When an observer moves with velocity through an isotropic cloud , she will notice an anisotropy in the incident particle flux. The anisotropy is measured by the ratio of the difference of the extreme fluxes to the sum of the extremes

If the velocity of the observer is much smaller than the typical velocity of the particles in the cloud , the anisotropy will be linear in the ratio of the velocities

To understand this result, let us consider a one dimensional ensemble with some velocity distribution . We further assume that the distribution is isotropic so and . If some observer moves with velocity she would see a slightly different velocity distribution

The flux is just the product of the distribution function and the velocity. The anisotropy is therefore

Assuming is constant (or at least a weak function of the velocity), we reproduce the qualitative behaviour of the Compton - Getting effect.