226 BRIDGMAN. 



be open to grave question. Born developed the potential of the cube 

 at external points in a power series, of which the first term was the 

 inverse fifth, the development being good at points whose distance 

 from the center of the cube is large compared with the semi-diagonal, 

 or in other words, the dimensions of the atom are assumed small in 

 comparison with their distances apart. Now this is almost certainly 

 not the case, but a number of lines of argument indicate that the 

 atoms pretty completely fill the total space, and that their external 

 shells are nearly in contact. Hence in most of the cases in practise we 

 can certainly say that more terms than the first of the series are neces- 

 sary to give an adequate representation, and that probably under 

 many actual conditions the series is actually divergent. 



There is another important consideration with regard to the series 

 development. In computing the compressibility it is necessary to 

 differentiate the expression for the potential. Now although the 

 numerical magnitude of the potential itself may perhaps be given with 

 sufficient approximation by the first term of the series, it is quite 

 another matter to expect the derivative to be given by the derivative 

 of the first term. 



Apart from these considerations, which after all are concerned with 

 the method of computing the results, there is still another considera- 

 tion which reaches deeper, and involves the physical picture back of 

 the computations. This has been suggested by Schottky 21 in a recent 

 paper. He finds quite general theorems for electromagnetic systems 

 like the system of ions and electrons in a crystal which connect the 

 changes of internal kinetic and potential energy of the system with the 

 external forces acting on the system. In particular, for a system 

 under external hydrostatic pressure, Schottky obtains the result, 



dl= - dU+ 3d (pV) 

 dE = 2dU - U (pV), 



where L is the internal kinetic energy, E the internal electro-magnetic 

 energy, and U the total energy of the system. The dashes indicate 

 average values over a time sufficiently long for the average values to 

 be constant. If in particular we now subject the system to an iso- 

 thermal change of pressure, we have by thermodynamics 



dU = 



