480 



Dr. H. S. Allen on Atomic 



This is exactly the relation obtained later by Lindemann * 

 for the atomic frequency at the melting-point. For an 

 element of atomic weight A the relation may be written 



The value of the multiplying constant k, which is found 

 empirically, was given by Lindemann as 2\06 x 10 12 . 



The same formula was afterwards employed by Nernst 

 for the calculation of the characteristic frequency, using 

 for k the value 3' 08 X 10 12 , which is almost exactly half as 

 large again as the factor employed by Lindemann for the 

 frequency at the melting-point. 



§ 3. Results obtained by using Lindemann 3 s Formula. 



With Nernst's value for the constant and with experimental 

 data from the Smithsonian Physical Tables (1914), the 

 atomic frequency, v, and the product, Nv, have been calcu- 

 lated for a large number of elements. For our present 

 purpose Lindemann's formula has an important advantage 

 in the fact that the melting-point in many cases is known 

 accurately, whilst the value of V*, the only quantity in the 

 formula varying with temperature, does not differ greatly 

 for most of the elements. 



For a test of the formula we select seven of the metals 

 for which results derived from the specific heats have been 

 given in the former paper. For these metals the data 

 required in Lindemann's formula are known with consider- 

 able accuracy. The results- are collected for comparison in 

 the following Table. 







Tabls I. 





Element. 



N. 



NvXlO- 1 *. 



Specific Heat, 



Lindemann. 



Al 



13 

 26 

 29 

 30 



47 

 48 



82 



i 



107-5= 5x21-5 

 209-0=10x20-9 

 191-7= 9x21-3 

 144-2= 7x20-6 

 211-0=10x211 

 168-8= 8x21-1 

 1540= 7x220 



108-2= 5x21-6 

 236-8=11x21-5 

 214-5=10x21-4 

 143-6= 7x20-5 

 225-2=11x20-5 

 1445= 7x20-6 

 163-2= 8x20-4 



Fe 



Cu 



Zn 



As 



Od 



Pb 





Mean value of v A from Lindemann's formula =20'9Xl0 12 sec. K 

 * Lindemann, Phys. Zehschr. vol. xi. p. 609 (1910). 



