Kind of long winded, but I would appreciate a second veiw on untangling EA's thinking about this. § 2. On the Relativity of Lengths and Times We imagine further that at the two ends A and B of the rod, clocks are placed which synchronize with the clocks of the stationary system, that is to say that their indications correspond at any instant to the “time of the stationary system” at the places where they happen to be. These clocks are therefore “synchronous in the stationary system.” AE has previously defined the synchronization of clocks in § 1, but just to be clear at this point that I follow his reasoning, let's make sure these conclusions are consistent with his reasoning... - synchronous clocks to not need to display the same time indication with their hands "at the same time"; they just need to advance at the same rate, that is say they operate at the same rate when both are at rest relative to each other. I think this is clear from the method used in § 1 where it is only the differences in clock readings that are used to verify their synchrony. - from the above, if one desires, one may indeed set all the synchronous clocks to display the "same display indications at the same time" by taking into account c and adjusting them to do so. - synchronous clocks means clocks in the same inertial reference frame... all clocks at rest with respect to each other within an inertial reference frame are synchronous. If all that is well, it seems clear that the "clocks" placed at the A and B ends of the moving rod are not really clocks. They are indicators that use clock faces to show the time of the moving rod ends in the stationary system. They cannot be clocks in the moving system synchronous with clocks in the stationary system... why are these two rod end "clocks" needed to indicate the stationary time of the moving rod ends? Cannot observers in either the stationary or moving system read the clocks EA has imagined populate the stationary system? If the moving observers at the rod ends cannot read the stationary clocks directly, then what is the mechanism that allows the moving rod end "clock faces" to indicate the stationary clock times at the rod ends? In short, it looks like in § 1 synchronization of clocks was demonstrated to require that they be at inertial rest with respect to each other, but the moving rod end clocks are then somehow allowed to "synch" with the stationary clocks in order to be their proxy indicators. We imagine further that with each clock there is a moving observer, and that these observers apply to both clocks the criterion established in § 1 for the synchronization of two clocks. Let a ray of light depart from A at the time(*4) tA, let it be reflected at B at the time tB, and reach A again at the time t'A. Taking into consideration the principle of the constancy of the velocity of light we find that rB-tA=rAB/(c-v) and t'A-tB=rAB/(c+v) where rAB denotes the length of the moving rod — measured in the stationary system. Observers moving with the moving rod would thus find that the two clocks were not synchronous, while observers in the stationary system would declare the clocks to be synchronous. EA has the two moving observers test for synchronization between the ends of the moving rod... - surely they are not using the time tA and subsequent times from the stationary system to do this? - surely they are not using the c-v and c+v in their calculation? It seems to me that when EA says, "Taking into consideration the principle of the constancy of the velocity of light we find that..." that this "we" is meant to be those of us in the stationary system, not the two moving observers. He even says that rAB is the rod length "measured in the stationary system", so this pair of equalities are the stationary measures, not the two observers. So I'm thinking that when he writes "We imagine further that with each clock there is a moving observer, and that these observers apply to both clocks the criterion established in § 1 for the synchronization of two clocks. Let a ray of light depart..." what he means is "We imagine further that with each clock there is a moving observer, and that these observers apply to both clocks the criterion established in § 1 for the synchronization of two clocks, to which moving system we will return in a moment. Meanwhile from the standpoint of the stationary system, let a ray of light depart..." Assuming all that is well, it looks like what has happened is that the stationary observer has calculated what he thinks the moving observers will find - the moving observers are doing the synch test and the stationary observer is following along from his stationary perspective. EA concludes that the stationary observer will find the "clocks" at the moving rod ends to be synchronized, which is to be expected since as proxy indicators of clocks in the stationary system, they must show synchrony to a stationary observer. He concludes that the observers moving with the rod will find the clocks are not synchronous... but these observers are at rest with respect to the rod and the "clocks" at the rod ends, so all are at rest with respect to each other. Going back to the understanding of synchrony of clocks, are not both moving rod ends subject to the same rate of time with respect to the moving observers? Does EA mean to suggest that "actual moving clocks" at the rod ends in the moving system would not be synchronous with clocks in the stationary system (which seems correct to me)? It would just need to be clear that the "indicator clock faces" and the actual indications of real clocks at the rod ends would differ and not be synchronous. It looks to me that if these moving rod end indicator clock faces showing the time of the stationary system are taken to be real clocks by the moving observers, then yes, the moving observers would conclude that the rod end clocks were not synchronous - because they are using measures from the stationary system! It seems to me that if by chance the time reading tA for both the stationary and moving systems just happened to be the same value, and then both the stationary and moving system observers tested for synchrony of real clocks at the moving rod ends, the stationary observers would find that those clocks were not in synchrony, but the moving observers would find that they were in synchrony... as would any test of two real clocks at the ends of a rigid rod with respect to which the observers were at inertial rest. Any learned comments on whether I am understanding EA's reasoning here is much appreciated.