^{2} \frac{B * \ln{10}}{ ( C + T - 273.15 )^2 }$">|; 

$key = q/displaystyle-frac{g}{c_{p}^{dagger}}left(frac{1+frac{lambda^{dagger}q}{R^{daggergger}}^{2}varepsilonq}{R^{dagger}c_{p}^{dagger}T^{2}}}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="85" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img241.png"
 ALT="$\displaystyle - \frac{g}{c_{p}^{\dagger}}
\left(
\frac{ 1 + \frac{\lambda^{\dag...
...da^{\dagger}}^{2} \varepsilon q}{R^{\dagger}
c_{p}^{\dagger} T^{2}} }
\right) .$">|; 

$key = q/c_{p}^{dagger}=c_{p}slashM;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img222.png"
 ALT="$c_{p}^{\dagger} = c_{p}/M$">|; 

$key = q/M_{v};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img55.png"
 ALT="$M_{v}$">|; 

$key = q/displaystyleTfrac{M_{d}}{M_d(p-e)slashp+M_{v}eslashp},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="204" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img233.png"
 ALT="$\displaystyle T \frac{M_{d}}{M_d (p - e)/p + M_{v} e/p } ,$">|; 

$key = q/displaystylefrac{(44492)^{2}}{30times8.31times(300)^{2}}X;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="174" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img174.png"
 ALT="$\displaystyle \frac{(44492)^{2}}{30 \times 8.31 \times (300)^{2}} X$">|; 

$key = q/displaystylefrac{g}{T}left[frac{g}{{c_{p}^{dagger}}_{d}}left{left(frac{lambda^{d_{d}}-frac{lambda^{dagger}}{R^{dagger}_{v}T}right)(rq)right},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="610" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img264.png"
 ALT="$\displaystyle \frac{g}{T}
\left[
\frac{g}{{c_{p}^{\dagger}}_{d}}
\left\{ \left(...
...{d} }
- \frac{ \lambda^{\dagger} }{ R^{\dagger}_{v} T}
\right) (r q)
\right\} ,$">|; 

$key = q/displaystyleMapproxM_{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img238.png"
 ALT="$\displaystyle M \approx M_{d}$">|; 

$key = q/displaystyle-frac{M_{v}gT}{lambda};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img118.png"
 ALT="$\displaystyle -
\frac{M_{v} g T}{\lambda}$">|; 

$key = q/displaystylefrac{({c_{p}}_{v}-{c_{p}}_{d})X}{{c_{p}}_{d}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="64" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img163.png"
 ALT="$\displaystyle \frac{( {c_{p}}_{v} - {c_{p}}_{d} ) X}{ {c_{p}}_{d}}$">|; 

$key = q/displaystyleleft(frac{lambda^{dagger}M_{v}}{R^{dagger}_{d}M_{d}T^{2}}DD{T}{z}+frac{Mg}{R^{dagger}_{d}MT}right)(rq),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="254" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img260.png"
 ALT="$\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) ,$">|; 

$key = q/displaystyleDD{T}{z}=-frac{M_{d}g}{{c_{p}}_{d}}left{frac{1+frac{(M_{v}-M_{d})X}{1+frac{lambdaX}{RT}}{1+frac{lambda^{2}X}{c_{p}RT^{2}}}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="375" HEIGHT="85" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img108.png"
 ALT="$\displaystyle \DD{T}{z} = - \frac{M_{d} g}{{c_{p}}_{d}}
\left\{
\frac{ 1 + \fra...
...\frac{ \lambda X}{R T}}
{ 1 + \frac{ \lambda^{2} X}{ c_{p} R T^{2}} }
\right)
.$">|; 

$key = q/displaystylec_{p}dT+Mgdz+lambdaleft(frac{lambdaX}{RT^{2}}dT+frac{MgX}{RT}dzright)=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="373" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img105.png"
 ALT="$\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,$">|; 

$key = q/displaystyledU;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img66.png"
 ALT="$\displaystyle dU$">|; 

$key = q/dTslashdz=Gamma_{m};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img257.png"
 ALT="$dT/dz = \Gamma_{m}$">|; 

$key = q/displaystylefrac{M_{d}g^{2}}{{c_{p}}_{d}T}left(frac{lambda}{RT}-frac{{c_{p}}_{d}frac{lambda}{{c_{p}}_{d}T}+frac{(M_{v}-M_{d})}{M_{d}}right)X.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="372" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img130.png"
 ALT="$\displaystyle \frac{M_{d} g^{2}}{{c_{p}}_{d} T}
\left(
\frac{ \lambda}{ R T}
- ...
...left(
\frac{\lambda}{{c_{p}}_{d} T}
+ \frac{ (M_{v} - M_{d})}{M_{d}}
\right) X.$">|; 

$key = q/M^{*}=M_{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img212.png"
 ALT="$M^{*} = M_{d}$">|; 

$key = q/{figure}center{{Depsf[120mm]{psslashJupiter2.ps}{center{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="543" HEIGHT="543" BORDER="0"
 SRC="|."$dir".q|img203.png"
 ALT="\begin{figure}\begin{center}
\Depsf[120mm]{ps/Jupiter2.ps}
\end{center}\end{figure}">|; 

$key = q/c_{p}approx{c_{p}}_{v};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img181.png"
 ALT="$c_{p} \approx {c_{p}}_{v}$">|; 

$key = q/_3;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img201.png"
 ALT="$_3$">|; 

$key = q/displaystyleC=224.92d0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img139.png"
 ALT="$\displaystyle C = 224.92d0$">|; 

$key = q/q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img226.png"
 ALT="$q$">|; 

$key = q/times;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$\times $">|; 

$key = q/r=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img227.png"
 ALT="$r = 1$">|; 

$key = q/displaystyle-frac{M_{d}g}{{c_{p}}_{d}}left(1+frac{lambdaX}{RT}right)left(1-frac{lambda^{2}X}{{c_{p}}_{d}RT^{2}}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="283" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img114.png"
 ALT="$\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) ,$">|; 

$key = q/T_{v}=M_{d}TslashM;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img215.png"
 ALT="$T_{v} = M_{d} T/ M $">|; 

$key = q/displaystyle4.76.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img166.png"
 ALT="$\displaystyle 4.76.$">|; 

$key = q/M=M_{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img208.png"
 ALT="$M = M_{d}$">|; 

$key = q/c_{v};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img78.png"
 ALT="$c_{v}$">|; 

$key = q/displaystylefrac{g}{T_{v}}left(DD{T_{v}}{z}+frac{g}{{c_{p}^{dagger}}_{d}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img229.png"
 ALT="$\displaystyle \frac{g}{T_{v}}
\left(
\DD{T_{v}}{z} + \frac{g}{{c_{p}^{\dagger}}_{d}}
\right)$">|; 

