Einstein in his "Relativity: The Special and General Theory" ch.VIII explains that simultaneity between events placed in two predetermined places A and B can be asserted if an observer in the mid-point M sees the light coming from the two events places in the same time. In ch.VII he says that since "light speed is a constant in any Galilean Co-ordinate System" is an axiom, you can't add or subtract the observer velocity to the light speed: any observer, despite his Galilean Co-ordinate System of reference, must see light speed = c. In ch.IX he explains the train experiment, and this looks inconsistent with the previous chapters: ina K Galilean Co-ordinate System of reference, events placed in A and B are simultaneous from the M mid-point of view, and when Einstein tells that the observer in M' mid-point on the carriage (K' GCS) sees the light coming from B earlier than the A he skates over any explanations. And the only explanation I can find is that he thinks the observer travelling at velocity w can be reached from the light coming from B earlier because in the mean time M' has moved forward from M to a place closer to B than M: this is equivalent to adding w and c and this is inconsistent with ch.VII assertion. I think that if M' is the mid-point between A' and B' (places in K' corresponding to A and B in K when the events happen) he must see the A' and B' lights coming in the same time since he is in the mid-point and c is constant, and we can't take in account he is moving because that movement is just a K-K' relation and this relation can't affect independent measurements on K'. If I don't express the M' mid-point concept using A'-B' reference, I must argue that M' is not a mid-point anymore (it has moved and isn't in the middle of A-B segment anymore when the lights comes) and the definition of simultaneity is not applicable to M' so the experiment must result in a nonsense. What do you think?