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).