SOLUTION OF THE EQUATIONS 
137 
100. The last formula of (99*2) is so frequently used that we have 
constructed an extended table for applying it. For practical purposes 
L will be expressed in magnitudes m according to the rule* 
Am = — |A log 10 L (100*1). 
In Table 14 the fixed value ¡x = 2*11 is used and corresponding values 
of M and 1 — /3 are tabulated by (84*6). Then by (100*1) and (99*2) 
Am = — f A log M — J^A log (1 — /?) — 2A log T e ...(100*2), 
and the column m in the table is computed from this formula, omitting 
the term containing T e . We have adjusted the zero of m so that the 
observed mass and absolute bolometric magnitude of Capella correspond 
to one another, and the table should accordingly give the absolute bolo 
metric magnitude for any other mass with the same effective temperature 
as Capella (about 5200°). 
For a different effective temperature, we have by (100*2) 
Am = — 2A log T e (100*3), 
and this correction should be applied as indicated at the foot of the table. 
With the range of effective temperature commonly occurring in the stars 
this correction is comparatively small, and the bolometric magnitude of 
a star is mainly a function of its mass. 
For the effect of small changes of /x see § 178. We need only note here 
that the result of a change of ¡x is not shown explicitly in (99*2), since there 
are consequential changes of (1 — /3) to be taken into account. 
Table 14. 
Mass M and Absolute Bolometric Magnitude m. 
(jx = 2*11, T e = 5200°.) 
1-0 
M 
m 
1-0 
M 
m 
1-0 
M 
m 
•001 
•1284 
14-143 
•04 
•879 
5-211 
•26 
3-774 
- 0-052 
•0015 
•1574 
13-173 
•05 
1-004 
4-645 
•28 
4-137 
- 0-312 
•002 
•1820 
12-484 
•06 
1-123 
4-178 
•30 
4-529 
- 0-562 
•0025 
•2036 
11-950 
•07 
1-240 
3-777 
•35 
5-675 
- 1156 
•003 
•2233 
11-513 
•08 
1-354 
3-426 
•40 
7-117 
- 1-718 
•004 
•2583 
10-823 
•09 
1-468 
3*111 
•45 
8-984 
- 2-264 
•005 
•2895 
10-286 
•10 
1-582 
2-825 
•50 
11-46 
- 2-805 
•006 
•3176 
9-848 
•12 
1-812 
2-322 
•55 
14-84 
- 3-354 
•008 
•3683 
9-154 
•14 
2-050 
1-884 
•60 
19-62 
- 3-919 
•010 
•4135 
8-615 
•16 
2-297 
1-494 
•65 
26-66 
- 4-516 
•015 
•5117 
7-632 
•18 
2-557 
1138 
•70 
37-67 
- 5-162 
•02 
•5968 
6-929 
•20 
2-831 
0-812 
•75 
56-15 
- 5-882 
•025 
•6739 
6-381 
•22 
3-124 
0-507 
•80 
90-63 
- 6-714 
•03 
•746 
5-929 
•24 
3-437 
0-220 
Add to m the temperature term, - 2 log 10 {TJ 5200).