236 BRIDGMAN. 



as to its behavior can be found in terms of the density, the compressi- 

 bility, and the change of compressibility with pressure. Let us put 

 in general: 



As before, the general condition of equilibrium is $ + p 8 3 is to be a 

 minimum with respect to changes of 8. This condition gives: 



= - — - L 

 P ' 35 4 35 2 ' 



If do is the value of 8 when p = 0, 



a = -8o 2 f(8o), 



and if we furthermore write (5/5o) 3 = V/Vo, we have the equation 



/ , (5)=/ / (5o)(yV-3^5o 2 (^. 



Here V and p are measured quantities, so that if /'(5 ) can be found, 

 we have here the means of getting/' (5) at any volume (or 5), and hence 

 f(8) itself, except for the constant of integration. The most informa- 

 tion would be given by the most compressible metals. It is unfortu- 

 nate that sodium and potassium, the most compressible of the metals 

 above, do not crystallize face centered cubic, so that it is not easy to 

 guess what the complete crystal structure of ions and electrons is, and 

 hence not possible to compute the "a" or the/'(5o). 



For less compressible metals, another way of treating the above 

 general equation gives more information. For these metals, the 

 compressibility is given with the accuracy of the experiment by a 

 linear function of the pressure, 



X = Xo(l + ap) 



where a is an experimental constant, and is negative for all the metals 

 studied above. Now the above equation for 4> can be treated in the 

 general case exactly as we did in the special cases above. Writing again 



X ~ V dp ' 



we may get x by differentiating the equation of equilibrium, and 

 keeping only small quantities of the first order, we may express x as a 



