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