THERMODYNAMICS OF RADIATION 
29 
ire travelling 
direction of 
nentum that 
> momentum 
in conveying 
not be repre- 
b not with a 
pie incidence 
travelling in 
lined so that 
bstructed by 
Id be ES for 
rce is in the 
components 
consists of 
alue of cos 2 9 
3 in this case 
nsity. 
to the radia 
f a fluid. In 
as at rest, in 
rds direction 
ill directions, 
tion or in a 
ar velocities 
tern with six 
on a surface 
the factor 
Tion 6 at the 
pressure. In 
iich is nearly 
this kind of 
/ is likely to 
involve consequentially smaller asymmetrical effects which modify the 
pressure by second order terms. 
The internal pressure, whether of radiation or of a fluid, may be defined 
without reference to the insertion of any extraneous material such as a 
screen. The isotropic pressure \E signifies that across any unit surface, say, 
in the plane yz, momentum is being transferred so that the region on the 
positive side of the surface is gaining \E units of positive ^-momentum 
from the negative side ; equivalently the negative side is gaining \E units 
of negative ^-momentum from the positive side. The internal pressure thus 
defines the boundary flow of momentum which it is necessary to take into 
account in applying the condition of conservation of momentum to any 
region. 
23 . The relations between the energy, momentum and pressure of 
aether waves can be brought into line with those of matter if we regard 
their energy as half kinetic and half potential. The mass E/c 2 , velocity c, 
momentum E/c, and kinetic energy \E are then related in the same way 
as the corresponding quantities 
m, V, mV, \mV 2 
for matter. Also for isotropic radiation the internal pressure is § of the 
kinetic energy-density \E, agreeing with the well-known result that the 
pressure of a gas is § of the density of kinetic (translatory) energy 
of its molecules. 
Accordingly the analogy between radiation and a gas will be 
rendered closer if we choose a gas in which the kinetic energy of the 
molecules is half their whole energy. Such a gas must (according to the 
elementary theory) have three internal or rotational degrees of freedom 
sharing equally in the equipartition of energy with the three external 
degrees of freedom for each molecule. The ratio of specific heats for such 
a gas is y = | ; and it is often convenient to regard radiation as a gas with 
ratio of specific heats f. 
By this analogy we may anticipate some results proved more rigorously 
later. For y = f the pressure varies as T 4 in adiabatic expansion or com 
pression; this law is also true for radiation (Stefan’s Law). Again, in 
calculating the distribution of density and temperature inside a star we 
pass from the theory of convective equilibrium to radiative equilibrium 
by substituting the constant f instead of the ratio of specific heats of the 
material. Since radiative equilibrium postulates that the heat is conveyed 
through the star by aether waves instead of by material transport it is 
appropriate that the ratio of specific heats for aether waves should appear 
instead of the ratio for the material. 
/