330 
THE OUTSIDE OF A STAR 
to the same depth provided that r v = r (the small divergences being those 
exhibited in Table 43); but if t„ is different the condition r sec 9 = I is 
evidently replaced by 
t v sec 9=1 or t — cos 9 . k/k v 
so that the intensity corresponds to temperature T v , where 
acT „ 4 = H (2 + 3 (k/k„) cos 9). 
Since Fig. 5 refers to the integrated light of the solar disc we must 
take cos 9 = f; and accordingly the equivalent temperature for frequency 
v will be given by = | (1 + T * (229-4). 
We can now by Planck’s law calculate the change in intensity due to our 
seeing down to a layer of temperature T v instead of T e and multiply the 
ordinates of the dotted curve in the ratio found. The result is shown by 
the continuous curve in Fig. 5. 
At first sight this curve for constant j v seems to deviate more from the 
observed spectral energy curve than the curve for constant k v did. But 
even if that is so, we must emphasize that it is the deviation from this 
new curve that requires a physical explanation rather than the deviation 
from the first curve which was merely a mathematical auxiliary. The new 
curve has the advantage that it accounts better for the falling off of the 
solar curve at short wave-lengths*. The high peak of the observed curve 
is still unaccounted for; assuming that this is due to less emissionf in the 
wave-lengths concerned, the general opacity k will be reduced and hence 
T v for other frequencies will be reduced according to (229-4). Thus the 
deviation on the right-hand side of the figure is likely to right itself 
automatically when the high peak is accounted for. 
We have calculated the effect of changes of k v on the energy-curve. 
By the converse process we can calculate what variation of k v would be 
necessary to account for the observed curve. Values of k v obtained in this 
way by Milne are tabulated in the second column of Table 44. The values 
which correspond to constant^, obtained from (229-2), are given in the 
third column. By division we obtain the values of 1/j „ given in the fourth 
column. (The unit in each column is arbitrary.) 
The last column indicates that the whole deviation of the observed 
curve is accounted for by a regular decrease in the emission with decreasing 
* H. H. Plaskett (Pub. Dominion Observatory, 2, p. 242) considers that the 
diminished intensity at short wave-lengths in Abbot’s curve is due to the large 
number of absorption lines, and that the intensity between the lines agrees with the 
black-body curve. This conclusion was also reached by Fabry and Buisson ( Comptes 
Rendus, 175, p. 156 (1922)) from measurements at five places free from absorption 
lines in the region 2920-3940 A. If this is correct we must emphasize that the agree 
ment is quite unexpected and unexplained. 
f Note that increased brightness indicates decreased emission.