$key = q/Xll1.1times10^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img177.png"
 ALT="$X \ll 1.1 \times 10^{-2}$">|; 

$key = q/displaystylefrac{g}{T_{v}}left(DD{T_{v}}{z}+frac{M_{d}g}{{c_{p}}_{d}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img228.png"
 ALT="$\displaystyle \frac{g}{T_{v}}
\left(
\DD{T_{v}}{z} + \frac{M_{d} g}{{c_{p}}_{d}}
\right)$">|; 

$key = q/N;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="$N$">|; 

$key = q/displaystyleln{e};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img134.png"
 ALT="$\displaystyle \ln{e}$">|; 

$key = q/displaystyleMapproxM_{d},;;;c_{p}approx{c_{p}}_{d},;;;frac{lambdaX}{RT}ll1,;;;frac{lambda^{2}X}{c_{p}RT^{2}}ll1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="383" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img111.png"
 ALT="$\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,$">|; 

$key = q/displaystyleA-frac{B}{C+T},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img135.png"
 ALT="$\displaystyle A - \frac{B}{C + T},$">|; 

$key = q/displaystyleDD{T}{z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img112.png"
 ALT="$\displaystyle \DD{T}{z}$">|; 

$key = q/{c_{p}}_{v};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img57.png"
 ALT="${c_{p}}_{v}$">|; 

$key = q/displaystyle-frac{Mg}{c_{p}}left(frac{1+frac{lambdaX}{RT}}{1+frac{lambda^{2}X}{c_{p}RT^{2}}}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="76" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img239.png"
 ALT="$\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),$">|; 

$key = q/^2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img147.png"
 ALT="$^2$">|; 

$key = q/displaystyle88Xll1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img175.png"
 ALT="$\displaystyle 88 X \ll 1.$">|; 

$key = q/M_{d}=2.323times10^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$M_{d} = 2.323 \times 10^{-3}$">|; 

$key = q/displaystylefrac{M_{v}g^{2}}{{c_{p}}_{v}T}left(1-frac{{c_{p}}_{v}T}{lambda}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img133.png"
 ALT="$\displaystyle \frac{M_{v} g^{2}}{{c_{p}}_{v} T}
\left( 1 - \frac{{c_{p}}_{v} T}{\lambda} \right)$">|; 

$key = q/T;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$T$">|; 

$key = q/_2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="$_2$">|; 

$key = q/displaystyleN^{2}=frac{g}{T}left(DD{T}{z}+frac{Mg}{{c_{p}}_{d}}right)-gleft(frac{r(M_{v}-M_{d})}{M}DD{X^{sat}}{z}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="399" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img214.png"
 ALT="$\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)$">|; 

$key = q/displaystyle-RdT-Mgdz.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img75.png"
 ALT="$\displaystyle - R dT - M g dz .$">|; 

$key = q/frac{lambda^{2}X}{c_{p}RT^{2}}ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img172.png"
 ALT="$\frac{ \lambda^{2} X}{ c_{p} R T^{2} } \ll 1 $">|; 

$key = q/displaystyleM=M^{*};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img45.png"
 ALT="$\displaystyle M = M^{*}$">|; 

$key = q/displaystyle-pdV,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img71.png"
 ALT="$\displaystyle - p dV,$">|; 

$key = q/dT^{*}slashdz=-M_{d}gslash{c_{p}}_{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img210.png"
 ALT="$dT^{*}/dz = - M_{d} g/ {c_{p}}_{d}$">|; 

$key = q/{figure}center{{Depsf[120mm]{psslashEffLatentHeat.ps}{center{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="543" HEIGHT="543" BORDER="0"
 SRC="|."$dir".q|img195.png"
 ALT="\begin{figure}\begin{center}
\Depsf[120mm]{ps/EffLatentHeat.ps}
\end{center}\end{figure}">|; 

$key = q/8.180times10^{3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img150.png"
 ALT="$8.180 \times 10^{3}$">|; 

$key = q/displaystyleDD{T}{z}approx-frac{M_{v}g}{{c_{p}}_{v}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img96.png"
 ALT="$\displaystyle \DD{T}{z}
\approx - \frac{M_{v} g}{{c_{p}}_{v}}$">|; 

$key = q/Deqref{lapserate:Cond_LapseRate_high};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img178.png"
 ALT="$\Deqref{lapserate:Cond_LapseRate_high}$">|; 

$key = q/40.66times10^{3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img148.png"
 ALT="$40.66 \times 10^{3}$">|; 

$key = q/displaystylec_{p}={c_{p}}_{d}(1-X)+{c_{p}}_{v}X;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="197" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img60.png"
 ALT="$\displaystyle c_{p} = {c_{p}}_{d} (1 - X) + {c_{p}}_{v} X$">|; 

$key = q/displaystyle-frac{M_{v}g}{{c_{p}}_{v}}frac{frac{lambdaX}{RT}}{frac{lambda^{2}X}{{c_{p}}_{v}RT^{2}}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="69" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img117.png"
 ALT="$\displaystyle - \frac{M_{v} g}{{c_{p}}_{v}}
\frac{\frac{ \lambda X}{R T}}
{\frac{ \lambda^{2} X}{ {c_{p}}_{v} R
T^{2}} } ,$">|; 

$key = q/z=z_0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$z = z_0$">|; 

$key = q/MapproxM_{v};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img179.png"
 ALT="$M \approx M_{v}$">|; 

$key = q/displaystylec_{v}dT+RdT+Mgdz+lambdadX=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="277" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img84.png"
 ALT="$\displaystyle c_{v}dT + R dT + M g dz + \lambda dX = 0 ,$">|; 

$key = q/displaystylec_{p}dT+Mgdz+lambdadX=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="216" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img85.png"
 ALT="$\displaystyle c_{p}dT + M g dz + \lambda dX = 0 ,$">|; 

$key = q/deltaz=sin(Nt);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img42.png"
 ALT="$\delta z = sin(Nt)$">|; 

$key = q/displaystyle0.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img69.png"
 ALT="$\displaystyle 0.$">|; 

$key = q/M^{*};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$M^{*}$">|; 

$key = q/displaystyle-frac{g}{{c_{p}^{dagger}}_{d}}left{1-left(frac{lambda^{dagger}}{R^{dfrac{lambda^{dagger}q^{dagger}}{{c_{p}^{dagger}}_{d}T}right}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="276" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img243.png"
 ALT="$\displaystyle - \frac{g}{{c_{p}^{\dagger}}_{d}}
\left\{ 1 - \left(
\frac{\lambd...
...\right)
\frac{\lambda^{\dagger} q^{\dagger}}{{c_{p}^{\dagger}}_{d} T}
\right\}.$">|; 

