FORCES AND ATOMS 345 



surface, the pressure is greater by far than any of them; and yet, the average 

 density of the earth is less than double that of its superficial crust. 



We have imagined that as two atoms approach each other, the gravita- 

 tional force between them rises gently, the cohesive force remaining unde- 

 tectable till they come very close together, when at some critical distance it 

 begins a sharp and sudden rise which quickly carries its value far over that 

 of gravity. Now we are to conceive of yet a third force, repulsive, unde- 

 tectable till they come still closer together, then at a lesser critical distance 

 entering on a sharper more sudden rise which rapidly carries its value far 

 over those of both of the other two. 



This essential and powerful force has no name of its own. This is because 

 it is usually described in words not conveying directly the notion of force. 

 What we have now encountered is the concept of the incompressible atom, 

 the particle of irreducible volume — the doctrine that the atoms are to be 

 pictured not as infinitely small like the points of geometry, but as hard 

 impenetrable elastic pellets, minute indeed but not inconceivably so. This 

 is a doctrine frankly expressed by many a thinker of the past, who perhaps 

 was more unwilling than we to receive uncritically that difficult dogma of 

 the point of infinite smallness. Hearken again to Newton: "It seems 

 probable to me that God in the beginning formed matter in solid, hard, 

 massy, impenetrable, moveable particles . . . incomparably harder than 

 any porous bodies compounded of them; even so very hard, as never to wear 

 or break in pieces; no ordinary power being able to divide what God himself 

 made one in the first creation." 



The completely unsqueezable atom corresponds to a force of repulsion 

 which passes suddenly from zero to an infinite strength at a certain critical 

 distance. The critical distance is the "radius of the atom." Reversely the 

 idea of a force of repulsion rising rapidly indeed, but always continuously, 

 as two particles draw nearer — this corresponds to a squeezable atom, with- 

 out a definite radius. Solids and liquids in bulk are compressible, and this 

 seems to rule out the former idea, which anyhow is more drastic than one 

 likes to accept. It is not ruled entirely out, for there may be interstices 

 among the particles, and the shrinkage entailed by pressure may be ascribed 

 to the atoms so setting themselves that the cavities lessen in size. However, 

 this does not seem adequate, and it is better to accept a compressible atom 

 and make it share with the cavities the responsibility for the shrinkage. 

 Then there is also the fact that solids expand when warmed. This is 

 ascribed to the atoms dancing around with the heat, and so we approach a 

 new situation in which repulsion and motion are allied as the two antagonists 

 to cohesion. 



Instead of exploring this situation further, let us ask whether there is a 

 difference between the concept of the more-or-less squeezable atom and that 



