io8 SCIENCE AND METHOD. 



we can execute movements M^ which will be char- 

 acterized by the same muscular sensations. Then let 

 a be the situation of a certain point in the body, the 

 tip of the forefinger of the right hand, for instance, 

 in the initial position A, and let b be the position of 

 this same forefinger when, starting from that position 



A, we have executed the movements M. Then let cD- 

 be the situation of the forefinger in the position B, 

 and b^ its situation when, starting from the position 



B, we have executed the movements M^. 



Well, I am in the habit of saying that the points a 

 and b are, in relation to each other, as the points a)- 

 and <^\ and that means simply that the two series of 

 movements M and M^ are accompanied by the same 

 muscular sensations. And as I am conscious that, 

 in passing from the position A to the position B, my 

 body has remained capable of the same movements, 

 I know that there is a point in space which is to the 

 point d^ what some point b is to the point a, so that 

 the two points a and a^ are equivalent. It is this that 

 is called the homogeneity of space, and at the same 

 time it is for this reason that space is relative, since 

 its properties remain the same whether they are 

 referred to the axes A or to the axes B. So that the 

 relativity of space and its homogeneity are one and 

 the same thing. 



Now, if I wish to pass to the great space, which is 

 no longer to serve for my individual use only, but in 

 which I can lodge the universe, I shall arrive at it by 

 an act of imagination. I shall imagine what a giant 

 would experience who could reach the planets in a 

 few steps, or, if we prefer, what I should feel myself 

 in presence of a world in miniature, in which these 



