 The theory was described by Theodor Meyer on his thesis dissertation in 1908, along with his advisor Ludwig Prandtl, who had already discussed the problem a year before.The expansion fan consists of an infinite number of expansion waves or Mach lines.The first Mach line is at an angle formula_19 with respect to the flow direction, and the last Mach line is at an angle formula_20 with respect to final flow direction.