$key = q/displaystyle-frac{M_{d}g}{{c_{p}}_{d}}left{1-frac{lambdaX}{{c_{p}}_{d}T}left(frac{lambda}{RT}-frac{{c_{p}}_{d}}{R}right)right},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="280" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img115.png"
 ALT="$\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\},$">|; 

$key = q/rq;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img248.png"
 ALT="$r q$">|; 

$key = q/{figure}center{{Depsf[120mm]{psslashCpMean.ps}{center{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="543" HEIGHT="543" BORDER="0"
 SRC="|."$dir".q|img190.png"
 ALT="\begin{figure}\begin{center}
\Depsf[120mm]{ps/CpMean.ps}
\end{center}\end{figure}">|; 

$key = q/dqslashdz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img258.png"
 ALT="$dq/dz$">|; 

$key = q/displaystylefrac{T}{1+(varepsilon-1)eslashp}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img236.png"
 ALT="$\displaystyle \frac{T}{1 + (\varepsilon - 1) e/p }.$">|; 

$key = q/displaystyleDD{T}{p}=frac{RT}{c_{p}p},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img91.png"
 ALT="$\displaystyle \DD{T}{p} = \frac{ R T }{ c_{p} p },$">|; 

$key = q/displaystylerho|_{z=z_{0}}=rho^{*}|_{z=z_{0}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="$\displaystyle \rho\vert _{z=z_{0}} = \rho^{*}\vert _{z=z_{0}}$">|; 

$key = q/displaystylefrac{g}{T}left(DD{T}{z}+frac{g}{{c_{p}^{dagger}}_{d}}right)+gleft(frac{M_{d}}{M_{v}}-1right)DP{(rq)}{z},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="307" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img244.png"
 ALT="$\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},$">|; 

$key = q/displaystyle1.1times10^{-2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img176.png"
 ALT="$\displaystyle 1.1 \times 10^{-2}.$">|; 

$key = q/displaystyle0.21Xll1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img165.png"
 ALT="$\displaystyle 0.21 X \ll 1.$">|; 

$key = q/displaystyleDD{M^{*}}{z}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="$\displaystyle \DD{M^{*}}{z} = 0$">|; 

$key = q/X=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img188.png"
 ALT="$X = 1$">|; 

$key = q/2.323times10^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img146.png"
 ALT="$2.323 \times 10^{-3}$">|; 

$key = q/displaystyleT_{v}=frac{T}{1+(varepsilon-1)eslashp},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img218.png"
 ALT="$\displaystyle T_{v} =
\frac{T }{1 + (\varepsilon - 1) e /p },$">|; 

$key = q/displaystylede=frac{elambdadT}{RT^{2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img99.png"
 ALT="$\displaystyle de = \frac{e \lambda dT}{R T^{2}},$">|; 

$key = q/displaystyleDD[2]{}{t}deltaz=left{frac{g}{T}left(-DD{T}{z}+frac{M}{M^{*}}DD{T^{*}}{z}right)+gleft(Dinv{M}DD{M}{z}right)right}deltaz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="421" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img41.png"
 ALT="$\displaystyle \DD[2]{}{t} \delta z
=
\left\{
\frac{g} {T }
\left(
- \DD{T}{z}
+...
...} \DD{T^{*}}{z}
\right)
+ g
\left(
\Dinv{M} \DD{M}{z}
\right)
\right\} \delta z$">|; 

$key = q/rho;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="$\rho$">|; 

$key = q/displaystyleDD{(rq)}{z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img259.png"
 ALT="$\displaystyle \DD{ ( r q )}{z}$">|; 

$key = q/qll2.0times10^{-2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img253.png"
 ALT="$q
\ll 2.0 \times 10^{-2}$">|; 

$key = q/displaystyle-RdT+Vleft(frac{-Mpg}{RT}right)dz,;(∵静水圧平衡の式);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="377" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img74.png"
 ALT="$\displaystyle - R dT + V \left( \frac{- M p g}{R T} \right) dz,
\; (∵ 静水圧平衡の式)$">|; 

$key = q/MapproxM_{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img155.png"
 ALT="$M \approx M_{d}$">|; 

$key = q/displaystyleMapproxM_{v},;;;c_{p}approx{c_{p}}_{v},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="170" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img95.png"
 ALT="$\displaystyle M \approx M_{v}, \;\;\;
c_{p} \approx {c_{p}}_{v},$">|; 

$key = q/M=(1-rX^{sat})M_{d}+rX^{sat}M_{v};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="262" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img206.png"
 ALT="$M = (1 - rX^{sat}) M_{d} + rX^{sat} M_{v}$">|; 

$key = q/displaystyle-frac{g}{{c_{p}^{dagger}}_{d}}left(1+frac{lambda^{dagger}q}{R_{d}^{dagger}}^{2}q}{R_{v}^{dagger}{c_{p}^{dagger}}_{d}T^{2}}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="289" HEIGHT="76" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img252.png"
 ALT="$\displaystyle - \frac{g}{{c_{p}^{\dagger}}_{d}}
\left( 1 + \frac{\lambda^{\dagg...
...\lambda^{\dagger}}^{2} q}{R_{v}^{\dagger} {c_{p}^{\dagger}}_{d} T^{2}}
\right),$">|; 

$key = q/displaystylefrac{g}{T}left[frac{Mg}{c_{p}}+DD{T}{z}left{1-frac{(M_{v}-M_{d})}{M}{RT}right}right]-frac{g}{T}frac{(M_{v}-M_{d})}{M}frac{MgX}{R};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="500" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img123.png"
 ALT="$\displaystyle \frac{g}{T}
\left[
\frac{M g}{c_{p}} +
\DD{T}{z} \left\{
1 - \fra...
... T}
\right\}
\right]
-
\frac{g}{T} \frac{ (M_{v} - M_{d})}{M} \frac{M g X}{ R }$">|; 

$key = q/displaystyle5.6times10^{-2}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img171.png"
 ALT="$\displaystyle 5.6 \times 10^{-2}.$">|; 

$key = q/displaystyle6.7486Xll1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img158.png"
 ALT="$\displaystyle 6.7486 X
\ll 1.$">|; 

$key = q/displaystyleleft{frac{g}{T}left(-DD{T}{z}+frac{M}{M^{*}}DD{T^{*}}{z}right)+gleft(Dinv{M}DD{M}{z}right)right}deltaz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="350" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img40.png"
 ALT="$\displaystyle \left\{
\frac{g} {T }
\left(
- \DD{T}{z}
+ \frac{M}{M^{*}} \DD{T^{*}}{z}
\right)
+ g
\left(
\Dinv{M} \DD{M}{z}
\right)
\right\} \delta z$">|; 

