COMPRESSIBILITY OF METALS. 



237 



function of p. It is not worth while reproducing here the algebraic 

 details, but it will be readily found that 



X = 



95n 



10a 



3V 



- /"(*>) 



( 14 / 10a 



1+ 7fXo+ Xo 2 I — + 



f"(t n y 



275 ; 



V 



This formula may be checked in special cases by substituting the 

 particular values of / used above. 



In this expression for x> the term outside the square bracket 

 is xo- The factor of p inside the bracket is the empirical constant 

 a. A third relation is given by the stability relations under zero pres- 

 sure. These three relations may be solved for the three derivatives 

 of giving 



r <*) - - * + 



Xo 



10a 



35n 3 



/"'(*>) = 



10a 



So 3 



5o ado 



-42 — 4-27-1 

 Xo Xo" 



I am much indebted to Mr. J. C. Slater for pointing out to me an 

 error in the original form of my formula for the third derivative. 



These formulas may now be applied to numerical computation for 

 those metals above which crystallize face-centered cubic, for in these 

 cases we know the probable complete crystal structure, and can com- 

 pute the "a." Given the structure, the only additional information 

 needed to compute "a" is the magnitude of the charge on the ion. I 

 have assumed that this charge is three electrons for Al, two for Ca, 

 Fe, Co, Ni, Pd, and Pt, and one for Cu, Ag, Au, Ce, and Pb. With 

 these assumptions the results tabulated in Table VI may be found. 



In the first place we notice that the sign of any given derivative is 

 the same for all metals, and that the signs are alternately negative 

 and positive for the first, second, and third derivatives. This is the 

 general character to be expected for a force increasing more and more 

 rapidly as we approach the center of the atom (in particular, a po- 

 tential as 1/5" gives this relative arrangement of the derivatives). 



In general the derivatives are numerically larger for the more in- 



