rotation, if the molecule
were regarded as a rigid body incapable of vibration-energy. In this
case we should have s = 3R, S = 4R, S/s = 4/3 = 1.333. In 1879 Maxwell
considered it one of the greatest difficulties which the kinetic
theory had yet encountered, that in spite of the many other degrees of
freedom of vibration revealed by the spectroscope, the experimental
value of the ratio S/s was 1.40 for so many gases, instead of being
less than 4/3. Somewhat later L. Boltzmann suggested that a diatomic
molecule regarded as a rigid dumb-bell or figure of rotation, might
have only five effective degrees of freedom, since the energy of
rotation about the axis of symmetry could not be altered by collisions
between the molecules. The theoretical value of the ratio S/s in this
case would be the required 7/5. For a rigid molecule on this theory
the smallest value possible would be 4/3. Since much smaller values
are found for more complex molecules, we may suppose that, in these
cases, the energy of rotation of a polyatomic molecule may be greater
than its energy of translation, or else that heat is expended in
splitting up molecular aggregates, and increasing energy of vibration.
A hypothesis doubtfully attributed to Maxwell is that each additional
atom in the molecule is equivalent to two extra degrees of freedom.
From an m-atomic molecule we should then have S/s = 1 + 2/(2m + 1).
This gives a series of ratios 5/3, 7/5, 9/7, 11/9, &c., for 1, 2, 3,
4, &c., atoms in the molecule, values which fall within the limits of
experimental error in many cases. It is not at all clear, however,
that energy of vibration should bear a constant ratio to that of
translation, although this would probably be the case for rotation.
For the simpler gases, which are highly diathermanous and radiate
badly even at high temperature, the energy of vibration is probably
very small, except under the special conditions which produce
luminosity in flames and electric discharges. For such gases, assuming
a constant ratio of rotation to translation, the specific heat at low
pressures would be very nearly constant. For more complex molecules
the radiative and absorptive powers are known to be much greater. The
energy of vibration may be appreciable at ordinary temperatures, and
would probably increase more rapidly than that of translation with
rise of temperature, especially near a point of