An important mechanism involved in the variation of the magnetization of ferromagnets near saturation is the rotation of the magnetization vector under the combined influence of the magnetic field and crystalline anisotropy torques. The effect of this mechanism in polycrystalline specimens has been calculated by Akulov and Gans; their result is ${M}_{\mathrm{Av}}={M}_{0}[1\ensuremath{-}(\frac{c}{{{M}_{0}}^{2}}){H}^{\ensuremath{-}2}]$, where $H$ is the sum of the external and demagnetizing fields, ${M}_{0}$ the saturation magnetization, and $c$ a constant proportional to the square of the crystalline anisotropy constant. The Akulov-Gans derivation, however, is subject to a serious error; namely, neglect of the internal magnetic field arising from the magnetization itself. In the present paper, this internal field is taken into account; then, with the dual assumption, of randomness of orientation of crystallographic axes, and irregularity of shapes of the individual crystal grains, one obtains the formula, ${M}_{\mathrm{Av}}={M}_{0}[1\ensuremath{-}(\frac{{c}^{\ensuremath{'}}}{{{M}_{0}}^{2}}){H}^{\ensuremath{-}2}]$. Here, ${c}^{\ensuremath{'}}$ is a slowly varying function of $H$; for $H\ensuremath{\gg}4\ensuremath{\pi}{M}_{0}$, ${c}^{\ensuremath{'}}=c$; $H\ensuremath{\ll}4\ensuremath{\pi}{M}_{0}$, ${c}^{\ensuremath{'}}=\frac{1}{2}c$. Applications of the last formula to the analysis of the experimental data are discussed.