﻿ike Electron Theory of Solids. 659 



If A is the density of calcium, M the mass of an atom, 

 since our unit cube with side 2d contains 4 atoms, 



4M A 



Ay/ 3 



i -2 i3 r A v 



Hence the electrostatic potential energy per normal 

 atom is 



—-dr. 



and the electrostatic potential energy per unit volume is 

 <? 2 .6'15 2WA\ 4/3 



w 



_„2 



e 2 .7-75x 



A\ 4 / 3 



© 



Hence, by page 736 of the former paper, k the bulk 

 modulus for calcium will be given by 



. , 7-75 /A y/ 3 



For calcium A = 1*85, 



M = 40xl-64xKr 24 . 



This makes ljk the compressibility equal to 



5'9 xlO- 12 ; 



the value found by Richards is 5*5 x 10" 12 , so that the 

 agreement between the calculated and observed values is 

 again quite close. The other divalent metals Mg, Zn, Cd 

 crystallize in the hexagonal system ; in this system the elastic 

 properties vary in different directions, and a uniform pressure 

 would produce a change in shape as well as in volume. 

 The arrangement of electrons and atoms appropriate to this 

 case is when the electrons are at the corners of a hexagonal 

 prism and the atom at the centre. To fix the shape and 

 size of the prism we require two lengths, the radius of the 

 base and the height of the prism instead of the one which 

 sufficed for crystals in the regular system. The necessity 

 for taking two variables instead of one makes the calculations 

 more lengthy than those for the regular system, and 1 shall 

 defer their consideration for the present. 



2U2 



