2 
SURVEY OF THE PROBLEM 
relative abundance of the chemical elements—that a star showing strongly 
the iron spectrum is richer in that element than other stars; it is rather 
an indication of physical conditions of temperature and density favourable 
for exciting the respective spectra. Without entirely denying the possibility 
of differences of chemical composition, which may be necessary to account 
for some of the more unusual types of spectrum, we assume that in the 
main the observed differences of surface phenomena are not connected 
with chemical constitution. 
We have thus to consider an atmosphere of material of fixed composi 
tion, with free upper surface and density increasing downwards. Its 
physical state—distribution of density, temperature and pressure; hence 
also its radiative and optical properties—will then depend entirely on the 
extraneous controlling influences to which it is subjected; and these 
extraneous influences are, as already stated, the force of gravity holding 
it down to the star and the stream of radiant heat poured into it from 
below. In order to remain in a steady state the atmosphere must adjust 
itself to let the radiant heat pass through. Thus the surface conditions 
depend on two parameters, viz. the value of g at the surface and the 
“effective temperature” T e . The effective temperature is a conventional 
measure specifying the rate of outflow of radiant heat per unit area; it 
is not to be regarded as the temperature at any particularly significant 
level in the star. 
By varying the controlling factors g and T e the state of the stellar 
atmosphere can be varied in two directions. Accordingly we must expect 
that the possible varieties of stellar spectrum will form a twofold sequence, 
that is to say, will be capable of arrangement in two-dimensional order. 
This is in fact the case. For a long time only a one-dimensional order was 
recognised, viz. the well-known Draper sequence of types. But the 
spectroscopic method of determining absolute magnitudes, due to Adams 
and Kohlschiitter in 1914, introduces a classification of spectra transverse 
to the Draper classification. Roughly speaking the Draper criterion follows 
the parameter T e and the absolute magnitude criterion the parameter g; 
but the correspondence is probably not so close as was at one time sup 
posed. The observational criteria divide the two-dimensional distribution 
of states into one system of meshes, and the parameters T e and g into 
another system. There is no reason to anticipate any close coincidence of 
the two methods of partition. 
The same twofold sequence of possible states appears when we con 
sider the star as a whole. Evidently one sequence is obtained by considering 
stars of different mass. A transverse sequence is formed by stars of the 
same mass but different radius (or mean density). Thus a third way of 
dividing into meshes the two-dimensional distribution of states is obtained 
by taking the mass and radius of the star, M and R, as parameters.