RELATIVITY OF LENGTH 143 



chosen so that it might not be prevented by casual in- 

 fluences from keeping the same relative length — relative 

 to what? Relative to some length inalienably associated 

 with the region in which it is placed. I can conceive 

 of no other answer. An example of such a length 

 inalienably associated with a region is the directed radius. 



The long and short of it is that when the standard 

 metre takes up a new position or direction it measures 

 itself against the directed radius of the world in that 

 region and direction, and takes up an extension which 

 is a definite fraction of the directed radius. I do not 

 see what else it could do. We picture the rod a little 

 bewildered in its new surroundings wondering how 

 large it ought to be — how much of the unfamiliar terri- 

 tory its boundaries ought to take in. It wants to do 

 just what it did before. Recollections of the chunk of 

 space that it formerly filled do not help, because there 

 is nothing of the nature of a landmark. The one thing 

 it can recognise is a directed length belonging to the 

 region where it finds itself; so it makes itself the same 

 fraction of this directed length as it did before. 



If the standard metre is always the same fraction of 

 the directed radius, the directed radius is always the 

 same number of metres. Accordingly the directed 

 radius is made out to have the same length for all 

 positions and directions. Hence we have the law of 

 gravitation. 



When we felt surprise at finding as a law of Nature 

 that the directed radius of curvature was the same for 

 all positions and directions, we did not realise that our 

 unit of length had already made itself a constant fraction 

 of the directed radius. The whole thing is a vicious 

 circle. The law of gravitation is — a put-up job. 



