364 
PHYSICS: P. W. BRIDGMAN 
Proc. N. a. S. 
A number of theoretical considerations are suggested by these meas- 
urements of compressibihty. In the first place, and most important, I have 
shown in the detailed paper by a dimensional argument that the correct 
order of magnitude for the compressibilities of all these metals may be found 
by taking over for the metal the same picture of the structure that has given 
such suggestive results when appHed to the salts, namely the picture of 
the metal as composed of two interpenetrating lattices, one of positively 
charged atomic ions, and the other of negative electrons, the electron 
lattice in the case of the metal taking the place of the lattice of negatively 
charged atoms in the case of the salts, as for example the chlorine lattice 
in NaCl. The same conclusion as to the structure of a metal has been 
recently drawn by Kraus^ on the basis of a large number of chemical facts. 
The expression of Born^ for the compressibility of salts, in which a re- 
pulsive potential between atoms as the inverse ninth power is found to 
give good values for the compressibility, cannot be extended to metals, 
for neither is the absolute value of the compressibility nor its variation with 
pressure such as would be given by this sort of a potential. There seems 
to be no simple repulsive potential that will account for the compressibility 
data for the various metals. It is possible, however, to represent the re- 
pulsive potential by an arbitrary function, and then to find the numerical 
value of several of its derivatives from experimental data. For those metals 
which crystallize face-centered cubic, and which therefore probably con- 
sist of interpenetrating lattices of ions and electrons of the type of NaCl, 
it is possible to calculate the grating constants, and to evaluate the first 
three derivatives of the repulsive potential in terms of the absolute di- 
mensions of the crystal, the compressibility, and the change of compressi- 
bility with pressure. These derivatives for a number of metals are listed 
in the detailed paper. The sign of the derivatives is alternately positive and 
negative, and their successive absolute values differ by factors of the order 
of magnitude of the distance of separation of atomic centers. This is 
all as one would expect. To make more detailed use of these numerical 
values of the derivatives demands that more attention be paid to 
the details of the atomic structure than we have hitherto been able to do. 
An effect recently discussed by Schottky,^ namely a distortion of the 
atoms under pressure, I have shown by a detailed numerical examination 
to be of such a magnitude as to essentially modify the simple calculations 
of compressibility given by Born. 
By the use of simple thermodynamics I have been able to modify the 
arguments of Born, which applied only at the absolute zero of tempera- 
ture, so as to take account of the effect of temperature on the compressi- 
bility to be calculated in terms of the lattice structure. The new terms 
introduced by temperature are not large enough to seriously modify Born's 
argument. 
