The effect of air drag on satellite orbits of small eccentricity, $e < 0.2$, is considered. A model of the atmosphere that allows for oblateness is adopted, in which the density behaviour approximates to the observed diurnal variation. The equations governing the changes due to drag in the semi-major axis $a$, and in $x = ae$, during one revolution of the satellite are integrated, the density scale-height $H$ being assumed constant. The resulting expressions for $\Delta a$ and $\Delta x$ are presented to third order in $e$. Compact expressions for the gradient $da/dx$, and for the mean air density at perigee altitude $\rho_1$ are obtained, when $H$ is allowed to vary with altitude. An equivalence between the variable-$H$ and the constant-$H$ equations is demonstrated, provided that the value of $H$ used in the latter is chosen appropriately.