How should we naturally decide whether two events in different places were simultaneous? One would naturally say: they are simultaneous if they are seen simultaneously by a person who is exactly half-way between them. (There is no difficulty about the simultaneity of two events in the _same_ place, such, for example, as seeing a light and hearing a noise.) Suppose two flashes of lightning fall in two different places, say Greenwich Observatory and Kew Observatory. Suppose that St. Paul’s is half-way between them, and that the flashes appear simultaneous to an observer on the dome of St. Paul’s. In that case, a man at Kew will see the Kew flash first, and a man at Greenwich will see the Greenwich flash first, because of the time taken by light to travel over the intervening distance. But all three, if they are ideally accurate observers, will judge that the two flashes were simultaneous, because they will make the necessary allowance for the time of transmission of the light. (I am assuming a degree of accuracy far beyond human powers.) Thus, so far as observers on the earth are concerned, the definition of simultaneity will work well enough, so long as we are dealing with events on the surface of the earth. It gives results which are consistent with each other, and can be used for terrestrial physics in all problems in which we can ignore the fact that the earth moves. But our definition is no longer so satisfactory when we have two sets of observers in rapid motion relatively to each other. Suppose we see what would happen if we substitute sound for light, and defined two occurrences as simultaneous when they are heard simultaneously by a man half-way between them. This alters nothing in the principle, but makes the matter easier owing to the much slower velocity of sound. Let us suppose that on a foggy night two men belonging to a gang of brigands shoot the guard and engine driver of a train. The guard is at the end of the train; the brigands are on the line, and shoot their victims at close quarters. An old gentleman who is exactly in the middle of the train hears the two shots simultaneously. You would say, therefore, that the two shots were simultaneous. But a station master who is exactly half-way between the two brigands hears the shot which kills the guard first. An Australian millionaire uncle of the guard and the engine driver (who are cousins) has left his whole fortune to the guard, or, should he die first, to the engine driver. Vast sums are involved in the question of which died first. The case goes to the House of Lords, and the lawyers on both sides, having been educated at Oxford, are agreed that either the old gentleman or the station master must have been mistaken. In fact, both may perfectly well be right. The train travels away from the shot at the guard, and towards the shot at the engine driver; therefore the noise of the shot at the guard has farther to go before reaching the old gentleman than the shot at the