GEOMETRY AND MECHANICS 137 



unlike. There is no reason to regard the partitions of 

 the sciences made in the early stages of human thought 

 as irremovable. 



But mechanics in becoming geometry remains none 

 the less mechanics. The partition between mechanics 

 and geometry has broken down and the nature of each 

 of them has diffused through the whole. The apparent 

 supremacy of geometry is really due to the fact that it 

 possesses the richer and more adaptable vocabulary; 

 and since after the amalgamation we do not need the 

 double vocabulary the terms employed are generally 

 taken from geometry. But besides the geometrisation of 

 mechanics there has been a mechanisation of geometry. 

 The proposition about the space-triangle quoted above 

 was seen to have grossly material implications about the 

 behaviour of scales which would not be realised by any- 

 one who thinks of it as if it were a proposition of pure 

 mathematics. 



We must rid our minds of the idea that the word 

 space in science has anything to do with void. As pre- 

 viously explained it has the other meaning of distance, 

 volume, etc., quantities expressing physical measure- 

 ment just as much as force is a quantity expressing 

 physical measurement. Thus the (rather crude) state- 

 ment that Einstein's theory reduces gravitational force 

 to a property of space ought not to arouse misgiving. 

 In any case the physicist does not conceive of space 

 as void. Where it is empty of all else there is still the 

 aether. Those who for some reason dislike the word 

 aether, scatter mathematical symbols freely through the 

 vacuum, and I presume that they must conceive some 

 kind of characteristic background for these symbols. I 

 do not think any one proposes to build even so relative 

 and elusive a thing as force out of entire nothingness. 



