= Saturated vapor column on a dry adiabat
{title2=$W\sim\frac{c_{pA}T_s e_s(T_s)}{gL}$}
For a dilute saturated vapour with constant <latent heat> $L$ in a dry atmosphere, set $x=R_A/c_{pA}$, $\epsilon=R_A/R_B$ and $\beta=L/(R_BT_s)$. Its <mass path> is $W=\epsilon e_s(T_s)e^\beta E_1(\beta)/(gx)$. Substituting $y=\beta e^{x\zeta}$ in the log-pressure column integral proves this identity. For $\beta\gg1$, $W\sim c_{pA}T_s e_s(T_s)/(gL)$ with relative correction $-1/\beta+O(\beta^{-2})$.
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