COMPRESSIBILITY OF METALS. 



235 



AV . , „ 

 We may write the factor of ~rr in the form 



a(n - 1) (n - 2) 



8 + 2,i + -> ^ L x 



ado* 



Now apply this again to calcium. We have the two equations: 



95o 4 



(n - 1) a - 



/3 



5.7 X 10 



-12 



(), 



n_2 



a(n - 1) (n - 2) 



8 + 2n+ ^ L x 



ado 4 



2 9 



with the numerical values of a, 5o, and x already used. We notice 

 that /3 does not enter the second of the two equations above, which is a 

 quadratic in n. Solving this for n, we find 



n = 7.34. 



Now for /3 we have the equation 



j8 - 5 n " 2 a + 



95o 4 



X (n - 1). 



Substituting numerical values, we find 



(3 = 2.03 X 10- 56 . 



The result found for n does not appear unreasonable, but the value 

 for |3 appears to be of the wrong order of magnitude. It would seem, 

 therefore, that the assumption of an inverse ninth power is so poor 

 an approximation when computation involving two differentiations 

 is involved that the inclusion of the Schottky term (which there is 

 every reason to believe actually exists) cannot help matters. 



It is to be noticed that if conversely we regard as sufficiently ap- 

 proximate the formula above for the initial compressibility with the 

 Schottky term included, the value of n is very closely determined, if 

 we know merely the order of magnitude of (3, by the requirement that 

 /8/5o n_2 be of the same order as " a." 



If instead now of assuming a specific form for the repulsive potential, 

 we substitute an arbitrary function, a certain amount of information 



