A comparison of these numbers shows how much the result depends on the
special stars selected. By leaving out 26 stars the apex is changed by
5° in R. A., and 7° in declination.
It is to be remarked that the stars used by Boss are all contained in a
belt four degrees wide, extending from 1° to 5° north of the equator.
Dr. Oscar Stumpe, of Berlin, made a list of 996 stars having proper
motions between 16″ and 128″ per century. He divided them into three
groups, the first including those between 16″ and 32″; the second
between 32″ and 64″; the third between 64″ and 128″. The number of
stars in each group and the position of the apex derived from them are
as follows:
Gr. I, 551 stars; A = 287°.4; D = × 45°.0
II, 339 282°.2 43°.5
III, 106 280°.2 33°.5
Porter, of Cincinnati, made a determination from a yet larger list of
stars with results of the same general character.
These determinations have the advantage that the stars are scattered
over the entire heavens, the southern as well as the northern ones.
The difference of more than 10° between the position derived from
stars with the largest proper motions, and from the other stars, is
remarkable.
The present writer, in a determination of the precessional motion,
incidentally determined the solar motion from 2,527 stars contained in
Bradley’s Catalogue which had small proper motions, and from about 600
more having larger proper motions. Of the latter the declinations only
were used. The results were:
From small motions: A = 274°.2; D = × 31°.2
From large motions: 276°.9 31°.4
From all these results it would seem that the most likely apex of the
solar motion is toward the point in
Right Ascension, 280°
Declination, 38° north.
This point is situated in the constellation Lyra, about 2° from the
first magnitude star Vega. The uncertainty of the result is more than
this difference, four or five degrees at least. We may therefore state
the conclusion in this form:
_The apex of the solar motion is in the general direction of the
constellation Lyra, and probably very near the star Vega, the brightest
of that constellation._
It must be admitted that the wide difference between the position of
the apex from large and from small proper motions, as found by Porter,
Boss and Stumpe, require explanation. Since the apparent motions of the
stars are less the greater their distance, these results, if accepted
as real, would lead to the conclusion that the position of the solar
apex derived from stars near to us was much further south than when
derived from more distant stars. This again would indicate that our
sun is one of a cluster or group of stars, having, in the general
average, a different proper motion from the more distant stars. But
this conclusion is not to be accepted as real until the subject has
been more exhaustively investigated. The result may depend on the
selection of the stars; and there is, as yet, no general agreement
among investigators as to the best way of making the determination.
The next question which arises is that of the velocity of the solar
motion. The data for this determination are more meagre and doubtful
than those for the direction of the motion. The most obvious and direct
method is to determine the parallactic motion of the stars of known
parallax. Regarding any star 90° from the apex of the solar motion as
in a state of absolute rest, we have the obvious rule that the quotient
of its parallactic motion during any period, say a century, divided
by its parallax, gives the solar motion during that period, in units
of the earth’s distance from the sun. In fact, by a motion of the sun
through one such unit, the star would have an apparent motion in the
opposite direction equal to its annual parallax. If the star were not
90° from the apex we can easily reduce its observed parallactic motion
by dividing it by the sign of its actual distance from the apex.
Since every star has, presumably, a proper motion of its own, we can
draw no conclusion from the apparent motion of any one star, owing to
the impossibility of distinguishing its actual from its parallactic
motion. We should, therefore, base our conclusion on the mean result
from a great number of stars, whose average position or center of mass
we might assume to be at rest. Here we meet the difficulty that there
are only about 60 stars whose parallaxes can be said to be determined;
and one-half of these are too near the apex, or have too small a
parallax, to permit of any conclusion being drawn from them.
A second method is based on the spectroscopic measures of the motion
of stars in the line of sight, or the line from the earth to the star.
A star at rest in the direction of the solar apex would be apparently
moving toward us with a velocity equal to that of the solar motion.
Assuming the center of mass of all the stars observed to be at rest, we
should get the solar motion from the mean of all.
Thus far, however, there are only about 50 stars whose motions in the
line of sight have been used for the determination, so that the data
are yet more meagre than in the case of the proper motions. From them,
however, using a statistical method Kapteyn has derived results which
seem to show that the actual velocity of the solar system through space
is about 16 kilometres, or 10 statute miles, per second.