COMPRESSIBILITY OF METALS. 233 



The term r I — ) is small compared with 3v, and since it becomes in- 

 \or/p 



creasingly smaller at higher pressures, we will neglect it. We have 



seen that at low pressures ( — ) is positive. But the term p ( — j is 



negative, so that there is here the possibility of a reversal of sign of 



— ) at sufficiently high pressures. Now this is an exceedingly un- 

 dp/T 



likely state of affairs, because it would mean that at low pressures 



the atoms shrink with increasing pressure, but that at sufficiently 



high pressures they begin to expand again. Hence if we assume that 



at the utmost ( — ) can only become zero, we find that the upper 



\dp/T 



limit of p - ( — ) is 3/4 (numerically). If this constitutes any real 



V \Op/T 



restriction, the place to look for it is in the compressible substances. 



Of the metals above, potassium is the most compressible. At 12000 



1 /dv\ 

 kg., the maximum pressure of these experiments,^-!— 1 has the 



value 0.19, and thus is still safely below the upper limit. However, 



1 /dv\ . , . . 



if we plot p - I — ) against p, we obtain approximately a straight line, 



V \up/T 



so that at some pressure below 50,000 kg. there must be an essential 

 change in the character of the relation between pressure and volume. 

 In this connection the possibility of a new polymorphic modification 

 of potassium at high pressures must be kept in mind ; it is natural to 

 expect one in analogy with the new form of caesium which I have re- 

 cently found. A new polymorphic form of potassium at very high 

 pressures also seemed indicated to me a number of years ago 23 by the 

 character of the curve giving change of volume on melting against 

 pressure. 



1 /dv\ 

 The extreme value of p - I t" ) for potassium is somewhat higher 



than the value for the most compressible of the organic liquids in- 

 vestigated at high pressures, ether, which has the value 0.17 at 12000 

 kg. 



Change oj Compressibility with Pressure. The theory of Born as 

 extended above gives the compressibility as a function of pressure (or 



