The Lorentz transformation tells us what estimate of distances and periods of time will be made by an observer whose relative motion is known, when we are given those of another observer. We may suppose that you are in a train on a railway which travels due east. You have been traveling for a time which, by the clocks at the station from which you started, is _t_. At a distance _x_ from your starting point, as measured by the people on the line, an event occurs at this moment—say the line is struck by lightning. You have been traveling all the time with a uniform velocity _v_. The question is: How far from you will you judge that this event has taken place, and how long after you started will it be by your watch, assuming that your watch is correct from the point of view of an observer on the train? [3] So long as he has no considerable acceleration. The treatment of acceleration belongs to the _general_ theory of relativity. Our solution of this problem has to satisfy certain conditions. It has to bring out the result that the velocity of light is the same for all observers, however they may be moving. And it has to make physical phenomena—in particular, those of electromagnetism—obey the same laws for different observers, however they may find their measures of distances and times affected by their motion. And it has to make all such effects on measurement reciprocal. That is to say, if you are in a train and your motion affects your estimate of distances outside the train, there must be an exactly similar change in the estimate which people outside the train make of distances inside it. These conditions are sufficient to determine the solution of the problem, but the method of obtaining the solution cannot be explained without more mathematics than is possible in the present work.