235 
1907-8.] The Systematic Motions of the Stars. 
directions, the figures obtained would be approximately circular. If a 
proper motion in one particular direction were added to a chance distribu- 
tion of proper motions giving a stream of stars (such as would result, e.g., 
from the motion of the solar system in space), the figures would he elongated 
but symmetrical about the direction of general drift. The figures of 
diagram 2 are not of this character, but inspection shows that they could 
be derived by the composition of two curves symmetrical about the direc- 
tions marked I and II. These curves are in general similar to those 
calculated by Mr Eddington for the distribution of the direction of proper 
motion in a stream when proper motions of all magnitudes are included. 
I have endeavoured to effect the analysis graphically, mainly from the 
principle that the number of proper motions should be equal in two direc- 
tions, equally inclined to the direction of the stream. 
For the purpose of this analysis, the numbers were plotted in rectangular 
co-ordinates in diagram 3, the abscissae corresponding to the direction and 
the ordinates to the number of stars moving within 3f° on either side of 
that direction. In A, whose centre may be taken as the North Pole, the 
abscissae increase positively from 0 h to 24 h . In B, C, and D, 0° indicates 
a direction N. from the given centre (points on the equator at 0 h , 4 h , and 
8 h ), and the angles increase towards 6 h in each case. 
The analysis of the resulting figures into two symmetrical curves is, to 
a fairly high degree of accuracy, simple, in consequence of the pronounced 
character of the maxima and their distance apart. Taking B as an example, 
the mode of analysis was as follows : — 
(i) There is a pronounced maximum between 90° and 100°. 
(ii) There is a maximum between 180° and 210 c . 
(iii) The second stream does not spread beyond 280°. 
(iv) If 180° is the position of maximum, the curve of the second stream 
will, if symmetrical, . reach the axis of x again at 80° ; if the maximum 
is at 210°, at 140°. 
Drawing provisional symmetrical curves on these two extreme hypotheses, 
and plotting the differences between the observations and the provisional 
curve II in each case on the left-hand side of the maximum, we have the 
material from which to construct curve I. If the maximum of II is at 180°, 
a symmetrical curve I with a maximum at 93J° (the highest dot in the 
diagram) will fit in excellently with the three or four observations on each 
side. If, however, the maximum of II is at 210°, curve II will only extend 
to 140°, and curve I near the maximum will be wholly independent of curve 
II. In this case the maximum of curve I will be near the position drawn 
at 97-|-°. 
