Lectures on Stellar Statistics | Page 3

distances the secular parallax, which is caused by the progressive
motion of the sun in space, may give better results, especially if the
mean distance of a group of stars is simultaneously determined. Such a
value of the secular parallax is also called, by KAPTEYN, the
systematic parallax of the stars.

When we speak of the proper motion of a star, without further
specification, we mean always the secular proper motion.
4. Terrestrial distances are now, at least in scientific researches,
universally expressed in kilometres. A kilometre is, however, an
inappropriate unit for celestial distances. When dealing with distances
in our planetary system, the astronomers, since the time of NEWTON,
have always used the mean distance of the earth from the sun as
universal unit of distance. Regarding the distances in the stellar system
the astronomers have had a varying practice. German astronomers,
SEELIGER and others, have long used a stellar unit of distance
corresponding to an annual parallax of 0".2, which has been called a
"Siriusweite". To this name it may be justly objected that it has no
international use, a great desideratum in science. Against the theoretical
definition of this unit it may also be said that a distance is suitably to be
defined through another distance and not through an angle--an angle
which corresponds moreover, in this case, to the harmonic mean
distance of the star and not to its arithmetic mean distance. The same
objection may be made to the unit "parsec." proposed in 1912 by
TURNER.
For my part I have, since 1911, proposed a stellar unit which, both in
name and definition, nearly coincides with the proposition of
SEELIGER, and which will be exclusively used in these lectures. A
siriometer is put equal to 10^6 times the planetary unit of distance,
corresponding to a parallax of 0".206265 (in practice sufficiently
exactly 0".2).
In popular writings, another unit: a light-year, has for a very long time
been employed. The relation between these units is
1 siriometer = 15.79 light-years, 1 light-year = 0.0633 siriometers.
5. In regard to time also, the terrestrial units (second, day, year) are too
small for stellar wants. As being consistent with the unit of distance, I
have proposed for the stellar unit of time a stellar year (st.),
corresponding to 10^6 years. We thus obtain the same relation between
the stellar and the planetary units of length and time, which has the

advantage that a velocity of a star expressed in siriometers per stellar
year is expressed with the same numerals in planetary units of length
per year.
Spectroscopic determinations of the velocities, through the
DOPPLER-principle, are generally expressed in km. per second. The
relation with the stellar unit is the following:
1 km./sec. = 0.2111 sir./st., = 0.2111 planetary units per year, 1 sir./st.
= 4.7375 km./sec.
Thus the velocity of the sun is 20 km./sec. or 4.22 sir./st. (= 4.22 earth
distances from the sun per year).
Of the numerical value of the stellar velocity we shall have opportunity
to speak in the following. For the present it may suffice to mention that
most stars have a velocity of the same degree as that of the sun (in the
mean somewhat greater), and that the highest observed velocity of a
star amounts to 72 sir./st. (= 340 km./sec.). In the next chapter I give a
table containing the most speedy stars. The least value of the stellar
velocity is evidently equal to zero.
6. Intensity of the radiation. This varies within wide limits. The faintest
star which can give an impression on the photographic plates of the
greatest instrument of the Mount Wilson observatory (100 inch
reflector) is nearly 100 million times fainter than Sirius, a star which is
itself more than 10000 million times fainter than the sun--speaking of
apparent radiation.
The intensity is expressed in magnitudes (m). The reason is partly that
we should otherwise necessarily have to deal with very large numbers,
if they were to be proportional to the intensity, and partly that it is
proved that the human eye apprehends quantities of light as
proportional to m.
This depends upon a general law in psycho-physics, known as
FECHNER's law, which says that changes of the apparent impression
of light are proportional not to the changes of the intensity but to these

changes divided by the primitive intensity. A similar law is valid for all
sensations. A conversation is inaudible in the vicinity of a waterfall. An
increase of a load in the hand from nine to ten hectograms makes no
great difference in the feeling, whereas an increase from one to two
hectograms is easily appreciable. A match lighted in the day-time
makes no increase in the illumination, and so on.
A mathematical analysis shows that from the law of FECHNER it
follows that the impression