666 SCIENCE AND HYPOTHESIS 



this system for example, their temperature, their electric potential, 

 etc.; and on the other hand their position in space. And among the 

 data which enable us to define this position we distinguish the mutual 

 distances of these bodies that define their relative positions, and the 

 conditions which define the absolute position of the system 

 and its absolute orientation in space. The law of the pheno- 

 mena which will be produced in this system will depend on the 

 state of these bodies, and on their mutual distances; but because 

 of the relativity and the inertia of space, they will not depend on the 

 absolute position and orientation of the system. In other words, the 

 state of the bodies and their mutual distances at any moment will 

 solely depend on the state of the same bodies and on their mutual dis- 

 tances at the initial moment, but will in no way depend on the abso- 

 lute initial position of the system and on its absolute initial orientation. 

 This is what we shall call, for the sake of abbreviation, the law of rela- 

 tivity. 



So far I have spoken as a Euclidean geometer. But I have said 

 that an experiment, whatever it may be, requires an interpretation 

 on the Euclidean hypothesis; it equally requires one on the non- 

 Euclidean hypothesis. Well, we have made a series of experiments. 

 We have interpreted them on the Euclidean hypothesis, and we have 

 recognized that these experiments thus interpreted do not violate this 

 " law of relativity." We now interpret them on the non-Euclidean 

 hypothesis. This is always possible, only the non-Euclidean distances 

 of our different bodies in this new interpretation will not generally 

 be the same as the Euclidean distances in the primitive interpretation. 

 Will our experiment interpreted in this new manner be still in agree- 

 ment with our " law of relativity," and if this agreement had not 

 taken place, would we not still have the right to say that experiment 

 has proved the falsity of non-Euclidean geometry? It is easy to see 

 that this is an idle fear. In fact, to apply the law of relativity in all 

 its rigor, it must be applied to the entire universe; for if we were to 

 consider only a part of the universe, and if the absolute position of 

 this part were to vary, the distances of the other bodies of the universe 

 would equally vary; their influence on the part of the universe con- 

 sidered might therefore increase or diminish, and this might modify 

 the laws of the phenomena which take place in it. But if our system 

 is the entire universe, experiment is powerless to give us any opinion 

 on its position and its absolute orientation in space. All that our 

 instruments, however perfect they may be, can let us know will be the 

 state of the different parts of the universe, and their mutual distances. 

 Hence, our law of relativity may be enunciated as follows : The 

 readings that we can make with our instruments at any given moment 

 will depend only on the readings that we were able to make on the 

 same instruments at the initial moment. Now such an enunciation is 



