DISPLACEMENT 



PROPOSITION XX. 



The primary spheres which are built up into 

 atoms of elementary substance occupy less space 

 in the Universe than did the same number of pri- 

 mary spheres in void matter. 



Because the atoms of elementary substance pos- 

 sess an identity. (Scientific data.) 



And because they are built up of primary 

 spheres. (Prop. XIX.) 



Therefore, the primary spheres must be in them 

 placed in a fixed, unalterable system. 



But the only way of uniformity possible is the 

 closest possible contact in spheres. 



And since every substance must have length and 

 breadth and height, therefore, the primary spheres 

 of atoms must be placed in the closest possible 

 conjunction. (Ocular demonstration.*) 



But the primary spheres of void matter cannot 

 all be in the closest possible contact. (Prop. IV.) 



Again, let a measure be filled with spheres 

 double B shot, for instance. Let them be poured 

 in or placed layer by layer in any possible way. 

 Let them be shaken and stirred. Then the measure 

 will be full no more, for the spheres have arranged 



* The ocular demonstration referred to is the laying to- 

 gether in closest possible contact of spheres equal in size. 

 This becomes difficult after the spheres begin to be numer- 

 ous, but affords a fascinating study, particularly when ap- 

 plied in attempts to ascertain the physical shapes of atoms. 



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