SPACE 667 



independent of all interpretation by experiments. If the law is true 

 in the Euclidean interpretation, it will be also true in the non-Eucli- 

 dean interpretation. Allow me to make a short digression on this 

 point. I have spoken above of the data which define the position of 

 the different bodies of the system. I might also have spoken of those 

 which define their velocities. I should then have to distinguish the 

 velocity with which the mutual distances of the different bodies are 

 changing, and on the other hand the velocities of translation and 

 rotation of the system; that is to say, the velocities with which its 

 absolute position and orientation are changing. For the mind to be 

 fully satisfied, the law of relativity would have to be enunciated as 

 follows : The state of bodies and their mutual distances at any 

 given moment, as well as the velocities with which those distances are 

 changing at that moment, will depend only on the state of those bodies, 

 on their mutual distances at the initial moment, and on the velocities 

 with which those distances were changing at the initial moment. But 

 they will not depend on the absolute initial position of the system 

 nor on its absolute orientation, nor on the velocities with which that 

 absolute position and orientation were changing at the initial moment. 

 Unfortunately, the law thus enunciated does not agree with experi- 

 ments at least, as they are ordinarily interpreted. Suppose a man 

 were translated to a planet, the sky of which was constantly covered 

 with a thick curtain of clouds, so that he could never see the other 

 stars. On that planet he would live as if it were isolated in space. 

 But he would notice that it revolves, either by measuring its ellipticity 

 (which is ordinarily done by mean? of astronomical observations, but 

 which could be done bv purely geodesic means), or by repeating the 

 experiment of Foucault's pendulum. The absolute rotation of this 

 planet might be clearly shown in this way. Now, here is a fact which 

 shocks the philosopher, but which the physicist is compelled to accept. 

 We know from this fact Newton concluded the existence of absolute 

 space. I myself cannot accept this way of looking at it. I shall ex- 

 plain why in Part III., but for the moment it is not my intention to 

 discuss this difficulty. I must therefore resign myself, in the enun- 

 ciation of the law of relativity, to including velocities of every kind 

 among the data which define the state of the bodies. However that 

 may be, the difficulty is the same for both Euclid's geometry and for 

 Lobatschewsky's. I need not therefore trouble about it further, and 

 I have only mentioned it incidentally. To sum up, whichever way we 

 look at it, it is impossible to discover in geometric empiricism a ra- 

 tional meaning. 



6. Experiments only teach us the relations of bodies to one another. 

 They do not and cannot give us the relations of bodies and space, nor 

 the mutual relations of the different parts of space. " Yes ! " you 

 reply, " a single experiment is not enough, because it only gives us 



