158 Proceedings of the Royal Society of Edinburgh. [Sess. 
forces under which the atoms of a body oscillate are merely the ordinary 
elastic forces of the body, and hence calculated the free periods of the atoms 
from the compressibility of the body. The wave-lengths obtained varied 
from 45 /x to 168 ja. He found that these oscillations were very rapidly 
damped.* Also, from his theory of the variation of atomic heat with 
temperature and Nernst’s observations on the latter for silver, he was able 
to calculate the wave-length of the radiation emitted by silver in the infra- 
red, and found it to be 90 ju, while the value given by elastic considerations 
was 73 /ul. He was not able to make the test for other substances owing 
to the want of the necessary data. 
A class of electrons executing harmonic vibrations causes an absorption 
band, and influences the index of refraction in the neighbourhood of the 
absorption band. Drude’s results were all derived from this influence on 
the refractive index. It occurred to me that the results would be more 
certain if derived from the variation of the coefficient of absorption 
throughout the band itself, and in 1909 f I derived the following formula 
for this purpose : 
— — l*300 v — ~ ^o) . 
m c A 0 3 
This formula applies to any well - defined absorption band. k is the 
maximum value of the coefficient of absorption in the band, k being 
defined by 
47 TKd 
I=V~ 
where d is the thickness of a layer and I 0 , I the intensities of the wave 
before and after traversing the layer. A 0 is the wave-length of the 
maximum ; J \ the wave-length for which k has half its maximum value ; 
c the concentration of the colouring matter in gm.-mols. per litre ; v the 
refractive index of the substance ; e the unit charge of electricity ; m the 
mass of its carrier ; and p the number of such vibrators per molecule of 
colouring matter. The formula is applicable only if the class of electrons or 
ions concerned is uninfluenced by any others in the field. I nevertheless 
* A. Einstein, “ Elementare Betrachtungen liber die thermische Molekularbewegung 
in festen Korpern,” Ann. d. Phys. (4), 35, p. 679, 1911. 
+ “ On the Mechanism of the Absorption Spectra of Solutions,” Proc. Pay. Soc ., A, 82, 
p. 607, 1909. 
| I think that, in view of the difficulties connected with the friction term and the 
irregularities in the shape of the bands, it is an over-refinement to distinguish between the 
maximum of absorption and the natural free period of the electrons. Gf. Havelock, 
“ Optical Dispersion : a Comparison of the Maxima of Absorption and Selective Reflection 
for Certain Substances,” Proc. Roy. Soc., A, 86, p. 1, 1911. 
