248 
THE COEFFICIENT OF OPACITY 
atoms. Laboratory experiments show no such additional absorption 
beyond that given by Kramers’ theory. 
This last difficulty could be met by supposing that the loss of energy 
at the nuclear collision is slight and the electron is first captured in a high 
quantum orbit. Then (if it is not at once ionised away) it will drop to the 
lowest vacant level, this second step giving the main emission of energy. 
By this device laboratory tests are eluded, because in the emission and in 
the converse absorption the electron requires an intermediate resting-place 
which is not afforded in the un-ionised atoms of laboratory experiment. 
But whilst this suggestion seems not unreasonable when we think only of 
the emission, it becomes, I think, entirely incredible when we consider the 
reverse steps in the absorption. 
The last remark reveals the essentially weak point in the idea of capture 
by collision with the nucleus—that its plausibility does not survive re 
versal. To suppose that when absorbing the electron retraces its steps— 
descends to the nucleus and then bounds off into a hyperbolic orbit—is 
not particularly plausible. Again, the exact formula for emission on a 
nuclear capture theory must involve the radius of the nucleus; but it 
seems impossible that this can play any part in the corresponding absorp 
tion. 172 
172. A summary of the position reached with regard to the coefficient 
of absorption divides itself into two parts, (1) the law k oc p/pT 7 ^, and 
(2) the absolute value of k. 
(1) The law k oc p/pT- or something sufficiently near to it for most 
stellar applications is given by— 
{a) The most general theoretical considerations of absorption and 
emission coupled with the observed approximate constancy of brightness 
from type M to type A in the giant series. 
(6) Kramers’ theory, or equivalently the classical theory of emission. 
(c) Laboratory data as to absorption of X rays coupled with the 
thermodynamic theory of ionisation. 
(d) The theory of nuclear capture. 
(e) The observed agreement of the luminosities of stars with the 
mass-luminosity curve based on this law. 
We do not lay overmuch stress on the half-power of T, nor exclude 
corrections varying with the level of ionisation of the atoms; but the 
“guillotine corrections” suggested by Kramers’ theory seem to be 
definitely too large. 
(2) The predicted opacity from (6) or (c) is only of the observed 
opacity of the stars; and no satisfactory explanation of the discordance