$key = q/displaystyle-RdT+Vdp,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img73.png"
 ALT="$\displaystyle - R dT + V dp,$">|; 

$key = q/displaystyleDD{X}{z}=frac{lambdaX}{RT^{2}}DD{T}{z}+frac{MgX}{RT};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="202" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img120.png"
 ALT="$\displaystyle \DD{X}{z}
= \frac{ \lambda X }{ R T^{2}} \DD{T}{z} + \frac{M g X}{ R T}$">|; 

$key = q/M_{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img54.png"
 ALT="$M_{d}$">|; 

$key = q/displaystylefrac{g}{T}left(Gamma_{m}+frac{g}{{c_{p}^{dagger}}_{d}}right)-gleft(frac{r(M_{v}-M_{d})}{M_{d}}frac{M_{d}}{M_{v}}DD{q}{z}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="342" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img255.png"
 ALT="$\displaystyle \frac{g}{T}
\left(
\Gamma_{m} + \frac{ g}{{c_{p}^{\dagger}}_{d}}
...
...
g \left(
\frac{r (M_{v} - M_{d})}{M_{d}} \frac{M_{d}}{M_{v}} \DD{q}{z}
\right)$">|; 

$key = q/r;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img205.png"
 ALT="$r$">|; 

$key = q/varepsilon=M_{v}slashM_{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img225.png"
 ALT="$\varepsilon = M_{v}/M_{d}$">|; 

$key = q/{figure}center{{Depsf[120mm]{psslashLapseRate2.ps}{center{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="543" HEIGHT="543" BORDER="0"
 SRC="|."$dir".q|img196.png"
 ALT="\begin{figure}\begin{center}
\Depsf[120mm]{ps/LapseRate2.ps}
\end{center}\end{figure}">|; 

$key = q/displaystylefrac{23.5-27.66}{27.66}X,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img164.png"
 ALT="$\displaystyle \frac{23.5 - 27.66}{27.66}X,$">|; 

$key = q/displaystylefrac{lambdaX}{RT};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img168.png"
 ALT="$\displaystyle \frac{ \lambda X}{R T}$">|; 

$key = q/displaystyleTfrac{M_{d}}{M},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img231.png"
 ALT="$\displaystyle T \frac{M_{d}}{M} ,$">|; 

$key = q/displaystyleq=frac{M_{v}X}{M_{d}(1-X)+M_{v}X}approxfrac{M_{v}}{M_{d}}X.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="275" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img237.png"
 ALT="$\displaystyle q
= \frac{M_{v} X}{M_{d} (1 - X) + M_{v} X}
\approx \frac{M_{v}}{M_{d}} X.$">|; 

$key = q/displaystyleDD{T}{p}=frac{RT}{c_{p}p}left(frac{1+frac{lambdaX}{RT}}{1+frac{lambda^{2}X}{c_{p}RT^{2}}}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="208" HEIGHT="76" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img109.png"
 ALT="$\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),$">|; 

$key = q/T=324.5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$T = 324.5$">|; 

$key = q/{figure}center{{Depsf[80mm]{psslashparcel.eps}{center{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="360" HEIGHT="332" BORDER="0"
 SRC="|."$dir".q|img44.png"
 ALT="\begin{figure}\begin{center}
\Depsf[80mm]{ps/parcel.eps}
\end{center}\end{figure}">|; 

$key = q/T=300;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$T = 300$">|; 

$key = q/displaystylefrac{M_{d}g^{2}}{{c_{p}}_{d}T}left{frac{lambdaX}{{c_{p}}_{d}T}left(f{{c_{p}}_{d}T}frac{(M_{v}-M_{d})}{M_{d}}frac{{c_{p}}_{d}X}{R};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="585" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img128.png"
 ALT="$\displaystyle \frac{M_{d} g^{2}}{{c_{p}}_{d} T}
\left\{
\frac{\lambda X}{{c_{p}...
...g^{2}}{{c_{p}}_{d} T}
\frac{ (M_{v} - M_{d})}{M_{d}} \frac{ {c_{p}}_{d} X}{ R }$">|; 

$key = q/{figure}center{{Depsf[120mm]{psslashLapseRateList.ps}{center{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="543" HEIGHT="543" BORDER="0"
 SRC="|."$dir".q|img197.png"
 ALT="\begin{figure}\begin{center}
\Depsf[120mm]{ps/LapseRateList.ps}
\end{center}\end{figure}">|; 

$key = q/displaystyleleft(-frac{lambda^{dagger}}{R^{dagger}_{v}T^{2}}frac{g}{{c_{p}^{dagger}}_{d}}+frac{g}{R^{dagger}_{d}T}right)(rq),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="222" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img261.png"
 ALT="$\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) ,$">|; 

$key = q/displaystylefrac{gT^{*}}{M^{*}}left{MDD{}{z}left(Dinv{T}right)+Dinv{T}DD{M}{z}-Mz}left(Dinv{T^{*}}right)-Dinv{T^{*}}DD{M^{*}}{z}right}deltaz,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="474" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img38.png"
 ALT="$\displaystyle \frac{g T^{*}}{ M^{*} }
\left\{
M \DD{}{z} \left( \Dinv{T} \right...
...z} \left( \Dinv{T^{*}} \right)
- \Dinv{T^{*}} \DD{M^{*}}{z}
\right\} \delta z ,$">|; 

$key = q/T=422.6;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$T = 422.6$">|; 

$key = q/displaystyleM=M_{d}(1-X)+M_{v}X;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="206" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img59.png"
 ALT="$\displaystyle M = M_{d} (1 - X) + M_{v} X$">|; 

$key = q/R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img81.png"
 ALT="$R$">|; 

$key = q/displaystyleT_{v};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img230.png"
 ALT="$\displaystyle T_{v}$">|; 

$key = q/displaystylefrac{left(rho-rho^{*}right)g}{rho^{*}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="$\displaystyle \frac{\left(\rho - \rho^{*}\right) g}{\rho^{*}}$">|; 

$key = q/{figure}center{{Depsf[120mm]{psslashMolWtMean.ps}{center{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="543" HEIGHT="543" BORDER="0"
 SRC="|."$dir".q|img189.png"
 ALT="\begin{figure}\begin{center}
\Depsf[120mm]{ps/MolWtMean.ps}
\end{center}\end{figure}">|; 

$key = q/textstyleapprox;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img113.png"
 ALT="$\textstyle \approx$">|; 

$key = q/displaystyleDD[2]{}{t}deltaz=frac{left(rho-rho^{*}right)g}{rho^{*}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="$\displaystyle \DD[2]{}{t} \delta z
= \frac{\left(\rho - \rho^{*}\right) g}{\rho^{*}}$">|; 

