234 BRIDGMAN. 



change of volume). Neglecting at first the Schottky effect, or putting 

 /3 = 0, we have 



95o 4 



x = - 



a(n— 1) 



10 + n AV 



1 + ^t; 



It is most interesting to notice that the lattice constants are not con- 

 tained explicitly in the term giving the variation of compressibility 

 with change of volume, but only the exponent n. 



1 d5 3 . 

 If we had defined the compressibility as — — instead of as we 



AV 7 + ?i _,. 



did above, then the factor of -==- would have become — - — . This 



V o o 



agrees with a formula which" Born has been so kind as to communicate 

 to me in a personal letter. 



AV 



At high pressures -zzr is negative, so that the formula predicts a 



numerical decrease of compressibility at high pressures, as is most 

 natural. Furthermore, the compressibility decreases more rapidly 

 than the volume itself, and by a factor of the order of a small integer. 

 Now this factor has already been tabulated in Table IV in the column 

 under 2b/ a 2 . We see that this quantity is indeed of the predicted 

 order of magnitude, so that Born's theory is suggestive also with 

 regard to the pressure change of compressibility, as well as its absolute 

 magnitude. But the exact value cannot be given by his expression, 

 which demands values of n ranging from negative numbers for Ca and 

 Sr to positive values as high as 95 for W. It is not surprising that the 

 theory does not give precise results here. If we had to object to the 

 single differentiation of the first term of a power series involved in 

 computing the compressibility, still more must we object to the 

 double differentiation involved in the computation of the change of 

 compressibility with pressure. 



It is difficult to know exactly how much significance should be 

 attached to the prediction of a correct order of magnitude for the 

 change of compressibility with pressure. Griineisen's theory of the 

 solid -state, which rested on a physically very different picture from 

 Born's, also gave the right order of magnitude. 



It is perhaps interesting to consider whether the Schottky term 

 gives plausible results here. If we assume as given by experiment 

 both the compressibility and its variation with pressure, then we have 

 two equations from which we may find both n and /3. 



