Lectures on Stellar Statistics | Page 9

first proposed by HERTZSPRUNG and has been extensively used
by BERGSTRAND, LUNDMARK and LINDBLAD at the observatory of
Upsala and by others.
15. Colour-index. We have already pointed out in §9 that the colour
may be identified with the mean wave-length ([lambda]0). As further
[lambda]0 is closely connected with the spectral index (s), we may use
the spectral index to represent the colour. Instead of s there may also

be used another expression for the colour, called the colour-index. This
expression was first introduced by SCHWARZSCHILD, and is defined
in the following way.
We have seen that the zero-point of the photographic scale is chosen in
such a manner that the visual magnitude m and the photographic
magnitude m' coincide for stars of spectral index 0.0 (A0). The
photographic magnitudes are then unequivocally determined. It is
found that their values systematically differ from the visual magnitudes,
so that for type B (and O) the photographic magnitudes are smaller
than the visual, and the contrary for the other types. The difference is
greatest for the M-type (still greater for the N-stars, though here for the
present only a few determinations are known), for which stars if
amounts to nearly two magnitudes. So much fainter is a red star on a
photographic plate than when observed with the eye.
The difference between the photographic and the visual magnitudes is
called the colour-index (c). The correlation between this index and the
spectral-index is found to be rather high (r = +0.96). In L. M. II, 19 I
have deduced the following tables giving the spectral-type
corresponding to a given colour-index, and inversely.
TABLE 1.
GIVING THE MEAN COLOUR-INDEX CORRESPONDING TO A
GIVEN SPECTRAL TYPE OR SPECTRAL INDEX.
+-------------------+----------------+ | Spectral | Colour-index | | type |
index | | +-------+-----------+----------------+ | B0 | -1.0 | -0.46 | | B5 |
-0.5 | -0.23 | | A0 | 0.0 | 0.00 | | A5 | +0.5 | +0.23 | | F0 | +1.0 | +0.46 |
| F5 | +1.5 | +0.69 | | G0 | +2.0 | +0.92 | | G5 | +2.5 | +1.15 | | K0 |
+3.0 | +1.38 | | K5 | +3.5 | +1.61 | | M0 | +4.0 | +1.84 |
+-------+-----------+----------------+
TABLE 1*.
GIVING THE MEAN SPECTRAL INDEX CORRESPONDING TO A
GIVEN COLOUR-INDEX.

+----------------+-------------------+ | Colour-index | Spectral | | | index |
type | +----------------+---------+---------+ | | | | | -0.4 | -0.70 | B3 | | -0.2
| -0.80 | B7 | | 0.0 | +0.10 | A1 | | +0.2 | +0.50 | A5 | | +0.4 | +0.90 | A9
| | +0.6 | +1.30 | F3 | | +0.8 | +1.70 | F7 | | +1.0 | +2.10 | G1 | | +1.2 |
+2.50 | G5 | | +1.4 | +2.90 | G9 | | +1.6 | +3.30 | K3 | | +1.8 | +3.70 |
K7 | | +2.0 | +4.10 | M1 | +----------------+---------+---------+
From each catalogue of visual magnitudes of the stars we may obtain
their photographic magnitude through adding the colour-index. This
may be considered as known (taking into account the high coefficient of
correlation between s and c) as soon as we know the spectral type of
the star. We may conclude directly that the number of stars having a
photographic magnitude brighter than 6.0 is considerably smaller than
the number of stars visually brighter than this magnitude. There are,
indeed, 4701 stars for which m < 6.0 and 2874 stars having m' < 6.0.
16. Radial velocity of the stars. From the values of [alpha] and [delta]
at different times we obtain the components of the proper motions of
the stars perpendicular to the line of sight. The third component (W), in
the radial direction, is found by the DOPPLER principle, through
measuring the displacement of the lines in the spectrum, this
displacement being towards the red or the violet according as the star
is receding from or approaching the observer.
The velocity W will be expressed in siriometers per stellar year (sir./st.)
and alternately also in km./sec. The rate of conversion of these units is
given in §5.
17. Summing up the remarks here given on the apparent attributes of
the stars we find them referred to the following principal groups:--
I. The position of the stars is here generally given in galactic longitude
(l) and latitude (b). Moreover their equatorial coordinates ([alpha] and
[delta]) are given in an abridged notation ([alpha][delta]), where the
first four numbers give the right ascension in hours and minutes and
the last two numbers give the declination in degrees, the latter being
printed in italics if the declination is negative.

Eventually the position is given in galactic squares, as defined in §2.
II. The apparent motion of the stars will