= Solution
Displace a small parcel upward, with negligible heat exchange, rapid pressure balance, and the same composition as its surroundings. Define the environmental gradient $\nabla=d\log T/d\log P$. An adiabatic <ideal gas> parcel obeys $P\rho^{-\gamma}=\mathrm{constant}$ and hence $T\propto P^{(\gamma-1)/\gamma}$, giving $\nabla_{\rm ad}=(\gamma-1)/\gamma$.
The upward displacement has $\delta\log P<0$. If $\nabla<\nabla_{\rm ad}$, the parcel's temperature changes more negatively than the environment's. At their common <pressure> it is cooler, denser and driven back down. Therefore the <Schwarzschild criterion> for stability is
$$
\boxed{\nabla=\frac PT\frac{dT}{dP}<\nabla_{\rm ad}=\frac{\gamma-1}{\gamma}.}
$$
The reversed inequality produces buoyant growth, and equality is neutrally stable in this approximation. A composition gradient requires the <Ledoux criterion>; pressure equilibrium alone does not ensure equal mean molecular weight.
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