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A new derivation of the Earth-flattening approximation (EFA) for body waves from geometric ray theory is given which results in an improved version of the EFA. This version agrees with the EFA, derived by Chapman (1973) from wave theory. Moreover, it allows absolute, not only relative, body-wave amplitude calculations for given source time functions. The choice of the density transformation of the EFA is shown, by numerical calculations, to be uncritical for body-wave amplitudes in the period range up to 30 s. An error in an earlier derivation of the EFA (Muller, 1973a) is corrected. This error requires a new investigation of the range of applicability of the EFA, which is performed for the P-wave propagation through a homogeneous sphere. The results are similar to those of the earlier paper: long-period P waves with dominant periods up to about 20s can be treated practically exactly, as long as they do not pass closer than about 800 km to the Earth's center.
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