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When we say that the lightning strokes A and B are simultaneous

with respect to be embankment, we mean: the rays of light emitted

at the places A and B, where the lightning occurs, meet each

other at the mid-point M of the length A → B of the embankment.

But the events A and B also correspond to positions A and B on

the train. Let M′ be the mid-point of the distance A → B on the

travelling train. Just when the flashes (as judged from the

embankment) of lightning occur, this point M′ naturally coincides

with the point M but it moves towards the right in the diagram

with the velocity v of the train. If an observer sitting in the

position M′ in the train did not possess this velocity, then he

would remain permanently at M, and the light rays emitted by the

flashes of lightning A and B would reach him simultaneously, i.e.

they would meet just where he is situated.