30 
THERMODYNAMICS OF RADIATION 
Entropy. 
24 . Quantitatively energy is conserved; qualitatively there is a con 
tinuous unidirectional change in the character of the energy of the 
universe. 
In the ultimate analysis this change appears to be in all cases a change 
from a more organised to a more chaotic condition. For example, a train 
of plane waves may by irregular reflection or scattering be converted into 
radiation moving in all directions at random. We cannot invert this 
process or discover an appliance which will automatically convert dis 
organised radiation into plane waves. Spherical waves can be converted 
into plane waves by a parabolic mirror and back again to spherical waves 
by another mirror. But spherical waves are in their way as highly or 
ganised as plane waves ; no chance disturbances of regularity have befallen 
them. When once the random element has been introduced it cannot be 
eliminated by any natural process. If we construct a machine which 
receives chaotic radiation and sends it out again as trains of plane waves 
we must infer that the organisation has been given to the waves at the 
expense of other energy put through the machine; and this energy is 
drained of organisation and ejected from the machine in a more chaotic 
state than it was originally. Such a machine continually requires fresh 
supplies of energy not because it uses up energy but because it uses up 
organisation of energy. 
Thus in the vicissitudes of things energy is liable to take a step down 
in rank which it cannot recover by any natural process. The potentiality 
inherent in organisation—which is of immense importance for the practical 
utilisation of energy—is lost to the universe, irrecoverably so far as we 
can see. 
25 . We introduce a numerical measure of the disorganisation caused 
by these irreversible steps. Such a measure should evidently be propor 
tional to the quantity of energy disorganised ; the other factor measuring 
the degree of disorganisation will consist of the difference of two terms 
dependent respectively on the initial and final states of the energy and 
therefore functions of the physical variables used to specify those states. 
The measure of disorganisation is thus expressed by a quantity S such 
that 
dS = dQ (6 2 — dj) (25-1), 
where dQ is the quantity of energy passing from state 1 to state 2 and 9 
is a function of the physical variables describing the states. 
When several such transfers are contemplated it is convenient to express 
the result in terms of the additions to the energy in the respective states. 
Thus, in the above example, energy in state 1 receives an addition