486 Dr. H. S. Allen on Atomic 



§ 5. The Formula of Altertliun. 

 A formula for the atomic frequency involving the 

 coefficient of linear expansion, a, has been proposed by 

 Alterthun*. For a number of elements the product aT, is 

 found to be approximately constant. If, then, for T g in 

 Lindemann's formula we substitute the reciprocal of the 

 coefficient of expansion, we find 



v=£ v /( 1 /A«V f ). 



The constant is taken as 4*2 x 10 11 . 



The frequencies calculated by Blom by means of this 

 formula have been used in the preparation of the corre- 

 sponding column in Table IV. As might have been antici- 

 pated from the fact that the coefficient of expansion at 

 ordinary temperatures has been employed in the calculation, 

 the agreement here is only moderately good. 



§ 6. The Formula of Gruneisen. 

 On the basis of his theory of the solid state Gruneisen f 

 has obtained a relation between the coefficient of expansion, 

 the compressibility, and the specific heat of a substance. 

 The relation, however, involves a coefficient which, according 

 to Gruneisen, is approximately but not strictly constant for 

 different elements. By using this relation in connexion 

 with Einstein's formula an equation for the atomic frequency 

 is found, which may be written 



v = 2-9 2 xlOV(^/3«V f ), 



where C v is the specific heat expressed in gram calories per 

 degree. Taking the values of the frequency given in 

 Table V. of Griineisen's paper, the values of NvxlO -12 

 have been calculated and are recorded in Table IV. It 

 should be mentioned that the value given for the frequency 

 of silicon is regarded as open to question. The majority of 

 these results show good agreement with the proposed relation. 

 For the sake of completeness the results obtained from the 

 specific heat and by the formula of Debye have been included 

 in the Table. It must be remembered that the fractional 

 values in the Table are in all cases provisional. 



§ 7. Comparison of Frequency Formula?. 



A comparison of the frequency numbers given in Table IV. 

 for a specified element shows that in many cases the numbers 

 differ according to the formula employed. When allowance 



* Altertliun, Deutsch. Phys. GeselL Ver/i. vol. xv. pp. 25, 65 (1913). 

 t Griineisen, Ann. d. Physik, vol. xxxix. p. 257 (1912). 



