SOLUTION OF THE EQUATIONS 
139 
/ 
Table 15 is calculated from Nutting’s measures of the visual intensities 
of energy of different wave-lengths*. In the last column the intensity- 
ratio p has been converted into magnitudes (Aw = — flog p) so as to 
give the correction Aw reducing bolometric to visual magnitude. 
Since the radiation per unit area is proportional to Tf the surface 
brightness is proportional to jpT* ; or, denoting by J the surface brightness 
expressed in magnitudes 
J = const. — 10 log T e + Aw (101-2). 
The following approximate formula for J was given by E. Hertzsprung 
in a rather inaccessible paper in 1906f 
/14-3OO\0' 93 
J = const. + 2-3 (-*—) (101-3). 
F. W. SearesJ has pointed out that Table 15 (which was computed by me 
10 years later) agrees entirely with this formula, the greatest difference 
being 0 m -04. As Aw and J are very frequently required in practical calcu 
lation we give a more extended table computed from Hertzsprung’s 
formula. The values from 12,000°-20,000° are subject to some reserve, 
because Hertzsprung’s formula was derived as an interpolation formula 
and it has not been ascertained how far his approximation remains 
satisfactory above 12,000°. 102 
Table 16. 
Effective Temperature and Surface Brightness (Hertzsprung’s Formula). 
T e 
Am 
J 
T e 
Am 
J 
T e 
Am 
J 
2500° 
m 
2-71 
+ 6-27 
6000° 
m 
0-02 
- 0-22 
11500° 
m 
0-50 
-2-56 
2750 
213 
5-28 
6500 
0-00 
0-58 
12000 
0-58 
2-67 
3000 
1-67 
4-44 
7000 
0-00 
0-91 
13000 
0-73 
2-86 
3250 
1-32 
3-74 
7500 
0-02 
1-19 
14000 
0-89 
3-03 
3500 
1-03 
3-13 
8000 
0-06 
1-43 
15000 
1-04 
3-18 
3750 
0-80 
2-60 
8500 
0-10 
1-65 
16000 
1-19 
3-31 
4000 
0-62 
2-14 
9000 
0-16 
1-84 
17000 
1-34 
3-42 
4250 
0-47 
1-73 
9500 
0-22 
2-01 
18000 
1-49 
3-52 
4500 
0-35 
1-36 
10000 
0-29 
2-17 
19000 
1-63 
3-61 
5000 
0-18 
0-73 
10500 
0-36 
2-31 
20000 
1-77 
3-70 
5500 
0-08 
+ 0-22 
11000 
0-43 
2-44 
102. The correction Aw will not be accurate because the radiation of 
a star is not distributed exactly in accordance with the law of black-body 
radiation. The radiation comes from layers extending over an appreciable 
* Phil. Mag. 1915, Feb. p. 304. 
f Zeits. für Wissenschaftliche Photographie, 4, p. 43. 
J Astrophys. Journ. 55, p. 197. Another independent computation has been 
made by W. Rabe, Astr. Nach. 225, p. 223.