THE OUTSIDE OF A STAR 
327 
At the foot of the table the means of these intensities are taken. By 
the above rule this gives the intensity of the emergent radiation. The 
black-body temperature corresponding to this emergent intensity is 
deduced by the converse application of (229T5). Besides the equivalent 
black-body temperatures for the three wave-lengths, we give the equivalent 
black-body temperature 6039° for the whole intensity. This is deduced 
from the mean value of r by (229-1). It is not quite the same as the actual 
effective temperature of the centre of the sun’s disc (6068°) because we 
have, so to speak, left out a little bit of the sun in replacing the integral 
by the sum of 10 terms; but it is evidently proper to use the exact result 
for the distribution under discussion rather than the actual value for the 
celestial object which it approximately represents*. Finally, the intensities 
for a black-body at 6039° are given in the last line of the table, so that a 
comparison with the mean intensities gives the deviation from the black- 
body law arising from the spread of temperature. It is seen that these 
deviations are quite small. 
The second part of the Table gives similar results for a region near the 
sun’s limb. Since the spread of temperature is proportionately smaller, 
the deviations from black-body radiation are smaller. 
Table 43. 
Effect of Spread of Temperature of Radiating Layers. 
Centre of Disc 
Sec 9 = 3 
e~T 
T 
T 
Int. 
A4157 
Int. 
A 6235 
Int. 
A 12470 
T 
Int. 
A4157 
Int. 
A 12470 
•95 
•0513 
4920° 
•00091 
•0095 
•107 
4850° 
•00083 
•104 
•85 
•1625 
5100 
•00116 
•0111 
•117 
4920 
•00091 
•107 
•75 
•2877 
5280 
•00147 
•0131 
•128 
4990 
•00101 
•111 
•65 
•4308 
5470 
•00185 
•0153 
•140 
5060 
•00109 
•116 
•55 
•5979 
5660 
•00230 
•0177 
•152 
5150 
•00125 
•121 
•45 
•7985 
5880 
•00285 
•0205 
•165 
5250 
•00142 
•125 
•35 
1-0498 
6110 
•00359 
•0239 
•180 
5360 
•00163 
•133 
•25 
1-3863 
6390 
•00459 
•0283 
•199 
5500 
•00193 
•142 
•15 
1-8971 
6760 
•00617 
•0347 
•224 
5700 
•00239 
•154 
•05 
2-9958 
7390 
•00954 
•0467 
•268 
6070 
•00341 
•177 
Mean 
•9658 
•00344 
•0221 
•168 
— 
•00159 
•129 
Eff. temp. 
6039° 
— 
6070° 
5987° 
5924° 
5326° 
5342° 
5290° 
B.B. int. 
— 
— 
•00334 
•0228 
•176 
— 
•00156 
•132 
* It will be noticed that most of the intensity comes from the deeper partitions, 
and for exact calculation we should naturally sub-divide these. The purpose of the 
table, however, is to enable us to find our bearings with regard to the problem. If 
the calculations are worth pursuing further, recourse may be had to the analytical 
treatment of the integral (228-6) developed in Milne’s researches ( loc. tit.).