$key = q/displaystyleX;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img159.png"
 ALT="$\displaystyle X$">|; 

$key = q/displaystylefrac{(M_{v}-M_{d})X}{M_{d}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img156.png"
 ALT="$\displaystyle \frac{(M_{v} - M_{d}) X}{M_{d}}$">|; 

$key = q/R^{dagger}=RslashM;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img221.png"
 ALT="$R^{\dagger} =
R/M$">|; 

$key = q/{figure}center{{Depsf[120mm]{psslashjupiter.ps}{center{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="543" HEIGHT="543" BORDER="0"
 SRC="|."$dir".q|img204.png"
 ALT="\begin{figure}\begin{center}
\Depsf[120mm]{ps/jupiter.ps}
\end{center}\end{figure}">|; 

$key = q/dT^{*}slashdz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img48.png"
 ALT="$dT^{*}/dz$">|; 

$key = q/displaystyleN^{2}=frac{g}{T_{v}}left(DD{T_{v}}{z}+frac{M_{d}g}{{c_{p}}_{d}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img216.png"
 ALT="$\displaystyle N^{2} =
\frac{g}{T_{v}}
\left(
\DD{T_{v}}{z} + \frac{M_{d} g}{{c_{p}}_{d}}
\right)$">|; 

$key = q/displaystyleMapproxM_{d},;;;c_{p}approx{c_{p}}_{d},;;;;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="186" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img93.png"
 ALT="$\displaystyle M \approx M_{d}, \;\;\;
c_{p} \approx {c_{p}}_{d}, \;\;\;$">|; 

$key = q/displaystyledeltaQ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img68.png"
 ALT="$\displaystyle \delta Q$">|; 

$key = q/{c_{p}^{dagger}}_{d}=c_{p}slashM_{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img223.png"
 ALT="${c_{p}^{\dagger}}_{d}=c_{p}/M_{d}$">|; 

$key = q/displaystyleTfrac{M_{d}p}{M_dp+(M_{v}-M_{d})e},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img234.png"
 ALT="$\displaystyle T \frac{M_{d} p}{M_d p + (M_{v} - M_{d}) e } ,$">|; 

$key = q/195.40;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img152.png"
 ALT="$195.40$">|; 

$key = q/T=271.9;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$T = 271.9$">|; 

$key = q/23.35times10^{3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img149.png"
 ALT="$23.35 \times 10^{3}$">|; 

$key = q/lambda^{dagger}=lambdaslashM_{v};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img224.png"
 ALT="$\lambda^{\dagger}=\lambda/M_{v}$">|; 

$key = q/{figure}center{{Depsf[120mm]{psslashStabList.ps}{center{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="543" HEIGHT="543" BORDER="0"
 SRC="|."$dir".q|img199.png"
 ALT="\begin{figure}\begin{center}
\Depsf[120mm]{ps/StabList.ps}
\end{center}\end{figure}">|; 

$key = q/displaystylefrac{M_{d}g^{2}}{{c_{p}}_{d}T}left(frac{lambda}{RT}-frac{{c_{p}}_{d}_{d}}left(1-frac{lambda^{2}X}{{c_{p}}_{d}RT^{2}}right)right}X;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="492" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img129.png"
 ALT="$\displaystyle \frac{M_{d} g^{2}}{{c_{p}}_{d} T}
\left(
\frac{ \lambda}{ R T}
- ...
...{M_{d}}
\left( 1 - \frac{\lambda^{2} X}{{c_{p}}_{d} R T^{2}} \right)
\right\} X$">|; 

$key = q/displaystyleDD{T}{z}=-frac{M_{v}g}{{c_{p}}_{d}}left{frac{1+frac{(M_{v}-M_{d})X}{{d}}}{1+frac{({c_{p}}_{v}-{c_{p}}_{d})X}{{c_{p}}_{d}}}right}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="265" HEIGHT="85" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img90.png"
 ALT="$\displaystyle \DD{T}{z} =
- \frac{ M_{v} g }{ {c_{p}}_{d}}
\left\{
\frac{ 1 + \...
...}{M_{d}} }
{ 1 + \frac{( {c_{p}}_{v} - {c_{p}}_{d} ) X}{{c_{p}}_{d}}}
\right\}.$">|; 

$key = q/Xle1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img187.png"
 ALT="$X \le 1$">|; 

$key = q/{figure}center{{Depsf[120mm]{psslashJupiter.ps}{center{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="543" HEIGHT="543" BORDER="0"
 SRC="|."$dir".q|img202.png"
 ALT="\begin{figure}\begin{center}
\Depsf[120mm]{ps/Jupiter.ps}
\end{center}\end{figure}">|; 

$key = q/displaystyleN^{2}=frac{g}{T_{v}}left(DD{T_{v}}{z}+frac{g}{{c_{p}^{dagger}}_{d}}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="197" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img217.png"
 ALT="$\displaystyle N^{2} =
\frac{g}{T_{v}}
\left(
\DD{T_{v}}{z} + \frac{g}{{c_{p}^{\dagger}}_{d}}
\right),$">|; 

$key = q/dX;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img83.png"
 ALT="$dX$">|; 

$key = q/displaystylefrac{gT^{*}}{M^{*}}left{-frac{M}{T^{2}}DD{T}{z}+frac{M^{*}}{{T^{*}}^{2}}DD{T^{*}}{z}+Dinv{T}DD{M}{z}right}deltaz,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="328" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img39.png"
 ALT="$\displaystyle \frac{g T^{*}}{ M^{*} }
\left\{
- \frac{M}{T^{2}} \DD{T}{z}
+ \frac{M^{*}}{{T^{*}}^{2}} \DD{T^{*}}{z}
+ \Dinv{T} \DD{M}{z}
\right\} \delta z ,$">|; 

$key = q/rho,rho^{*};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="$\rho, \rho^{*}$">|; 

$key = q/{figure}center{{Depsf[120mm]{psslashLapseRateDry.ps}{center{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="543" HEIGHT="543" BORDER="0"
 SRC="|."$dir".q|img191.png"
 ALT="\begin{figure}\begin{center}
\Depsf[120mm]{ps/LapseRateDry.ps}
\end{center}\end{figure}">|; 

$key = q/displaystylefrac{g}{T}left(Gamma_{m}+frac{g}{{c_{p}^{dagger}}_{d}}right)+gleft(frac{M_{d}}{M_{v}}-1right)DD{(rq)}{z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="297" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img256.png"
 ALT="$\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}$">|; 

$key = q/90.68;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img153.png"
 ALT="$90.68$">|; 

