THE OUTSIDE OF A STAR 325 
On the other hand, the intensity of the emergent radiation corresponds to 
an effective temperature given by (227-3) 
acT* = 2H (1 + | cos d) (228-2). 
The ratio T m /T e is 1-08 at the centre (cos 0=1) and falls to unity at 
the limb. We might perhaps expect the quality of the light (distribution 
in wave-length) to correspond to the mean temperature of its origin. In 
that case T m jT e will be the ratio of the effective temperature judged by 
quality of the radiation to the effective temperature judged by quantity. 
This, however, is a lazy way of handling the problem and it is not sur 
prising that the result fails to accord with observation. The proper course 
is to find the spectral distribution of the emergent radiation by treating 
each wave-length separately using its own proper value of j and Jc. 
The chief published investigations of the theory of the spectral dis 
tribution of the emergent radiation are by E. A. Milne* and B. Lindbladf. 
Reference may be made to these to supplement the present account in 
matters of detail. 
The observed spectral energy-curve of the sun is shown by the broken 
line in Fig. 5 (p. 328). It is derived from Abbot’s measurements as combined 
by Lindblad. The ordinate is proportional to the amount of energy emitted 
within a fixed range of wave-length dX. (In our previous theoretical work 
we have generally considered a fixed range of frequency dv.) When plotted 
in this way the maximum ordinate of the black-body curve is given by 
( 102 ' 3 ) A max . T = 0-288 cm. deg (228-3). 
The dotted curve (constant absorption coefficient) in the figure, although 
not precisely the black-body curve, is barely distinguishable from it on 
the scale of the diagram, so that the difference of the two curves is 
practically the deviation of the sun’s radiation from a black-body. 
Three causes may contribute to this deviation— 
(а) What we see is a superposition of radiation from layers at different 
temperatures, and the spread of temperature distorts the black-body 
curve. 
(б) Since the absorption coefficient is different for different wave 
lengths we see farther into the sun in some wave-lengths than in others 
and so receive radiation from a hotter stratum. 
(c) The conditions in the radiating layers are beginning to deviate from 
thermodynamical equilibrium and deviations from Planck’s Law may 
arise at the source of the radiation. 
* Monthly Notices, 81, p. 375 (1921); Phil. Trans. 223 a, p. 201 (1922). 
f Uppsala Universitets Ârsskrift, 1920, No. 1 ; Nova Acta Reg. Soc. Sci. Upsaliensis, 
Ser. 4, Vol. 6, No. 1 (1923).