RELATIVITY OF LENGTH 141 



The fact that this directed radius which, one would 

 think, might so easily differ from point to point and 

 from direction to direction, has only one standard value 

 in the world is Einstein's law of gravitation. From it 

 we can by rigorous mathematical deduction work out the 

 motions of planets and predict, for example, the eclipses 

 of the next thousand years; for, as already explained, 

 the law of gravitation includes also the law of motion. 

 Newton's law of gravitation is an approximate adapta- 

 tion of it for practical calculation. Building up from 

 the law all is clear; but what lies beneath it? Why is 

 there this unexpected standardisation? That is what we 

 must now inquire into. 



Relativity of Length. There is no such thing as absolute 

 length; we can only express the length of one thing in 

 terms of the length of something else.* And so when 

 we speak of the length of the directed radius we mean 

 its length compared with the standard metre scale. 

 Moreover, to make this comparison, the two lengths 

 must lie alongside. Comparison at a distance is as un- 

 thinkable as action at a distance; more so, because com- 

 parison is a less vague conception than action. We must 

 either convey the standard metre to the site of the 

 length we are measuring, or we must use some device 

 which, we are satisfied, will give the same result as if we 

 actually moved the metre rod. 



Now if we transfer the metre rod to another point of 

 space and time, does it necessarily remain a metre long? 

 Yes, of course it does; so long as it is the standard of 

 length it cannot be anything else but a metre. But does 

 it really remain the metre that it was? I do not know 



* This relativity with respect to a standard unit is, of course, addi- 

 tional to and independent of the relativity with respect to the observer's 

 motion treated in chapter n. 