$key = q/MapproxM_{d},R^{dagger}_{v}=R^{dagger}slashvarepsilon;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="171" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img249.png"
 ALT="$M \approx M_{d},
R^{\dagger}_{v} = R^{\dagger} / \varepsilon$">|; 

$key = q/c_{p}=c_{v}+R;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img87.png"
 ALT="$c_{p} = c_{v} + R$">|; 

$key = q/displaystyledX;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img100.png"
 ALT="$\displaystyle dX$">|; 

$key = q/{figure}center{{Depsf[120mm]{psslashLapseRate.ps}{center{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="543" HEIGHT="543" BORDER="0"
 SRC="|."$dir".q|img194.png"
 ALT="\begin{figure}\begin{center}
\Depsf[120mm]{ps/LapseRate.ps}
\end{center}\end{figure}">|; 

$key = q/deltaQ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img63.png"
 ALT="$\delta Q$">|; 

$key = q/displaystylelambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img142.png"
 ALT="$\displaystyle \lambda$">|; 

$key = q/displaystyle17.8Xgg1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img183.png"
 ALT="$\displaystyle 17.8 X \gg 1.$">|; 

$key = q/displaystyleTfrac{M_{d}}{M_d(1-X)+M_{v}X},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="183" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img232.png"
 ALT="$\displaystyle T \frac{M_{d}}{M_d (1 - X) + M_{v} X} ,$">|; 

$key = q/frac{lambda^{2}X}{c_{p}RT^{2}}gg1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img185.png"
 ALT="$\frac{ \lambda^{2} X}{ c_{p} R T^{2} } \gg 1 $">|; 

$key = q/displaystylefrac{44492}{8.31times300}X;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img169.png"
 ALT="$\displaystyle \frac{44492}{8.31 \times 300} X$">|; 

$key = q/displaystyleMapproxM_{v},;;;c_{p}approx{c_{p}}_{v},;;;frac{lambdaX}{RT}gg1,;;;frac{lambda^{2}X}{c_{p}RT^{2}}gg1,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="384" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img116.png"
 ALT="$\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,$">|; 

$key = q/z+dz;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$z+dz$">|; 

$key = q/displaystyleDD{T}{z}approx-frac{M_{d}gRT^{2}}{lambda^{2}}left{Dinv{X}+frac{(M_{v}+frac{lambda}{RT}+frac{(M_{v}-M_{d})lambdaX}{M_{d}RT}right},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="521" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img193.png"
 ALT="$\displaystyle \DD{T}{z} \approx - \frac{M_{d} g R T^{2} }{\lambda^{2}}
\left\{
...
...\frac{ \lambda }{R T}
+ \frac{(M_{v} - M_{d}) \lambda X }{M_{d} R T}
\right\}
,$">|; 

$key = q/displaystyle-d(pV)+Vdp,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img72.png"
 ALT="$\displaystyle - d(pV) + V dp,$">|; 

$key = q/lambda;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img82.png"
 ALT="$\lambda$">|; 

$key = q/displaystyleDD{T}{z}=-frac{Mg}{c_{p}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img89.png"
 ALT="$\displaystyle \DD{T}{z} = - \frac{ M g }{c_{p}},$">|; 

$key = q/MslashT=M^{*}slashT^{*};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$M/T = M^{*}/T^{*}$">|; 

$key = q/displaystyleDD{T}{z}=-frac{g}{c_{p}^{dagger}}left(frac{1+frac{lambda^{dagger}q}{agger}}^{2}varepsilonq}{R^{dagger}c_{p}^{dagger}T^{2}}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="209" HEIGHT="85" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img219.png"
 ALT="$\displaystyle \DD{T}{z} = - \frac{g}{c_{p}^{\dagger}}
\left(
\frac{ 1 + \frac{\...
...mbda^{\dagger}}^{2} \varepsilon q}{R^{\dagger} c_{p}^{\dagger} T^{2}} }
\right)$">|; 

$key = q/displaystylec_{p}left(1+frac{lambda^{2}X}{c_{p}RT^{2}}right)dT+Mgleft(1+frac{lambdaX}{RT}right)dz=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="370" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img106.png"
 ALT="$\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,$">|; 

$key = q/M=M^{*};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img211.png"
 ALT="$M = M^{*}$">|; 

$key = q/displaystylefrac{lambdaX}{RT^{2}}dT+frac{MgX}{RT}dz.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="165" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img104.png"
 ALT="$\displaystyle \frac{ \lambda X }{ R T^{2}} dT
+ \frac{M g X}{ R T} dz .$">|; 

$key = q/displaystylec_{p}dT+Mgdz=0,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img88.png"
 ALT="$\displaystyle c_{p}dT + M g dz = 0,$">|; 

$key = q/displaystyleln{e}=left(A-frac{B}{C+T-273.15}right)ln{10}+ln{133.322};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="392" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img141.png"
 ALT="$\displaystyle \ln{e} = \left(
A - \frac{B}{C + T - 273.15 }
\right) \ln{10} + \ln{133.322}$">|; 

$key = q/textstylegg;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img184.png"
 ALT="$\textstyle \gg$">|; 

$key = q/V;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img80.png"
 ALT="$V$">|; 

$key = q/displaystyleN^2equivfrac{g}{T}left(DD{T}{z}-frac{M}{M^{*}}DD{T^{*}}{z}right)-gleft(Dinv{M}DD{M}{z}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="338" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img43.png"
 ALT="$\displaystyle N^2
\equiv
\frac{g}{T}
\left(
\DD{T}{z} - \frac{M}{M^{*}}\DD{T^{*}}{z}
\right)
-
g
\left(
\Dinv{M} \DD{M}{z}
\right)$">|; 

$key = q/displaystyleA=7.9186968d0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="143" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img137.png"
 ALT="$\displaystyle A = 7.9186968d0$">|; 

$key = q/T=304.5;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$T = 304.5$">|; 

$key = q/displaystyleDD{T}{z}approx-frac{M_{d}g}{{c_{p}}_{d}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img94.png"
 ALT="$\displaystyle \DD{T}{z}
\approx - \frac{M_{d} g}{{c_{p}}_{d}}$">|; 

$key = q/displaystyle-frac{g}{T}frac{(M_{v}-M_{d})}{M_{d}}frac{M_{d}gX}{R};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="187" HEIGHT="63" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img127.png"
 ALT="$\displaystyle -
\frac{g}{T} \frac{ (M_{v} - M_{d})}{M_{d}} \frac{M_{d} g X}{ R }$">|; 

$key = q/displaystyle-frac{g}{{c_{p}^{dagger}}_{d}}left(frac{1+frac{lambda^{dagger}q}{R_{gger}}^{2}q}{R_{v}^{dagger}{c_{p}^{dagger}}_{d}T^{2}}}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="89" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img251.png"
 ALT="$\displaystyle - \frac{g}{{c_{p}^{\dagger}}_{d}}
\left(
\frac{ 1 + \frac{\lambda...
...mbda^{\dagger}}^{2} q}{R_{v}^{\dagger} {c_{p}^{\dagger}}_{d} T^{2}} }
\right) ,$">|; 

