230 



BRIDGMAN. 



- 95o 4 - 



x= 



(n- l)(a- — 



1+1 



7 + 



2w+l 

 a(n + 3) - 2 P 

 oo 



a — 







5 n - 2 



The initial compressibility 



<?.-•)> 



is therefore, 



-9 So 4 



Xo 



/ i8 



(to- 1)1 a- — 



F 



This agrees with Bom's expression on putting j3 = 0. 



Now apply this formula to numerical computation. What we are 

 interested in is the order of magnitude of /3, to see whether it checks 

 with what might be expected by Schottky's theorem. We apply the 

 formula to calcium. For this metal the evidence is particularly strong 

 that we are dealing with a space lattice of doubly charged positive ions 

 and electrons, the ions occupying the position of Ca in CaF 2 , and the 

 electrons the position of F. Born has worked out the analysis for 

 this type of lattice, so that we may apply his results directly. We 

 have numerically 



a 



Xo 



38.7e 2 = 8.78 X 10- 18 , 

 5.56 X 10- 8 , 

 - 5.7 X 10- 12 . 



Let us assume at first that /3 = 0. Then solving for to, we find 



to = 2.72, 



which is much lower than the 5 suggested by Born's analysis for 

 neutral cubes and electrons. 



Let us now assume n = 5, and see what this gives for j8. 



= 8.5 X 10- 40 



Now let us see what Schottky's theorem would lead us to expect 

 for the order of magnitude of /3. We have 



