FUNDAMENTAL PROPERTIES OF THE ELEMENTS—RICHARDS. 205 
what could give the rigidity of steel to such an unstable structure 2 
The 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 Griineisen + 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 6 in the equation of van 
der Waals, but the new views affect seriously the application of this 
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 
1E. Griineisen, 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, 
