FUNDAMENTAL. PROPERTIES OF THE ELEMENTS RICHARDS. 205 



what could give the rigidity of steel to such an unstable structure ? 

 Tho most reasonable conclusion, from all the evidence taken together, 

 seems to be that the interstices between atoms in solids and liquids 

 must usually be small even in proportion to the size of the atoms 

 themselves, if, indeed, there are any interstices at all. 



Very direct and convincing evidence of another sort is at hand. 

 The idea that atoms may be compressible receives striking confirma- 

 tion from a recent interesting investigation of Gruneisen * concerning 

 the small effect of low temperatures on the compressibility of metals. 

 The average compressibility of aluminium, iron, copper, silver, and 

 platinum falls off only 7 per cent between the temperature of the 

 room and that of liquid air. Extrapolation of the curves indicates 

 that at the absolute zero very little further diminution should occur. 

 As far as we can guess, therefore, the hard metals are almost as com- 

 pressible at the absolute zero as at room temperatures. But at the 

 absolute zero all heat-vibration is supposed to stop; hence this 

 remaining compressibility must needs be ascribed to the atoms 

 themselves. 



If the atoms are compressible, all mathematical reasoning which 

 assumes them to be incompressible rests upon a false basis. The 

 kinetic theory of gases remains unmolested by these considerations, 

 except as they indicate the changeability of b in the equation of van 

 der Waals, but the new views affect seriously the application of tins 

 equation to solids and liquids. 



Let us proceed to trace a few of the outcomes of our hypothesis. 

 If atoms may really be packed closely together, the volumes of solids 

 and liquids should afford valuable knowledge concerning the relative 

 spaces occupied by the atoms themselves under varying conditions. 

 The densities of solids and liquids then assume a significance far more 

 interesting to the chemical philosopher than before, because they have 

 a more definite connection with the fundamental nature of things. 



An apparent objection at once suggests itself; if the particles in 

 condensed material are really touching one another, how can we 

 account for heat within the material? Would such closely packed 

 atoms be able to vibrate? 



The theory of compressible atoms supplies as one of its own corol- 

 laries the immediate answer to this question. If atoms are com- 

 pressible throughout their whole substance, they may contract and 

 expand, or vibrate within themselves, even when their surfaces are 

 prevented from moving by being closely packed together. It is thus 

 possible to conceive of a vibrational effect, even in contiguous atoms, 

 provided we can conceive of these atoms as being elastic throughout 



» E. Gruneisen, Ann. Physik, 1910 (iv), vol. 33, p. 1239. The relative values for the compressibilities 

 recorded in this investigation are doubtless trustworthy, although the absolute magnitudes are somewhat 

 uncertain because they depend on the rather inadequate theory of elasticity. 



