PRINCIPLES OF MATHEMATICAL PHYSICS 611 



factory that is! Is it not evident that from a principle so under- 

 stood we could no longer get anything? It could no longer tell us 

 anything just because it would no longer fear any contradiction. 



If we succeed in measuring anything, we should always be free 

 to say that this is not the absolute velocity in relation to the ether, 

 it might always be the velocity in relation to some new unknown 

 fluid with which we might fill space. 



Indeed, experience has taken on itself to ruin this interpretation 

 of the principle of relativity; all attempts to measure the velocity 

 of the earth in relation to the ether have led to negative results. 

 This time experimental physics has been more faithful to the prin- 

 ciple than mathematical physics; the theorists, to put in accord 

 their other general views, would not have spared it; but experiment 

 has been stubborn in confirming it. 



The means have been varied in a thousand ways and finally 

 Michelson has pushed precision to its last limits; nothing has come 

 of it. It is precisely to explain this obstinacy that the mathematicians 

 are forced to-day to employ all their ingenuity. 



Their task was not easy, and if Lorentz has gotten through it, 

 it is only by accumulating hypotheses. 



The most ingenious idea has been that of local time. 



Imagine two observers who wish to adjust their watches by 

 optical signals; they exchange signals, but as they know that the 

 transmission of light is not instantaneous, they take care to cross 

 them. 



When the station B perceives the signal from the station A, its 

 clock should not mark the same hour as that of the station A at the 

 moment of sending the signal, but this hour augmented by a con- 

 stant representing the duration of the transmission. Suppose, for 

 example, that the station A sends its signal when its clock marks 

 the hour 0, and that the station B perceives it when its clock marks 

 the hour t. The clocks are adjusted if the slowness equal to t repre- 

 sents the duration of the transmission, and to verify it the station B 

 sends in its turn a signal when its clock marks 0; then the station A 

 should perceive it when its clock marks t. The time-pieces are then 

 adjusted. And in fact, they mark the same hour at the same phys- 

 ical instant, but on one condition, namely, that the two stations are 

 fixed. In the contrary case the duration of the transmission will not 

 be the same in the two senses, since the station A, for example, 

 moves forward to meet the optical perturbation emanating from B, 

 while the station B flies away before the perturbation emanating 

 from A. The watches adjusted in that manner do not mark, there- 

 fore, the true time; they mark what one may call the local time, so 

 that one of them goes slow on the other. It matters little, since we 

 have no means of perceiving it. All the phenomena which happen 



