We obtained the barometric distribution for an isothermal atmosphere; indeed, in § 26.10 (see Vol. 1) we assumed the temperature at all points to be constant. Meanwhile, in the real atmosphere the temperature decreases with increasing altitude. It can be shown that if the temperature decreases linearly with height, i.e. T=To(1 - ah), then the barometric formula has the form. Prove that if a is a small value, then this formula turns into the barometric distribution formula for an isothermal atmosphere.

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