346 
THE OUTSIDE OF A STAR 
the tests applied by Eggert in the interior of a star and especially by Saha 
in the exterior that it has gained credence. As shown in Chapter in the 
theory appears to be logically inevitable, but it is easier to perceive the 
inevitability of a conclusion when one is already persuaded by experiment 
of its truth. 
The ionisation depends mainly on the temperature, but also to some 
extent on the pressure or strictly the electron pressure; and the conclusions 
depend on the pressure adopted for the layer where the spectral absorption 
takes place. But Saha showed in a general way that the spectrum varies 
with the photospheric temperature in the manner corresponding to the 
theoretical degree of ionisation. For example, it is calculated that calcium 
will not be ionised in the coolest stars; these show mainly the lines of the 
neutral atom. At somewhat higher temperature ionisation begins, and as 
soon as a reasonable proportion of ionised atoms is present the spectrum 
of Ca + appears. In the sun both kinds of atoms should be plentiful, and 
in fact both spectra are prominent. At still higher temperature ionisation 
is nearly complete; the Ca spectrum disappears, leaving only Ca + . At 
very high temperatures Ca + disappears, the atoms being now all reduced 
to Ca ++ . 
241. There is an important difference of behaviour of 'principal and 
subordinate lines of a spectrum. The former are absorbed by the atom or 
ion in its normal state, the latter in an excited state. The conditions for 
obtaining abundance of ions in an excited state are rather critical. On 
the one hand the fraction excited is increasing with temperature according 
to Boltzmann’s formula e ~ x ^ RT ; on the other hand the atoms capable of 
this excitation are disappearing owing to the increasing ionisation. The 
atom in fact has to juggle with its electron without dropping it; and the 
increasing stimulation of temperature ultimately defeats itself because 
so many of the electrons are dropped. 
If we arrange the stars in temperature sequence and trace along the 
sequence the changes in intensity of the spectral lines, a subordinate line 
rises to a fairly sharp maximum and drops again. A principal line on the 
other hand has a very flat maximum, and persists with nearly the same 
intensity for a long range of temperature, since it requires a considerable 
change of condition before one stage of ionisation gives way to the next. 
At the maximum of a subordinate line the number of atoms in the 
required excited state is found to be of the order 10~ 3 to 10 -5 of the whole 
number of atoms of the element*. At the maximum of a principal line 
practically all the atoms are in the appropriate absorbing condition, i.e. 
unexcited atoms in the proper stage of ionisation. The material for pro 
duction of a principal line is thus about 10,000 times as abundant as the 
* Fowler and Milne, Monthly Notices, 84, p. 510.