the star to be nearer
to us than 5 siriometers, corresponding to a parallax greater than
0".04. More seldom we may in this manner obtain trustworthy values for a
distance amounting to 10 siriometers ([pi] = 0".02), or even still
greater values. For such large 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 st