3 i8 POPULAR SCIENCE MONTHLY 



ment ; it might be contradicted by it if the results of different measure- 

 ments were not concordant. We should think ourselves fortunate that 

 this contradiction has not happened and that the slight discordances 

 which may happen can be readily explained. 



The postulate, at all events, resembling the principle of sufficient 

 reason, has been accepted by everybody; what I wish to emphasize is 

 that it furnishes us with a new rule for the investigation of simul- 

 taneity', entirely different from that which we have enunciated above. 



This postulate assumed, let us see how the velocity of light has been 

 measured. You know that Eoemer used eclipses of the satellites of 

 Jupiter, and sought how much the event fell behind its prediction. 

 But how is this prediction made? It is by the aid of astronomic laws, 

 for instance Newton's law. 



Could not the observed facts be just as well explained if we at- 

 tributed to the velocity of light a little different value from that 

 adopted, and supposed Newton's law only approximate? Only this 

 would lead to replacing Newton's law by another more complicated. 

 So for the velocity of light a value is adopted, such that the astronomic 

 laws compatible with this value may be as simple as possible. When 

 navigators or geographers determine a longitude, they have to solve 

 just the problem we are discussing; they must, without being at Paris, 

 calculate Paris time. How do they accomplish it? They carry a 

 chronometer set for Paris. The qualitative problem of simultaneity 

 is made to depend upon the quantitative problem of the measurement 

 of time. I need not take up the difficulties relative to this latter 

 problem, since above I have emphasized them at length. 



Or else they observe an astronomic phenomenon, such as an 

 eclipse of the moon, and they suppose that this phenomenon is per- 

 ceived simultaneously from all points of the earth. That is not alto- 

 gether true, since the propagation of light is not instantaneous; if 

 absolute exactitude were desired, there would be a correction to make 

 according to a complicated rule. 



Or else finally they use the telegraph. It is clear first that the recep- 

 tion of the signal at Berlin, for instance, is after the sending of this 

 same signal from Paris. This is the rule of cause and effect analyzed 

 above. But how much after? In general, the duration of the trans- 

 mission is neglected and the two events are regarded as simultaneous. 

 But, to be rigorous, a little correction would still have to be made by 

 a complicated calculation; in practise it is not made, because it would 

 be well within the errors of observation; its theoretic necessity is none 

 the less from our point of view, which is that of a rigorous definition. 

 From this discussion, I wish to emphasize two things: (1) The rules 

 applied are exceedingly various. (2) It is difficult to separate the 

 qualitative problem of simultaneity from the quantitative problem of 