$key = q/displaystylefrac{g}{T}left[frac{M_{d}g}{{c_{p}}_{d}}-frac{M_{d}g}{{c_{p}}_{d}}leeft{1-frac{(M_{v}-M_{d})}{M_{d}}frac{lambdaX}{RT}right}right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="545" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img126.png"
 ALT="$\displaystyle \frac{g}{T}
\left[
\frac{M_{d} g}{{c_{p}}_{d}}
- \frac{M_{d} g}{{...
...\{
1 - \frac{ (M_{v} - M_{d})}{M_{d}} \frac{ \lambda X }{ R T}
\right\}
\right]$">|; 

$key = q/M;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$M$">|; 

$key = q/displaystyle1.5times10^{-1}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img161.png"
 ALT="$\displaystyle 1.5 \times 10^{-1}.$">|; 

$key = q/c_{p};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img86.png"
 ALT="$c_{p}$">|; 

$key = q/1.0times10^{-1}leXle1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img192.png"
 ALT="$1.0 \times 10^{-1} \le X \le 1 $">|; 

$key = q/displaystyle-lambdadX.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img77.png"
 ALT="$\displaystyle - \lambda dX.$">|; 

$key = q/T=400;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$T=400$">|; 

$key = q/displaystyledeltaW;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img70.png"
 ALT="$\displaystyle \delta W$">|; 

$key = q/displaystyleTfrac{1}{1+(M_{v}-M_{d})slashM_{d}eslashp},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="211" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img235.png"
 ALT="$\displaystyle T \frac{1}{1 + (M_{v} - M_{d})/M_{d} e/p } ,$">|; 

$key = q/displaystylefrac{g}{T}left[frac{M_{d}g}{{c_{p}}_{d}}left{frac{1+frac{(M_{v}-M_{d}}{M_{d}left{1+frac{(M_{v}-M_{d})X}{M_{d}}right}}right}right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="509" HEIGHT="85" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img124.png"
 ALT="$\displaystyle \frac{g}{T}
\left[
\frac{M_{d} g}{{c_{p}}_{d}}
\left\{
\frac{ 1 +...
...}}
{M_{d} \left\{ 1 + \frac{(M_{v} - M_{d})X}{M_{d}} \right\}}
\right\}
\right]$">|; 

$key = q/displaystyleDinv{p}de-frac{e}{p^{2}}dp,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img101.png"
 ALT="$\displaystyle \Dinv{p} de - \frac{e}{p^{2}} dp,$">|; 

$key = q/T=271.9K;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$T = 271.9K$">|; 

$key = q/displaystylefrac{g}{T}left(Gamma_{m}+frac{Mg}{{c_{p}^{dagger}}_{d}M}right)-gleft(frac{r(M_{v}-M_{d})}{M}DD{X}{z}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="340" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img254.png"
 ALT="$\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)$">|; 

$key = q/displaystylefrac{g}{T}left[frac{M_{v}g}{{c_{p}}_{v}}left(1-frac{{c_{p}}_{v}T}{lalambdaX}{RT}-frac{(M_{v}-M_{d})}{M_{v}}frac{M_{v}gX}{R}right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="554" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img132.png"
 ALT="$\displaystyle \frac{g}{T}
\left[
\frac{M_{v} g}{{c_{p}}_{v}}
\left( 1 - \frac{{...
...lambda X }{ R T}
-
\frac{ (M_{v} - M_{d})}{M_{v}} \frac{M_{v} g X}{ R }
\right]$">|; 

$key = q/DD{T^{*}}{z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img46.png"
 ALT="$\DD{T^{*}}{z}$">|; 

$key = q/displaystyleXapprox1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img180.png"
 ALT="$\displaystyle X \approx 1.$">|; 

$key = q/displaystyleN^{2}=frac{g}{T}left(DD{T}{z}+frac{M_{d}g}{{c_{p}}_{d}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="190" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img53.png"
 ALT="$\displaystyle N^{2}
=
\frac{g}{T}
\left(
\DD{T}{z} + \frac{M_{d} g}{{c_{p}}_{d}}
\right)$">|; 

$key = q/R_{v}^{dagger}=RslashM_{v};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img247.png"
 ALT="$R_{v}^{\dagger} = R/M_{v}$">|; 

$key = q/(1+lambdaXslashRT)slash(1+{lambda}^{2}Xslashc_{p}RT^{2});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="266" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$(1 + \lambda X/ RT)/ (1 + {\lambda }^{2}X / c_{p} R T^{2})$">|; 

$key = q/displaystyleDD{T}{p}=frac{RT}{{c_{p}}_{d}p}left{Dinv{1+frac{({c_{p}}_{v}-{c_{p}}1+frac{lambdaX}{RT}}{1+frac{lambda^{2}X}{c_{p}RT^{2}}}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="357" HEIGHT="85" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img110.png"
 ALT="$\displaystyle \DD{T}{p} = \frac{R T}{{c_{p}}_{d} p}
\left\{
\Dinv{ 1 + \frac{( ...
... \frac{ \lambda X}{R T}}
{ 1 + \frac{ \lambda^{2} X}{ c_{p} R T^{2}} }
\right).$">|; 

$key = q/displaystyleB=1636.909d0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img138.png"
 ALT="$\displaystyle B = 1636.909d0$">|; 

$key = q/T=200;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$T=200$">|; 

$key = q/displaystyleN^{2}=-frac{g}{M}DD{M}{z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img52.png"
 ALT="$\displaystyle N^{2}
= - \frac{ g}{M} \DD{M}{z}$">|; 

$key = q/displaystyleN^{2}=frac{g}{T}left(DD{T}{z}+frac{Mg}{c_{p}}right)-gleft(frac{1}{M}DD{M}{z}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="313" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img50.png"
 ALT="$\displaystyle N^{2}
=
\frac{g}{T}
\left(
\DD{T}{z}
+ \frac{M g}{c_{p}}
\right)
-
g \left(
\frac{1}{M} \DD{M}{z}
\right) .$">|; 

$key = q/deltaW;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img64.png"
 ALT="$\delta W$">|; 

$key = q/displaystyledX=Dinv{p}de-left(frac{e}{p^{2}}right)dp.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="185" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img97.png"
 ALT="$\displaystyle dX = \Dinv{p} de - \left( \frac{e}{p^{2}} \right) dp.$">|; 

$key = q/N^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="19" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$N^{2}$">|; 

