348 
THE OUTSIDE OF A STAR 
The number of atoms in a state to absorb a given line varies with 
temperature and density. Fowler and Milne take as their two variables 
the temperature T and the electron pressure P e ; the latter is presumably 
about half the total gas pressure since we may expect about 1 free electron 
per atom in photospheric conditions*. Keeping P e fixed we can trace how 
the proportion of atoms in the required state changes with T, and deter 
mine the temperature for which it is a maximum. If P e is rightly chosen 
this should be the temperature at which the line reaches maximum in 
tensity, and the spectral class of observed maximum intensity can thus 
be correlated with temperature. Conversely if we know the temperatures 
of the different spectral classes we can determine the value of P e for the 
reversing layer. 
The formulae for determining the number of atoms in a given state of 
ionisation when the electron density is given have been developed in § 47; 
the proportion of these in any given excited state is also known by Boltz 
mann’s formula. By differentiating with respect to T the temperature of 
maximum abundance of the given state can be found. We do not give the 
formulae here explicitly, since for practical computation simplifications 
appropriate to the particular conditions considered are introduced, and 
we are not here concerned with the technique of practical computation^. 
The following examples are taken from Fowler and Milne’s calculations— 
(1) H. Balmer Series. Maximum in type A 0 = 10,500° on temperature 
scale usually adopted. Temperatures of maximum abundance of hydrogen 
atoms in a state to absorb the Balmer series are— 
P e = 1-3.10- 4 atmos., T = 10,000°, 
P e = 7-2.10- 4 , T= 11,000, 
P e = 3-1.10- 3 , T = 12,000. 
(2) Mg + . A4481. Maximum in type A 0 = 10,500°— 
P e = 0-8.10~ 4 , T = 10,000, 
P e = 5-2.10~ 4 , T = 11,000, 
P e =M.10~ 3 , T = 12,000. 
(3) Mg. A5711, 5528, 4703, 4352. Maximum “between sun and sun 
spot” = 5500°— 
P e = 2-4.10- 5 , T = 5,000, 
P e =l-6.10- 4 , T = 5,500, 
P e = 7-8.10“ 4 , T= 6,000. 
(4) Ca + . H and K lines. Maximum in type K 0 = 4300°— 
P e = 9*9.10~ 7 , T = 5,000, 
P e = 5-0.10~ 5 , T = 6,000. 
* Some elements will not be ionised, others may be doubly ionised. 
f Reference may be made to Fowler and Milne, Monthly Notices, 83, pp. 408—410.