Frequency and Atomic Number, 



Table III. 

 Elements with Fractional Values for n. 



483 



Element. 



N. 



vXlO" 12 . 



Ni^xlO- 12 . 



Li 



3 



4 



11 



12 



15 



16 



i*9 



33 



37 

 49 

 53 



10-65 

 23-63 

 4-31 

 7-88 

 672 

 3-83 

 4-30 

 4-24 

 2-53 

 4-20 

 1-54 

 2-37 

 1-82 



HX21-3 

 4x21-0 

 2} X 21-0 

 4|x21-0 

 5 X20-2 

 2|x20-9 

 3^x21-1 

 3^x20-9 

 2±X21'4 

 6^x21-3 

 2|x20-7 

 5^x211 

 4|x21-5 

 5jx21-0 



Be 



Na 



Mg 



P (red) 



(yellow) 



S (rhombic) 



(monoclinic) 



K 



As 



Eb 



In 



I 



B> 



80 1 -38 









It should be noted that the product Ny is the same for 

 beryllium as it is for magnesium, and practically the same 

 for sodium as it is for potassium. 



The data for hydrogen and nitrogen are not known very 

 accurately, but it may be mentioned that v for hydrogen 

 (4*88 x 10 12 ) is approximately 5^ A , whilst for nitrogen (N = 7, 

 v=2f> x 10 12 ) the product Nv is approximately |^ A . 



§ 4. The Formula of Einstein. 



Einstein* has put forward an equation for the atomic 

 frequency depending upon the elastic properties of the solid. 

 He takes the restoring force proportional to the distance 

 between two molecules and to the bulk modulus of elasticity. 



Thus D = const.Y3K~ 1 , where K is the compressibility, 

 and therefore 



-V(fi) 



The constant k was evaluated by Einstein on certain 

 assumptions as to the arrangement and interaction of the 

 molecules, and found to be 2*8 X 10 7 , but the empirical value 

 3*3 x 10 7 is found to give more satisfactory agreement with 

 the frequency determined from the specific heat. The values 

 of the frequency calculated by Blom with the use of the 

 latter constant have been employed for the determination of 

 NvxlO -12 . The results are given in Table IV., and an 

 inspection of the column headed " Einstein" shows that the 

 product can be expressed in the form nv A , where n is an 

 integer in 23 cases, and differs from an integer by ^ in 4 

 cases. 



* Einstein, Ann. d. Physik, vol. xxxiv. p. 170 (1911). 



