242 THE QUANTUM [xvii. 5 
linear vibrations, similar to those in a solid body, or in an enclosure 
containing radiation. 
The quantization of the monatomic perfect gas has been dis 
cussed by Fermi.* If the heat theorem of Nernst is to hold good 
for the ideal gas it is necessary to assume that at low tempera 
tures the laws for an ideal gas deviate from the classical laws. 
This deviation is attributed to the “ degeneration ” of the gas, 
and according to Fermi its cause is to be sought in the quantization 
of the molecular motions. It is necessary to distinguish between 
this type of deviation and the deviation due to the fact that the 
gas is real and not perfect, the former having hitherto been 
masked by the latter under experimental conditions. The 
equation of state and the internal energy of the ideal gas are 
deduced by employing the hypothesis of Pauli, which for the 
purpose in hand may be stated in the form that one system can 
never contain two elements of equal value having their quantum 
numbers in absolute agreement. 
Results of a similar character have been obtained 
independently by Dirac, f whose work is based on the new 
quantum mechanics. It has been shown both by Dirac and by 
Heisenberg J that Pauli’s principle and its extension are satisfied 
in the new mechanics by a complete self-consistent solution of 
the equations of motion. Fowler § has employed the method 
of complex integration in an examination of a quite general form 
of statistical mechanics of which the classical form and Einstein’s 
and Fermi-Dirac’s are special cases. 
In a later paper Dirac || has treated the problem of an assembly 
of similar systems satisfying the Einstein-Bose statistical 
mechanics, which interact with another different system, a 
Hamiltonian function being obtained to describe the motion. 
The theory is applied to the interaction of an assembly of light- 
quanta with an ordinary atom, and it is shown that it gives 
Einstein’s laws for the emission and absorption of radiation. 
The interaction of an atom with radiation is also considered, 
assuming the radiation composed of electromagnetic waves. It is 
shown that a Hamiltonian function can be obtained of the same 
form as in the light-quantum treatment. The wave point of 
view is thus consistent with the light-quantum point of view. 
The theory leads to the correct expressions for the probability 
coefficients both for the absorption process and for the emission 
process (Einstein’s A’s and B’s). 
* Fermi, Rend. Acc. Lincei, ser. 6, vol. 3, p. 145, 1926 ; Zeits.f. Physik, 
vol. 36, p. 902, 1926. 
f Dirac, Proc. Roy. Soc., vol. 112, p. 661, 1926. 
t Heisenberg, Zeits. f. Physik, vol. 38, p. 411, 1926. 
§ Fowler, Proc. Roy. Soc., vol. 113, p. 432, 1926. 
|| Dirac, Proc. Roy. Soc., vol. 114, p. 243, 1927.