352 
DE. E. H. GRIFFITHS AND ME. EZER GRIFFITHS ON THE 
Table XVIII. 
(4) Comparison of Frequencies obtained by Calculation from the Physical Constants 
with the Values assumed in the above Tables. 
Frequencies x lO -12 . 
Metal. 
Einstein’s formulae. 
Nernst and Lindemann’s 
formulae. 
Debye’s formulae. 
Specific heat. 
Calculated. 
Specific heat. 
Calculated. 
Specific heat. 
Calculated. 
A1 
6 • 1 
6-7 
8-0 
5-8 
8-0 
8-3 
Cu 
4'6 
5-7 
5-9 
5-1 
5-9 
6-8 
Zn 
3-3 
3-7 
4-4 
3-3 
4.4 
6-5 
Ag 
3-3 
4-1 
4'3 
3-3 
4-3 
4.4 
Cd 
2-3 
2-7 
3-0 
2-1 
3-0 
3-5 
Pb 
1-4 
1-9 
1-9 
1-4 
1-9 
1 ‘5 
The above comparison of the frequencies shows that the values obtained from the 
specific heat equations are in fair agreement with those calculated from the elastic 
constants and that the limit frequency v m of Debye is comparable with the mono¬ 
chromatic frequency of Einstein. 
It was found that no progressive change with temperature in the value of the 
frequency assumed would bring the results into better agreement in all cases.* 
The work of Bosenhain and HuMFREYf and others give considerable support to 
the view that a cast metal consists of an agglomeration of crystals cemented together 
by an amorphous modification and that the elastic constants are intimately connected 
with this intercrystalline film. Now the glassy or amorphous forms of quartz, 
benzophenone, and betol possess higher specific heats than the corresponding 
crystalline forms. 
The presence of an amorphous modification would make the problem a more complex 
one than is taken into consideration in the preceding theories, since a single value of 
the frequency or the limit frequency would not suffice for the representation of the 
thermal agitation of the two different forms. 
It seems probable, however, that the proportion of an amorphous form present 
under ordinary conditions is very small. 
* Eitcken (‘ Verh. d. D. Phy. Ges.,’ 15, p. 571, 1913) has calculated the probable frequency values at low 
temperatures, taking into account the change in the elastic constants with temperature, but the values so 
obtained were not in agreement with the atomic heat curves. 
t ‘ Journ. Inst. Metals,’ p. 653, Part II., 1913. 
