39^ Structure of the Universe 



mathematical considerations that this grain is the smallest possible 

 entity which can exist in the universe. It is the "absolutely rigid 

 granule, ultimate atom or primordian." In Section VIII. of the 

 "Sub-mechanics" he says: 



"Although the absolutely rigid atom is as old as any conception 

 In physical philosophy, the properties attributed to it are outside any 

 experience derived from the properties of matter. In this respect the 

 perfect atom is in the same position, though in a different way, as 

 that other physical conception — the perfect fluid. Both of these con- 

 ceptions represent conditions to which matter in one or other of its 

 modes, apparently approximates, but to which, the results of all re- 

 searches show, it can never attain, although this experience shows 

 that there is still something beyond. * * * n becomes clear 

 therefore that any fundamental atom must be considered as something 

 outside — of another order than — material bodies, the properties of 

 which are not to be considered as a consequence of the laws of mo- 

 tion and conservation of energy in the medium, but as the prime 

 cause of these laws." 



This last statement involves a very important principle; for, 

 whereas other theories of the atom have been based on the motion 

 of a so-called perfect fluid continuously filling space, like Kelvin's 

 vortex atomic theory, or upon an electronic system of electrostatic 

 and electromagnetic forces, as developed by Thomson, Larmor and 

 Lodge, the atom in these systems being the result of the laws of mo- 

 tion and conservation of energy, Reynold's fundamental atoms or 

 cosmic grains, by their motions and arrangements are themselves the 

 cause of the laws of motion and conservation of energy, the whole 

 explanation and philosophy being purely dynamical, just as Newton's 

 explanation of the law of gravitation is purely dynamical. 



Arrangement or Piling of the Grains. 



We come now to one of the most important points in the whole 

 subject; that is, the arrangement or piling of the grains in the 

 medium. We have all doubtless seen cannon balls piled in heaps on 

 military reservations. Now, there are different ways in which shot 

 or other spheres may be piled. I have here before me on the table 

 six different regular arrangements or piling of small rubber balls, 

 and in these different arrangements the number of balls varies in 

 proportion to the total volume or space occupied by the balls. There 

 are six regular arrangements in which balls touching each other may 

 be piled, shown by these six models, and in each of these arrange- 

 ments, as stated, the full spaces or the spaces occupied by the balls, 

 and the empty spaces or the interstices between them vary. I have 

 calculated the relation or proportion of full space to empty space in 

 these six different arrangements, and find that in the closest arrange- 

 ment or piling, where the grains are arranged in parallel tiers in 

 triangular form, taking the total volume of the pile as 100, the full 

 space occupied by the balls amounts to 79.818 and the empty space to 

 20.182, or about 4 to 1, whereas in the most open arrangement of pil- 

 ing, where the grains are placed vertically over each other in parallel 

 tiers in the square position, like this model, the full space is only 



