THE OUTSIDE OF A STAR 
347 
material for a subordinate line. By (238-2) to produce a blackening of 
1:5, Jc'/Jc must be at least 33. For a subordinate line this absorption is 
due to say 10 -4 of the whole number of atoms of the element, which in 
turn will constitute say of the whole mass present. Hence material 
constituted wholly of the excited atoms should have h' equal to 10 7 Jc, if 
the subordinate lines are of the above blackness. If following Milne we 
take Jc = 10 3 , we are led to values of 1c' of the order 10 10 for line absorption. 
Monochromatic absorption coefficients are certainly very high, but it is 
doubtful whether they can be quite so high as this. Perhaps, however, 
the subordinate lines do not attain so deep a blackness; I think also that 
Milne’s value of lc should be reduced. 
A comparison of principal and subordinate lines should take account 
of the linkage in the formation of the lines. Consider a principal line formed 
by an atom going from state 1 to state 3, and a subordinate line formed 
by the atom going from state 2 to state 3. We should expect the principal 
line to darken the more rapidly, because of the much greater amount of 
absorbing material in state 1 than in state 2. But the emission in either 
line depends only on the number of atoms in state 3; and so long as there 
is energy in the subordinate line raising atoms to state 3, these will emit 
in both lines indiscriminately so that the principal line cannot become 
fully dark. There appears to be a tendency to equalise the two lines owing 
to this linkage of emission. But I am not sure whether that is really so. 
Suppose that not merely this one line but all the principal lines became 
entirely black; then there would be no radiation capable of exciting normal 
atoms, and hence no atoms in state 2 except a few produced by collision. 
The subordinate absorption line could not be formed at all, owing to lack 
of material. The question seems to be too complex to be decided here. 242 
242. Saha’s theory has dominated all recent progress in the observa 
tion and interpretation of stellar spectra. This is a highly specialised subject 
involving not only the collation of a great amount of astronomical and 
terrestrial spectroscopic data but the theory of series in optical spectra 
which, starting from principles similar to those involved in X ray spectra, 
has been elaborated in great detail. To pursue this subject would lead us 
far from our main purposes, and we shall here only touch on the fringe of 
these researches. 
The most precise mathematical development of Saha’s theory is due 
to R. H. Fowler and E. A. Milne*. Instead of determining the temperature 
at which a line should just appear or disappear (which involves estimates 
of the abundance of atoms or ions required to produce detectable absorp 
tion) they calculated the conditions for which the line should reach 
maximum intensity. 
* Monthly Notices, 83, p. 403; 84, p. 499; 85, p. 970.