46 
QUANTUM THEORY 
The first is distributed in a way which depends only on the temperature. 
The second is partitioned in a way depending only on the temperature, 
though the amount depends on the matter present. The third is distributed 
in a way peculiar to the chemical elements present. The uniform laws of 
distribution of the first two kinds and the arbitrary variability of the 
third makes it almost impossible to devise complex cycles for maintaining 
a balance*. The simple means of balancing proposed in Law I has at least 
great plausibility. 
Many fa mili ar experiments are performed in conditions far removed 
from thermodynamical equilibrium—in particular experiments on X rays 
and cathode rays. Unbalanced cycles are then prominent. 
35 . A second general principle is given by the quantum theory— 
Law II. (Quantum Law .) Whenever radiant energy is transformed into 
other forms of energy or vice versa the transformation occurs in finite 
amounts called quanta; the amount of energy constituting a quantum is 
hv, where v is the frequency of the radiation and h is a universal 
constant. 
It is not necessary to regard the emission of a quantum as instantaneous 
or unanalysable. The essential point of Law II is that the absorption or 
emission of a quantum marks one “process of transformation” in the 
sense of Law I. If two quanta are emitted at the same time this is merely 
a chance coincidence, whereas the emission of the second half of a quantum 
is the inevitable sequel to the emission of the first half. 
Einstein's Equation. 
36 . Consider two states of an atom with internal energy y x , y 2 re 
spectively (y 2 > Xi)- The atom can pass from state 2 to state 1 by emitting 
radiation of energy y 2 — , and the reverse process is a passage from state 1 
to state 2 with absorption of a like amount of radiation. By Law II the 
frequency v 12 of the radiation emitted or absorbed is given by 
X 2 Xi = hv u (36-1), 
and by Law I the number of passages in the two directions in matter in 
thermodynamical equilibrium will balance independently of any other 
processes of transition involving the two states. 
According to Bohr’s theory of the atom, the possible values of xi and 
y 2 form a discontinuous series; but we make no use of this in our argument 
except to afford a verbal simplification, viz. that we may speak of the 
* The argument apparently does not exclude a cycle involving only (1) and (2); 
but we believe we have sufficient knowledge of the law governing transformation 
of radiant into kinetic energy and vice versa (Compton Effect, § 52) to show that no 
such cycle occurs.