222 BRIDGMAN. 



that there are only three, Al, Pb, and Li, for which the thermal ex- 

 pansion initially decreases more rapidly than the compressibility. 

 Even potassium is in the list of those whose compressibility at first 

 decreases more rapidly than the expansion. But at high pressures we 

 have seen that this state of affairs is reversed in the case of potassium. 

 Computation will show that this is also the case for sodium, the ex- 

 pansion at 12000 kg. having dropped to about one third of its initial 

 value, while the compressibility has dropped to two thirds. This may 

 well be the behavior of all metals at sufficiently high pressures. 



Theoretical Considerations. 



By far the most successful theoretical attempt to account numeri- 

 cally for the compressibility of solid substances is that which Born 3 

 has developed and applied to crystals of the type of NaCl and also to 

 CaF 2 and ZnS. The fundamental thesis of this theory is that the 

 solid is maintained by electrostatic forces, there being in the position 

 of the center of each chlorine atom, in NaCl for example, a single 

 elementary negative charge, and at the center of the Xa atom a single 

 elementary positive charge. In addition to the forces between the 

 charged ions, which act on each other according to the inverse square 

 law, there are also mutual repulsions between adjacent atoms due to 

 the electrons in the outer shells of the atoms. Equilibrium is due to a 

 balance between the attractive and repulsive forces. It should be 

 possible to calculate the repulsive forces as well as the attractive 

 forces if the distribution of the electrons within the atom is known. 

 From the assumption that the electrons are in cubical array in the 

 interior of the atom, as they are supposed to be from other considera- 

 tions, Born has deduced that the potential of the repulsive forces is as 

 the inverse ninth power of the distance between atomic centers, and 

 has furthermore shown that the inverse ninth power gives numerically 

 very approximately the compressibility of crystals of the type of NaCl. 



Naturally the first inquiry of an attempt to extend this theory to 

 include metals is whether the fundamental thesis still holds, namely 

 that the forces are essentially electrostatic in nature and are due to 

 single elementary charges or small integral multiples of them situated 

 at the centers of the atoms. A dimensional argument as to the order 

 of magnitude of the quantities involved suggests that the same 

 fundamental thesis does indeed hold. A quantity of the dimensions 

 of compressibility (M _1 LT -2 ) is to be built up from the electronic 



