RADIATIVE EQUILIBRIUM
105
Multiply (74-1) first by dco/477- and integrate, and secondly by dco cos 0/4-77
and integrate. We obtain
The second equation agrees with (7IT) except that the actual operative
stress-component p R ' appears instead of the hydrostatic approximation
Pr• Reference to (74-2) shows that the error caused by using p R does not
depend on the fore-and-aft asymmetry arising from the presence of a net
In strict thermodynamical equilibrium with no outward flow H this
becomes
giving the well-known law that the emission coefficient is proportional to
the absorption coefficient for different kinds of matter at the same tempera
ture.
75. Let E (0) be expanded in zonal harmonics, viz.
E (6) — A + BP 1 (cos 9) + CP 2 (cos 9) + DP Z (cos 9) + ... (75T).
By integration over a sphere,
Hence the first three coefficients in the expansion have the interpretation
(74-3),
dp R _ kpH
(74-4).
dr c
flow H, but on the much smaller radial-transverse asymmetry which
makes the weighted mean value of cos 2 9 differ slightly from
Equation (74*3) can be written
or
cE = j/k,
j -= kacT 4
(74-5)
Multiplying the series by cos 9 and integrating,
H/c = ~ j E {9) P 1 (cos 9) doj = [ {P 1 (cos 0)} 2 do> =
Multiplying by P 2 (cos 9) = f cos 2 0 — and integrating,
I ( Pr ~ Pr) = f {f E (9) cos 2 9 - (9)} dco
{P 2 (cos 9)Y dco
A = E, B = 3 H/c, C = (pr' - pr) (75-2).