"The classical or Galilean transformations were x' = x - vt, y' = y, z' = z, t' = t, where v was the velocity of the frame with respect to a frame at rest in the ether, hence with respect to the ether itself; this velocity being directed along the x axis and the two frames being assumed to have coincided at the initial instant t = 0. Under the same conditions the Lorentz transformations were x' = \beta(x - vt), y' = y, z' = z; t' = \beta(t - \frac{vx}{c^2}) where \beta = \frac{1}{ \sqrt{1 - \frac{v^2}{c^2}}}"