344 
DR. E. H. GRIFFITHS AND MR. EZER GRIFFITHS ON THE 
Magnus found that while formula (7) accounted qualitatively for the decrease in 
atomic heat with temperature, it gave a too rapid decrease with temperature to 
represent accurately the form of the experimental line. 
( b ) Nernst and Lindemann.*—NernstI at first endeavoured to effect a better 
agreement between the formula and his experimental results by the addition of an 
empirical ten iff of the form //H 2 to equation (7). 
In a later memoir NERNST and Lindemann showed that the expression 
3R 
e T 
2 
(e T — l) 2 
+ 
\2T, 
2 j3y 
I e 2T 
Pv ’ 
(e 2T — l ) 2 
(9) 
where h/k — /3, more nearly expressed the experimental results than (7). 
Here again v, in the case of salts, is the frequency found by means of the 
reststrahlen, but in no case has an infra red hand been observed whose frequency 
is \v. 
Lindemann suggested another method for the indirect determination of v. 
He assumed that fusion was produced when the amplitude of the atomic vibrations 
became of the same order of magnitude as the distance between adjacent atoms, and 
thus obtained the expression 
, = 2-12x10 “VjN.(1®) 
where T s is the absolute temperature of the melting-point, 
Y, the atomic volume, 
m, the atomic weight. 
Expression (9) is empirical, but appears to have been a step in the right direction, 
as it takes into account more than one frequency, although Nernst was of opinion 
that the second term represented potential energy. 
It is difficult to conceive the atoms in solids, such as metals, as executing 
monochromatic vibrations; the wide range over which absorption takes place 
indicates that the vibrations are more complex and, were it possible to apply Fourier’s 
theorem, we should expect frequencies distributed over a continuous spectrum. 
( c) Debye’s Theory §— Debye has attempted the solution of the problem when 
the atomic vibrations are not regarded as monochromatic. He considers the possible 
vibrations of the substance as a whole, and proceeds on the supposition that the heat 
vibrations depend on the elastic forces in such a way that the longest heat waves are 
* Berlin, ‘ Sitz. Ber.,’ p. 494, 1911. 
t ‘Journal de Physique,’ vol. 9, p. 721, 1910. 
| Einstein had indicated that such a term was necessary to complete the expression on account of the 
difference between C p and C„. 
§ ‘ Annalen d. Physik,’ vol. 39, p. 789, 1912. 
