Electron Theory of Chemistry to Solids. 749 



Value of the bulk modulus. 



This can be calculated if we know the value of 2 e r e s jr 

 for the system. To make the calculation, consider first 

 the value of the contribution made by one of the' electrons 

 at the corners of the cube to this sum. Let A be 

 such a corner. We suppose the medium built up of face- 

 centred cubes : remove the eight that meet at A, and 

 calculate separately the contributions the charges so re- 

 moved would have made to the sum ; then treat each of 

 the remaining cells as a unit, and calculate the contribution 

 of each of these. This contribution diminishes very rapidly 

 as the distance from the electron increases. In this way 

 we find that the value of the sum of the terms %e r e s jr 

 which contain this corner electron is — 4*5£ 2 /D, where 

 D is a side of the cube. Now consider the contribution 

 to the sum of one of the electrons at the centre of a face. 

 Proceeding by a similar method, I find this equal to 

 — 3*2e 2 /D; while the contribution of a positively-charged 

 atom is -52'6^/D. 



As the charges carried by the electrons at the centre 

 of the faces is three times that carried by the electrons,. 

 the value of 2 e r e s /r for N cells is equal to 



~J(4'5 + 3x 3-2 + 52-6) <? 2 /D, 



i. e. to -33-35 e 2 /B. 



From p. 735 we see that this will correspond to a bulk 

 modulus k given by the equation 



7 33-35 /A\ 4/3 



So that for similar values of A/M the bulk modulus with^this 

 arrangement of electrons is about nine times that for the 

 alkali metals. 



For the diamond for which A = 3*52 the value of the bulk 

 modulus deduced from this formula is 8*1 x 10 12 . This is 

 much higher than the value 2 x 10 12 obtained by Richards 

 for carbon in the form of diamond. Richards puts a question 

 mark after this value, so that it may be inferred that there 

 is more uncertainty about this value than about those of the 

 other elements. The very high value for the diamond given 

 by the formula is due not merely to the value of the coefficient 

 but to the abnormally high value of A/M for the diamond — 

 a value far in excess of that for any other element. 



In this investigation we have supposed that each carbon 



