Pagina 43 de 212

Before we deal with this, we shall introduce the following

incidental consideration. Up to the present we have only

considered events taking place along the embankment, which had

mathematically to assume the function of a straight line. In the

manner indicated in Section II we can imagine this reference-body

supplemented laterally and in a vertical direction by means of a

framework of rods, so that an event which takes place anywhere

can be localised with reference to this framework. Similarly, we

can imagine the train travelling with the velocity v to be

continued across the whole of space, so that every event, no

matter how far off it may be, could also be localised with

respect to the second framework. Without committing any

fundamental error, we can disregard the fact that in reality

these frameworks would continually interfere with each other,

owing to the impenetrability of solid bodies.