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XVII. 5] THE NEW QUANTUM MECHANICS 
the atoms of which could assume a number of stationary states, 
and investigated the equilibrium subsisting between the atoms 
and the surrounding radiation. In thermodynamic equilibrium 
between the atoms and the radiation, the number of elementary 
processes in one direction ought to balance the number occurring 
in the opposite direction. This condition gives a formula express 
ing the energy density of the radiation in terms of the probability 
coefficients introduced by Einstein. The truth of Boltzmann’s 
formula for the relative number of systems in different states of 
energy in an assemblage at given temperature is assumed, and 
use is made also of Wien’s displacement-law. It is to be observed 
that although Einstein endeavoured to give a derivation which 
should be independent of classical theory, he had to employ 
certain classical results. Eddington * has shown that it is 
unnecessary to assume Boltzmann’s formula ; this, as well as 
Planck’s law, can be deduced directly from Einstein’s equation. 
Einstein’s method has been applied by Milne f to the photo 
electric effect, and the formulae obtained for the photo-electric 
activity of radiation agree with those developed by Kramers J 
and have a very close connection with formulae deduced by 
Richardson § prior to the publication of Bohr’s theory. 
Bose || has given a method of deriving Planck’s law which 
is independent of the classical theory. He employs the light 
quantum hypothesis and concludes that the phase-space of a 
light quantum is divided into “ cells ” of size h z . Considering 
a particular type of radiation, the number of possible arrange 
ments of the light quanta into these “ cells ” represents a certain 
“ probability.” The thermodynamic probability of a macro 
scopic state is calculated, and therefrom the entropy. Thus 
the thermodynamic characteristics of the radiation are deter 
mined, and a formula is obtained which is the equivalent of 
Planck’s law. Einstein emphasized the importance of the 
method and showed that it might be applied to the quantum 
theory of an ideal gas containing structureless mass-points. 
According to his views a light quantum (apart from its polarization 
property) differs from a monatomic molecule only in the fact 
that the static mass of the quantum is vanishingly small. This 
new form of statistical mechanics has been further analysed by 
Schrodinger,** who states that the precise meaning of the Einstein 
gas theory is that a gas may be considered as a system of separate 
* Eddington, Phil. Mag., vol. 50, p. 803, 1925. 
f Milne, Phil. Mag., vol. 47, p. 209, 1924. 
i Kramers, ibid., vol. 46, p. 836, 1923. 
§ Richardson, ibid., vol. 47, p. 975, 1924. 
|| Bose, Zeits. f. Physik, vol. 26, p. 178, 1924. 
Einstein, Preuss.Akad. Wiss. Berlin, 22, p. 261, 1924 ; 1, PP- 3> *8» 
1925. ** Schrodinger, Phys. Zeits., vol. 27, p. 95, 1926.