354 
DR. E. H. GRIFFITHS AND MR. EZER GRIFFITHS ON THE 
The atomic heat, as measured experimentally for a solid or liquid in equilibrium 
with full radiation at a negligible external pressure, is of the form (Curve I., dotted) 
d(E + PV)/7T = 3R(l +z+z 2 )e~\ 
which gives good agreement in the case of rock salt and sylvin, when the reststrahlen 
frequencies are inserted, in the neighbourhood of the temperature given by z — 2732, 
which corresponds to the maximum of the radiation curve plotted on a frequency base. 
In the case of an actual solid, it is impossible that all the molecules should 
simultaneously have the same frequency. Observation shows that the absorption and 
emission bands widen considerably with increase of density, so that rock salt, for 
instance, is opaque over a region extending approximately from 20 to 130 microns, 
the mean wave-length of the reststrahlen , according to Rubens, being 51‘2 microns. 
Below a certain limit of frequency the substance again becomes transparent. It 
would appear that resonance generally extends with diminishing amplitude for an 
equal interval of frequency on either side of the mean, and may be represented by 
supposing that the number of molecules having frequencies included in a given 
interval is the same for equal intervals on either side of the natural frequency. 
In the case of rock salt the probable distribution of frequencies can be approximately 
inferred from the absorption band and the dispersion formula, and is equivalent to a 
uniform distribution through a range of a little more than an octave on either side of 
the mean. The effect of this distribution on the specific heat is shown by the full 
Curve II., which represents the actual variation of the specific heat of rock salt as 
closely as can be expected from liquid hydrogen to the ordinary temperature. It will 
be seen that the agreement would be improved by adopting a slightly lower value for 
the mean frequency, and a smaller range of resonance. It is evident that the method 
employed by Rubens must give too small a value for the wave-length if the resonance 
is not perfectly sharp, and it is possible that the value 55 microns deduced from the 
specific heat at 0 = 2732 may be more accurate for the mean wave-length. 
The simple theory above sketched could not be expected to apply except in the case 
of an isotropic substance possessing a single absorption band. The specific heats of 
quartz, ice, and benzol show a different type of curve, No. III., as shown for quartz, 
on a reduced scale of temperature (l/6). Such a curve can be fairly represented by 
assuming two absorption bands, one agreeing with the position indicated by the 
reststrahlen , wave-length 8‘85 microns for quartz, and the other about two octaves 
lower. From our knowledge of absorption spectra it is extremely likely that most 
substances possess two or more bands of different intensities, and it is possible that 
the variation of specific heat could be consistently represented if we had all the 
required data. But a hypothetical selection of frequencies and intensities, though 
illustrating the possibility of the theory, would not serve as an experimental 
verification. 
It seems fairly certain that the curves often differ in type, and cannot possibly be 
