262 REPORT—1905. 
I took in hand first the distribution of the nwmbers of the proper 
motions over the angles of position, counted from the line towards the 
antapex. 
Were the hypothesis of random distribution of the directions satis- 
fied, these numbers, too, ought to show the bilateral symmetry. Only in 
the apex and the antapex itself, where the parallactic motion disappears, 
we would still have radial symmetry. 
For all the regions at the same distance from the apex and antapex 
we would expect quite similar figures. 
Now since in reality each figure shows anomalies, I made mean figures 
by combining together the data embodied in a/l the figures having the 
same distance (or rather sine of the distance) approximately from tbe 
apex and antapex. 
So, for instance, were the results of twelve such figures as those of 
fig. 2, of which the sine of the distance from the apex lies between 0-9 and 
1-0, summarised in a single set of results, 
This mean set proved to be all but perfectly symmetrical, and duly 
gave the maximum frequency for the direction towards the antapex. 
For these reasons I felt myself justified provisionally to adopt this set as 
representing the normal distribution for the corresponding distance from 
the apex ; that is, I supposed that this distribution would nearly repre- 
sent the distribution corresponding to a set of proper motions, really 
satisfying the random-distribution hypothesis cleared of the inequalities 
which it is our purpose to find out. 
In the possession of this xorma/ distribution we now at once obtain 
these inequalities themselves by simply subtracting the normal numbers 
from the corresponding ones found directly from the observations for the 
individual regions. 
It thus appeared that these inequalities consist in a manifest excess 
of proper motions in certain determinate angles of position. 
These favoured directions have been carefully determined for each of our 
twenty-eight areas. The greater part of them clearly show two favoured 
directions. For a minority but one of the maxima 1s well developed. 
A careful glance at fig. 2 even shows these maxima already tolerably 
well. 
Entering the two sets of favoured directions on a globe brought out 
the very striking fact that the directions of each set, separately, converged 
approximately to a single point. For the one set the approximation is 
an exceedingly good one ; for the other it is only tolerable. A better 
approximation, however, was not to be expected in this case, because the 
proper motions on which it rests are far smaller, consequently far less 
rigorously determined by observation. 
The two points lie some 140° apart; the one some 7° south of 
a Orionis, the other a couple of degrees south of » Sagittarii. 
What this fact means is clear. 
_ When we see that the motions of a certain group of stars converge to 
a same point on the sphere we conclude either that the rea! motions of 
the stars are in reality parallel, or that the motion is only apparent and 
due to a motion of the observer in the opposite direction. As long as we 
have no fixed point of reference we cannot decide between the two. 
When we see two groups of stars converging towards two different 
points the latter explanation fails, at least for one of the groups, because 
the observer can have but one motion. 
