744 Sir J. J. Thomson on the Application of the 



Hence the potential energy per unit volume dne to the 

 forces varying inversely as the square of the distance is 



so that (see p. 735) the bulk modulus will be 



28-8 e 2 (AY? 3 

 9 ^HM/ ' . 



Aluminium is a trivalenfc element, which crystallizes 

 in the regular system ; for this metal, A/M is equal to 

 2*65/27 x 6'4 xlO" 24 . Substituting this value in the pre- 

 ceding expression, we find that the value of the bulk modulus 

 is -98 X 10 12 ; the value found by experiment is '78 x 10 12 . 



The limiting frequency of the vibrations of the electrons. 



Following the method used for the monovalent elements, 

 I find that the limiting period for the vibrations of the octa- 

 hedral electrons is given by the equation 



,np* = 32-88^, 

 and that of the cubical electrons by 



where 



^ ; = 36-9^'|, 



1 _ A 

 d z " 4M* 



The stability of the system requires that c/d should be 

 greater than *3. If we compare these expressions with that 

 for sodium, and remember that A/M for aluminium is 

 2'4 times that for sodium, we see that the wave-length 

 of the critical frequency for aluminium will be less than 

 1700 A.U., i. e. far up in the ultra-violet. Thus it is only 

 in this region that we should expect to rind evidence of the 

 selective photo-electric effect with aluminium. 



Electrons arranged in face-centred cubes. 



With this arrangement the number of electrons is four 

 times the number of atoms. As this is the proportion 

 between the atoms and electrons in all binary compounds 



