THE RELATIVITY OF SPACE. 107 



he referred this restricted space would not change. 

 No doubt the rock to which he was chained would 

 not be motionless, since it would be involved in the 

 motion of our planet ; for us, consequently, these axes 

 would change every moment, but for him they would 

 not change. We have the faculty of referring our 

 extended space at one time to the position A of our 

 body considered as initial, at another to the position 

 B which it occupied some moments later, which we 

 are free to consider in its turn as initial, and, accord- 

 ingly, we make unconscious changes in the co-ordinates 

 every moment. This faculty would fail our imaginary 

 being, and, through not having travelled, he would 

 think space absolute. Every moment his system of 

 axes would be imposed on him ; this system might 

 change to any extent in reality, for him it would be 

 always the same, since it would always be the unique 

 system. It is not the same for us who possess, each 

 moment, several systems between which we can choose 

 at will, and on condition of going back by memory 

 more or less into the past. 



That is not all, for the restricted space would not 

 be homogeneous. The different points of this space 

 could not be regarded as equivalent, since some could 

 only be reached at the cost of the greatest efforts, 

 while others could be reached with ease. On the 

 contrary, our extended space appears to us homoge- 

 neous, and we say that all its points are equivalent. 

 What does this mean ? 



If we start from a certain position A, we can, 

 starting from that position, effect certain movements 

 M, characterized by a certain complexus of muscular 

 sensations. But, starting from another position B, 



