I have been trying to read Einstein's small book on relativity and to work out the results for myself, but I seem to be getting to the wrong conclusions. In Chapter 12 he says "The rigid rod is thus shorter when in motion than when at rest, and the more quickly it is moving, the shorter the rod." For a train moving away from the observer on the emankment, that seems to be right, but is the train is coming towards you, it seems to me it should be longer. Imagine you are standing by the track as the front of a train, say one light year long relative to a man on the train measuring it, and travelling at 1/3 the speed of light reaches you. The point on the embankment where the back of the train would be "simultaneously", relative to you, would be much further than one light year away from you because the light would take a while to arrive. In fact I make it that the length would be 1 + 1/3 + 1/9 + 1/27.........= 1.5 light years. If the speed of the train was 1/N the speed of light the length would be N/N-1 times its length at rest. If the train was going away from you it would be shorter, N/N+1 times its length at rest, in this particular case, 1 - 1/3 + 1/9 - 1/27....... Obviously these are the wrong results. Have I 1. miscalculated something or 2. misunderstood what is meant by relativistic length or 3. is this result in fact directional, putting -v for v if it is coming towards you? Can someone please sort me out? Simple explanation please! Many thanks in anticipation.