A possible solution to the problem was shown by Woldemar Voigt (1887), who investigated the Doppler effect for waves propagating in an incompressible elastic medium and deduced transformation relations that left the wave equation in free space unchanged, and explained the negative result of the Michelson–Morley experiment. The Voigt transformations include the Lorentz factor 1 / 1 − − v 2 / c 2 for the y- and z-coordinates, and a new time variable t ′ = t − − v x / c 2 which later was called "local time". However, Voigt's work was completely ignored by his contemporaries.