COMPRESSIBILITY OF METALS. 225 



which Born has applied to calculating the compressibility of CaF 2 . 

 There is also another group of metals about which we may make very 

 plausible assumptions about the positions of the electrons in the 

 lattice. The Na atoms by themselves or the CI atoms by themselves 

 form in NaCl a face centered cubic lattice. Hence it is natural to 

 expect that the complete crystal structure (meaning by this the 

 arrangement of ions and free electrons) of those metals which are 

 univalent, and therefore readily lose a single electron, and whose 

 atomic nuclei have been proved to crystallize face centered cubic, 

 should be exactly like that of NaCl. Several of the metals of the 

 above list are in this class: Cu, Ag, Au, and probably Pb. 



In addition to the crystal structure, we must also know the law of 

 repulsion. This is a much more uncertain matter. An uncritical 

 extension of the argument given by Born would indicate a repulsion 

 whose potential is as the inverse fifth power of the distance of separa- 

 tion of ions and electrons, since his first term in his fundamental de- 

 velopment for the potential of a neutral cube and a single point charge 

 is the inverse fifth. A more critical examination of this discussion 

 will raise several doubts, however, and in fact it is very questionable 

 to me how much significance is to be given to the inverse ninth power 

 which Born deduces for NaCl. It is in the first place disconcerting to 

 discover that the inverse fifth power term for a compound lattice of 

 electrons and ions has the wrong sign, so that instead of a repulsion 

 we have an attraction. However, in computing what the action is 

 between a neutral cube and an electron there are several matters with 

 regard to which we are in serious doubt and which may greatly affect 

 the result. Thus the statement that the force between an ion and an 

 external electron is of the wrong sign is based on the assumption that 

 the electron is situated on one of the three axes of the cube perpendicu- 

 lar to the faces at their mid-points. This corresponds to the arrange- 

 ment assumed by Born for the cubical atoms in NaCl. But it is evi- 

 dent that if the electron approaches the neutral cube along a diagonal, 

 the force will be of repulsion instead of attraction. In crystals not of 

 the simple type of NaCl it is not at all obvious what the arrangement 

 of the cubical atoms in the crystal lattice is, for the symmetry of the 

 crystal does not seem to be consistent with the cubical symmetry of 

 the atom. Thus in the case of CaF 2 , the Ca atom is surrounded by 12 

 other atoms symmetrically situated, so that the symmetry of the 

 dodecahedron is indicated. 



Even if the orientation of the atoms with respect to the electron is 

 known and is that assumed by Born, still the inverse fifth power must 



