78 
Gaseous Stars 
[ch. Ill 
72. To discuss the transfer of energy by radiation, it is convenient to 
replace equation (71T) by the equivalent equation 
*t = bp'C v cl (72T), 
where p is the density, and p’G v is the specific heat of the carriers per unit 
volume, c as before denotes their mean velocity, and l is their mean free path. 
The nuclei and the free electrons have, of course, quite definite free-paths. 
The same is true of the radiation if this is regarded as consisting of discrete 
quanta ; when a quantum is emitted a free-path begins, and when it is re 
absorbed the free-path ends. Whether we think in terms of undulatory theory 
or quanta, we may suppose that a beam of radiation is reduced in intensity 
by a factor e~ kpx on passing through a thickness x of matter of density p, 
where k is the “coefficient of opacity” of the matter. In ordinary kinetic 
theory a stream of molecules is reduced to e~*/ 1 of its original strength after 
traversing a distance x, where l is the free-path. By comparison the free-path 
of our molecules of radiation must be supposed to be 1/kp. The energy of 
these fictitious molecules per unit volume is aT*, so that the specific heat per 
d 
unit volume is ^ (aT*) or 4>aT 8 , which may be compared with the specific 
heat per unit volume pG v of ordinary material molecules. The velocity of 
these radiation-molecules is of course uniformly equal to G, the velocity of 
light. 
If now we make the appropriate substitutions in formula (72T), replacing 
c by G, l by 1/kp and pG v by 4aT 3 , the formula becomes 
4 aT*C 
*“3 kp 
(72-2), 
so that the transfer of energy by our fictitious radiation molecules is the same 
as if there were a coefficient of conduction having this value. On inserting 
numerical values suitable for the sun’s interior (say T — 3 x 10 7 , k — 1000, 
p = 10) and putting aC = 4<r = 2*3 x 10 -4 , we find that this coefficient of con 
duction is of the order of 10 14 . This so entirely outweighs the coefficients 
of conduction of heat by material conduction that the latter may be neglected 
by comparison. Further, the flow of heat produced by radiative conduction is 
at least of the same order of magnitude as that actually observed. Whether 
the two quantities are in complete agreement will be the subject of a careful 
enquiry below. 
With formula (72-2) for the coefficient of radiative conductivity, the radia 
tive flow of heat per unit area becomes 
dT__4>aT 3 CdT 
dr 3 kp dr 
(72-3). 
Both these formulae are only approximate; indeed the fundamental 
formula (72T) from which they are derived was only approximate.