viduals having great values of the attributes _A_
and small values of the attribute _B_, then we get a statistical series
regarding the attribute _C_, which consists of two seemingly distinct
normal frequency distributions. It is in like manner, however, that the
parallax stars are selected. The reason for this selection is the
following. The annual parallax can only be determined for near stars,
nearer than, say, 5 siriometers. The direct picking out of these stars
is not possible. The astronomers have therefore attacked the problem in
the following way. The near stars must, on account of their proximity,
be relatively brighter than other stars and secondly possess greater
proper motions than those. Therefore parallax observations are
essentially limited to (1) bright stars, (2) stars with great proper
motions. Hence the selected attributes of the stars are _m_ and [mu].
But _m_ and [mu] are both positively correlated to _M_. By the selection
of stars with small _m_ and great [mu] we get a series of stars which
regarding the attribute _M_ seem to be divided into two distinct
classes.

The distribution of the parallax stars gives us no reason to believe
that the stars of the types K and M are divided into the two supposed
classes. There is on the whole no reason to suppose the existence at all
of classes of giant and dwarf stars, not any more than a classification
of this kind can be made regarding the height of the men in a
population. What may be statistically concluded from the distribution of
the absolute magnitudes of the parallax stars is only that the
_dispersion_ in _M_ is increased at the transition from blue to yellow
or red stars. The filling up of the gap between the "dwarfs" and the
"giants" will probably be performed according as our knowledge of the
distance of the stars is extended, where, however, not the annual
parallax but other methods of measuring the distance must be employed.

TABLE 8.

_THE ABSOLUTELY FAINTEST STARS._

[Transcriber's Note: To conserve space (ad) is used in place of
([alpha][delta]).]

+--+---------------------+----------+--------+-----+-------+-------+-------+
| 1| 2 | 3 | 4 | 5 | 6 | 7 | 8 |
+--+---------------------+----------+--------+-----+-------+-------+-------+
| | | Position | Distance |
| | _Name_ |----------+--------+-----+-------+-------+-------+
| |