$key = q/dU;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img62.png"
 ALT="$dU$">|; 

$key = q/textstylell;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img160.png"
 ALT="$\textstyle \ll$">|; 

$key = q/displaystyleN^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img121.png"
 ALT="$\displaystyle N^{2}$">|; 

$key = q/p;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img79.png"
 ALT="$p$">|; 

$key = q/displaystyledU=deltaQ+deltaW+deltaZ,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img61.png"
 ALT="$\displaystyle dU = \delta Q + \delta W + \delta Z ,$">|; 

$key = q/displaystylefrac{g}{T}left[frac{M_{v}g}{{c_{p}}_{v}}-frac{M_{v}gT}{lambda}left{1X}{RT}right}-frac{(M_{v}-M_{v})}{M_{v}}frac{M_{v}gX}{R}right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="520" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img131.png"
 ALT="$\displaystyle \frac{g}{T}
\left[
\frac{M_{v} g}{{c_{p}}_{v}}
- \frac{M_{v} g T}...
...}{ R T}
\right\}
-
\frac{ (M_{v} - M_{v})}{M_{v}} \frac{M_{v} g X}{ R }
\right]$">|; 

$key = q/displaystyleただし;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img136.png"
 ALT="$\displaystyle ただし$">|; 

$key = q/18times10^{-3};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img145.png"
 ALT="$18 \times 10^{-3}$">|; 

$key = q/z=z_{0};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="$z = z_{0}$">|; 

$key = q/Deqref{lapserate:Cond_LapseRate_low};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img154.png"
 ALT="$\Deqref{lapserate:Cond_LapseRate_low}$">|; 

$key = q/displaystyleDD{T}{z}=-frac{Mg}{c_{p}}left(frac{1+frac{lambdaX}{RT}}{1+frac{lambda^{2}X}{c_{p}RT^{2}}}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="225" HEIGHT="76" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img107.png"
 ALT="$\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).$">|; 

$key = q/displaystyle88Xgg1.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img186.png"
 ALT="$\displaystyle 88 X \gg 1.$">|; 

$key = q/^{circ};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img140.png"
 ALT="$^{\circ}$">|; 

$key = q/deltaZ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img65.png"
 ALT="$\delta Z$">|; 

$key = q/displaystylefrac{g}{rho^{*}}left{left(rho|_{z=z_{0}}+DD{rho}{z}deltazright)-left(rho^{*}|_{z=z_{0}}+DD{rho^{*}}{z}deltazright)right},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="375" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="$\displaystyle \frac{g}{\rho^{*}}
\left\{
\left(
\rho\vert _{z=z_{0}} + \DD{\rho...
...-
\left(
\rho^{*}\vert _{z=z_{0}} + \DD{\rho^{*}}{z} \delta z
\right)
\right\},$">|; 

$key = q/displaystylefrac{g^{2}}{{c_{p}^{dagger}}_{d}T}left(frac{lambda^{dagger}}{R^{dagg{c_{p}^{dagger}}_{d}T}+left(1-frac{M_{d}}{M_{v}}right)right}q;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="354" HEIGHT="70" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img245.png"
 ALT="$\displaystyle \frac{g^{2}}{{c_{p}^{\dagger}}_{d} T}
\left(
\frac{\lambda^{\dagg...
...r}}{{c_{p}^{\dagger}}_{d} T}
+ \left(1 - \frac{M_{d}}{M_{v}} \right)
\right\} q$">|; 

$key = q/X;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img58.png"
 ALT="$X$">|; 

$key = q/displaystyleDD{T^{*}}{z}=-frac{Mg}{c_{p}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img49.png"
 ALT="$\displaystyle \DD{T^{*}}{z} = - \frac{M g}{c_{p}}.$">|; 

$key = q/displaystyleDD{T}{p}=frac{RT}{{c_{p}}_{d}p}left{Dinv{1+frac{({c_{p}}_{v}-{c_{p}}_{d})X}{{c_{p}}_{d}}}right}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="247" HEIGHT="85" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img92.png"
 ALT="$\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\}.$">|; 

$key = q/c_{p}approx{c_{p}}_{d};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img162.png"
 ALT="$c_{p} \approx {c_{p}}_{d}$">|; 

$key = q/373.15;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img151.png"
 ALT="$373.15$">|; 

$key = q/displaystyle-frac{g}{{c_{p}^{dagger}}_{d}}left(frac{1+frac{lambda^{dagger}q}{R_{agger}}^{2}q}{R_{v}^{dagger}{c_{p}^{dagger}}_{d}T^{2}}}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="171" HEIGHT="89" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img242.png"
 ALT="$\displaystyle - \frac{g}{{c_{p}^{\dagger}}_{d}}
\left(
\frac{ 1 + \frac{\lambda...
...lambda^{\dagger}}^{2} q}{R_{v}^{\dagger} {c_{p}^{\dagger}}_{d} T^{2}} }
\right)$">|; 

$key = q/frac{lambdaX}{RT}ll1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img167.png"
 ALT="$\frac{ \lambda X}{R T} \ll 1$">|; 

$key = q/{figure}center{{Depsf[140mm]{psslashcloud.eps}{center{{{{figure};LFS=12;FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="631" HEIGHT="236" BORDER="0"
 SRC="|."$dir".q|img47.png"
 ALT="\begin{figure}\begin{center}
\Depsf[140mm]{ps/cloud.eps}
\end{center}\end{figure}">|; 

$key = q/displaystylefrac{gT^{*}}{M^{*}}left{DD{}{z}left(frac{M}{T}right)-DD{}{z}left(frac{M^{*}}{T^{*}}right)right}deltaz,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="275" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img37.png"
 ALT="$\displaystyle \frac{g T^{*}}{ M^{*} }
\left\{
\DD{}{z} \left( \frac{M}{T} \right)
- \DD{}{z} \left( \frac{M^{*}}{T^{*}} \right)
\right\} \delta z ,$">|; 

$key = q/displaystylec_{v}dT.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img67.png"
 ALT="$\displaystyle c_{v} dT.$">|; 

$key = q/displaystyle-frac{Mg}{(Mc_{p}^{dagger})}left({1+frac{(M_{v}lambda^{dagger})(qM_{hM_{v})}{(M_{d}c_{p}^{dagger})(M_{d}R^{dagger})T^{2}}}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="515" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img240.png"
 ALT="$\displaystyle - \frac{M g}{( M c_{p}^{\dagger} ) }
\left(
{ 1 + \frac{ (M_{v} \...
...M_{d} / M_{v})}
{ (M_{d} c_{p}^{\dagger}) (M_{d} R^{\dagger}) T^{2}} }
\right),$">|; 

$key = q/T^{*};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$T^{*}$">|; 

1;