SURVEY OF THE PROBLEM 
13 
iterferometer 
ti reflector at 
merits of the 
is, begun by 
ual orbit. It 
nents can be 
aries; and it 
termined for 
is unusually 
ries between 
etween + 63 
lean velocity 
of recession 
must be in 
he brighter 
e may treat 
the line of 
be equal to 
ly; to allow 
here i is the 
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the period, 
of the two 
the usual 
nical units 
eriod P in 
1 already 
12 . In the orbit determined from the visual measures the semiaxis of 
the relative orbit (cq + a 2 ) is found to be 0"-0536. We have seen that in 
linear measure this is equal to 0-847 astronomical units. Hence 1 as 
tronomical unit corresponds to 0"-0632. Accordingly the parallax of 
Capella is 
w = 0"-0632. 
A rough parallax had previously been found trigonometrically in close 
agreement with the above value, but the parallax furnished by the orbital 
data is presumably of much superior accuracy. 
The observed visual magnitude of Capella is 0 m -21. To reduce to 
absolute magnitude, i.e. magnitude at the standard distance of 10 parsecs 
or parallax 0"-1, we must add 
51og 10 ( ra /0"-l), 
which gives 0-21 — 1-00 = — 0 m -79. This represents the sum of the light 
of the two components. It is estimated that they differ in visual magnitude 
by 0 m -5. The absolute visual magnitudes are then found to be — 0 m -26 
and + 0 m -24, since these would compound to give — 0 m -79. 
The spectral type of the bright component is classed as G 0, the same 
as that of the sun. The sun’s effective temperature is 5740°, but it appears 
from theory and observation that the same spectral characteristics will 
appear at lower temperature in a diffuse star like Capella than in the sun. 
We shall therefore adopt 5200° for the effective temperature. This, of 
course, is only the marginal temperature of the great furnace, and affords 
no idea of the terrific heat within. 
It is convenient to introduce the bolometric magnitude, which is a 
measure of the heat-intensity of a star in the same way that the visual 
magnitude is a measure of its luminous intensity or the photographic 
magnitude is a measure of its photographic intensity, the measures in 
each case being on a logarithmic scale. Black-body radiation has maximum 
luminous efficiency when it corresponds to a temperature of about 6500°, 
and the zero of the scale of bolometric magnitude is chosen so as to agree 
with visual magnitude for stars of this effective temperature. At any 
other temperature a greater amount of radiant energy is required to 
produce the same intensity of light, so that the bolometric magnitude is 
brighter (numerically smaller) than the visual magnitude. At 5200° the 
reduction to bolometric magnitude is 0 m -10, so that the absolute bolo 
metric magnitude of the bright component of Capella is 
- 0-26 - 0-10 - - 0 m -36. 
Since the bolometric magnitude indicates the total radiation emitted 
from the star and the effective temperature indicates the radiation per 
sq. cm., we are able to calculate the area of the surface and hence the 
radius of Capella. The calculation is most conveniently made by using