### 2.2 Boltzmann's transformation, Parabolic law

Introducing the parameter the partial differential equation 2.5 transforms to an ordinary differential equation:

 (2.8)

i.e. the composition depends only on . From this it follows that a plane with constant composition shifts proportionally to the square root of the time:

 (2.9)

The relation is often called as parabolic law, since . (see also later Fig. 2.1 in section 2.4)