Galileian transformation

This is incompatible with Maxwell s equations, as shown below by using Gauss s law, Eq. (2.7.16), and the Lorentz force, Eq. (2.7.24). Assume that the two systems S and S move at velocities v and v and relative velocity V= v — v. If we use the Galileian transformation and assume that the charge q and the electric displacement D is the same in the two systems ... 

Thanks to this result, Lorentz was forced to doubt the Galileian transformation (apparently the foundation of the whole science). 

---