(4) the radial velocity is for the present unknown,
but the others have, with few exceptions, a rather great velocity
amounting in the mean to 18 sir./st. (= 85 km./sec.), if no regard is
taken to the sign, a value nearly five times as great as the absolute
velocity of the sun. As this is only the component along the line of
sight, the absolute velocity is still greater, approximately equal to
the component velocity multiplied by [square root]2. We conclude that
the great proper motions depend partly on the proximity, partly on the
great linear velocities of the stars. That both these attributes here
really cooperate may be seen from the absolute magnitudes (_M_).

The apparent and the absolute magnitudes are for these stars nearly
equal, the means for both been approximately 7m. This is a consequence
of the fact that the mean distance of these stars is equal to one
siriometer, at which distance _m_ and _M_, indeed, do coincide. We find
that these stars have a small luminosity and may be considered as
_dwarf_ stars. According to the general law of statistical mechanics
already mentioned small bodies upon an average have a great absolute
velocity, as we have, indeed, already found from the observed radial
velocities of these stars.

As to the spectral type, the stars with great proper motions are all
yellow or red stars. The mean spectral index is +2.8, corresponding to
the type G8. If the stars of different types are put together we get the
table

_Type_ _Number_ _Mean value of M_
G 8 5.3
K 4 7.5
M 4 9.6

We conclude that, at least for these stars, the mean value of the
absolute magnitude increases with the spectral index. This conclusion,
however, is not generally valid.

32. _Stars with the greatest radial velocities._ There are some kinds of
nebulae for which very large values of the radial velocities have been
found. With these we shall not for the present deal, but shall confine
ourselves to the stars. The greatest radial velocity hitherto found is
possessed by the star (040822) of the eighth magnitude in the
constellation Perseus, which retires from us with a velocity of 72
sir./st. or 341 km./sec. The nearest velocity is that of the star
(010361) which approaches us with approximately the same velocity. The
following table contains all stars with a radial velocity greater than
20 sir./st. (= 94.8 km./se