Having obtained our theoretical curve, the first thing to do is to test
it by observation. That is to say, we gather together as many stars as
we can lay hands on for which both the mass and absolute brightness
have been measured. We plot the corresponding points (opposite to the
appropriate horizontal and vertical graduations) and see whether they
fall on the curve, as they ought to do if the theory is right. There
are not many stellar masses determined with much precision. Everything
that is reasonably trustworthy has been included in Fig. 7. The
circles, crosses, squares, and triangles refer to different kinds of
data--some good, some bad, some very bad.
The circles are the most trustworthy. Let us run through them from
right to left. First comes the bright component of Capella, lying
beautifully on the curve--because I drew the curve through it. You
see, there was one numerical constant which in the present state of
our knowledge of atoms and ether-waves, &c., it was not possible to
determine with any confidence from pure theory. So the curve when it
was obtained was loose in one direction and could be raised or lowered.
It was anchored by making it pass through the bright component of
Capella which seemed the best star to trust to for this purpose. After
that there could be no further tampering with the curve. Continuing to
the left we have the fainter component of Capella; next Sirius; then,
in a bunch, two components of α Centauri (the nearest fixed star) with
the Sun between them, and--lying on the curve--a circle representing
the mean of six double stars in the Hyades. Finally, far on the left
there are two components of a well-known double star called Krueger 60.
The observational data for testing the curve are not so extensive and
not so trustworthy as we could wish; but still I think it is plain from
Fig. 7 that the theory is substantially confirmed, and it really does
enable us to predict the brightness of a star from its mass, or vice
versa. That is a useful result, because there are thousands of stars of
which we can measure the absolute brightness but not the mass, and we
can now infer their masses with some confidence.
Public-domain text, read in full here on John Shaqi.
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