e change is 
(absorption 
equilibrium 
t after the 
chamber, 
evade the 
matter of 
nission and 
bter just as 
nd contrac- 
Le adiabatic 
act, setting 
ion has re- 
gy-density; 
al state. 
) no entropy 
mtropy has 
adiation to 
luced. But 
equilibrium 
so that the 
>een created 
it has never 
to convert, 
wersibly by 
istitution is 
en—moving 
wave is re- 
t there is a 
lowering of 
>"molly on a 
density and 
the Doppler 
....(33-1). 
n-equilibrium 
tician. 
The pressure on the walls is E + E' (§21). The work done on the walls 
per sq. cm. per sec. is therefore (E + E') V. This must be equal to the 
difference of energy of the incident and reflected waves, viz. Ec — E'c per 
sq. cm. per sec. Hence 
(E—E')c = (E + E')V (33-2). 
By (33-1) and (33-2) 
*/ E' c - V 
' E ~c+V 
If the incidence is oblique the same result is obtained except that 
V must now be the velocity of the reflector resolved in the oblique direction. 
We express the quantity E/v in units called quanta*. By (33-3) 
E/v = E'/v', that is to say, the number of quanta is unaltered by reflection at 
moving walls. 
Consider a small change of volume of the chamber causing a change of 
temperature of the radiation from T to T + dT. During this change let 
a quantum of frequency v change to frequency v by one or more reflections 
at the moving walls and write 
v = v' (1 + <5) (33*4). 
Then by (33-3) s depends on the circumstances of the reflections, but not 
on v. Hence if we denote by g (s) ds the proportion of the reflected quanta 
for which this coefficient lies between s and s + ds, g ( s ) will be the same 
function whatever frequency v we are considering, since there is no correla 
tion between v and s. 
By definition 
Let 
f g (s) ds = 1 
[ sg(s)ds = s 0 
....(33-5). 
Then s 0 is independent of v. 
Let J ( v , T) dv be the number of quanta of frequency v to v + dv in 
the chamber when the temperature is T , then 
J {v, T + dT) dv' = I g (s) ds J (v, T) dv, 
where the integral on the right is taken over all values of s, and (for each 
value of s) v and dv are related to the fixed values v , dv' by (33-4). Hence 
substituting for v and dv 
J (/, T + dT) —\g (s) ds (l + s)J(v'(l + s), T). 
* We use the modern nomenclature, but do not here introduce any of the 
principles of the quantum theory. The “number of quanta” is not assumed to be 
an integral number.