COMPRESSIBILITY OF METALS. 



207 



pressure. The initial point of the thermal expansion curve was taken 

 from the work of others; these measurements cannot give it. 



To obtain the initial compressibility I have proceeded as in the case 

 of sodium, passing a three constant power series in the pressure 

 through the three lowest points. The formula so found is : 



AV 



=y- = - 3.565 X 10- 5 p + 2.85 X 10- 9 f - 2 X KHV- 

 J o 



The formula is not good outside its range; at 4000 kg. it gives for 

 AV 0.1098 against 0.1091 experimental, and at 10000 kg. 0.27 against 

 0.22 experimental. The formula shows that the initial compressi- 

 bility at 45° is 356.5 X 10 -7 , and the average compressibility over the 

 range of 500 kg. 342.3 X 10 -7 . The above values for the dependence 

 of thermal expansion on pressure show that the temperature correc- 

 tion on this compressibility for reducing from 45° to 20° is 12.5 X 10~ 7 , 

 making the average compressibility over the first 500 kg. at 20° 

 329.8 X 10- 7 . The value given by Richards is 311 X 10- 7 . Perhaps 

 this is as good as could be expected in view of the experimental error 

 and the range of the extrapolation above. 



Especial attention is to be paid to the behavior of the thermal ex- 

 pansion under pressure, which is that anticipated theoretically. 

 There can be no question of the large decrease; at the minimum, 

 which is improbable, it has decreased by a factor of 3, and more 

 probably by a factor of 5. The compressibility in the same range has 

 decreased by a factor of 2. This reverses the initial behavior, for at 

 low pressures the relative decrease of compressibility with pressure is 

 about 50% greater than that of thermal expansion. The difference 

 of behavior of metallic potassium and an ordinary liquid is of interest. 

 Some time ago I measured the compressibility and expansion under 

 pressure of a number of organic liquids. 13 The behavior of all these 

 liquids is on the average roughly the same. The total change of 

 volume under 12000 kg. of these liquids is about the same as for solid 

 potassium, being 0.292 for the liquids against 0.254 for potassium. 

 But the compressibility of the liquids shows a change which is rela- 

 tively high, and is also much higher than the change of expansion. 

 In the range of 12000 kg. the average compressibility of the liquids has 

 changed by a factor of 15.2, whereas the expansion has changed by a 

 factor of 4.66; potassium on the other hand has a considerably larger 

 relative change in the expansion than in the compressibility. The 

 significance of the behavior of potassium I believe to be that the outer 

 shells of the atoms are being pushed tightly into permanent contact, 



