Gaseous Stars 
[ch. Ill 
provided a value for the coefficient of opacity k for ordinary stellar material. 
His theoretical investigation shews that k must be of the form 
cFp 
k = 
fiT™ 
■am. 
where c is a constant, F a numerical factor, and /a, p, T have the same 
meanings as before. The value of the constant c is found to be 
16tt 2 N 2 
e'Un 
c = 
3 V3 A m 2 aC 4 m e h (1 +f) 
•(77-2), 
where N is the atomic number and A the atomic weight, e is the charge and 
m e the mass of an electron, u 0 is the mean velocity of an electron at 1 ° 
absolute. The number F represents the ratio of the total absorption to that 
caused by free electrons, and 1 // is the number of free electrons per atomic 
nucleus. 
The formula has been tested under laboratory conditions and is found to 
agree well with observation. But under laboratory conditions there are 
practically no free electrons so that F and f are both very large and cancel 
out in the value of k. Under stellar conditions, where most of the atoms are 
highly ionised, f is quite small, so that the factor 1 +f may be put equal to 
unity. The value of F can now only be calculated from pure theory, laboratory 
experiments providing no means of checking this value. 
A preliminary investigation by Eddington* suggested that F had a fairly 
uniform value of from 8 to 10, but Milne f subsequently shewed that this 
value was too small by a factor of the order of 2 or 3. If we absorb in the 
factor F a further small correction in the opposite sense which RosselandJ 
shewed to be necessitated by the distribution of radiant energy over different 
wave-lengths, it is found that the value of F must be about 20§. 
In most investigations the numerical value of F is unimportant, the results 
depending only on the general form of the law for k, which has been tested 
by experiment. And when the value for F enters, it is generally through so 
low a power that small errors in the adopted value for F are unimportant. 
For instance, we shall find ultimately that the central temperature of a star is 
proportional to F^, so that an error of 100 per cent, in the assumed value for 
F results only in an error of 9'7 per cent, in the central temperatures of 
the stars. 
Adopting the value F = 20, and inserting numerical values into c for all 
quantities except N, A and /la, equation (77T) assumes the form 
P 
AJfiT*« 
k = 4-46 x 10 25 
.(77-3). 
M.N. lxxxiv. (1924), p. 104. 
Ibid, lxxxiv. (1924), p. 525. 
t Ibid, lxxxv. (1925), p. 750. 
§ Ibid, lxxxvi. (1926), p. 561.