I am very pleased with this suggestion, but for all that I cannot regard the matter as quite settled, because I feel constrained to raise the following objection: 

“Your definition would certainly be right, if only I knew that the light by means of which the observer at M perceives the lightning flashes travels along the length A arrow M with the same velocity as along the length B arrow M. But an examination of this supposition would only be possible if we already had at our disposal the means of measuring time.  It would thus appear as though we were moving here in a logical circle.”

After further consideration you cast a somewhat disdainful glance at me —­ and rightly so —­ and you declare: 

“I maintain my previous definition nevertheless, because in reality it assumes absolutely nothing about light.  There is only one demand to be made of the definition of simultaneity, namely, that in every real case it must supply us with an empirical decision as to whether or not the conception that has to be defined is fulfilled.  That my definition satisfies this demand is indisputable.  That light requires the same time to traverse the path A arrow M as for the path B arrow M is in reality neither a supposition nor a hypothesis about the physical nature of light, but a stipulation which I can make of my own freewill in order to arrive at a definition of simultaneity.”

It is clear that this definition can be used to give an exact meaning not only to two events, but to as many events as we care to choose, and independently of the positions of the scenes of the events with respect to the body of reference * (here the railway embankment).  We are thus led also to a definition of " time " in physics.  For this purpose we suppose that clocks of identical construction are placed at the points A, B and C of the railway line (co-ordinate system) and that they are set in such a manner that the positions of their pointers are simultaneously (in the above sense) the same.  Under these conditions we understand by the " time " of an event the reading (position of the hands) of that one of these clocks which is in the immediate vicinity (in space) of the event.  In this manner a time-value is associated with every event which is essentially capable of observation.

This stipulation contains a further physical hypothesis, the validity of which will hardly be doubted without empirical evidence to the contrary.  It has been assumed that all these clocks go at the same rate if they are of identical construction.  Stated more exactly:  When two clocks arranged at rest in different places of a reference-body are set in such a manner that a particular position of the pointers of the one clock is simultaneous (in the above sense) with the same position, of the pointers of the other clock, then identical " settings " are always simultaneous (in the sense of the above definition).

  Notes