382 
Proceedings of the Royal Society of Edinburgh. [Sess. 
In this way the stars were provisionally divided as follows : — 
110 moving in directions more than 60° from both apices. 
1023 belonging to Stream I. 
574 „ „ Stream II. 
217 doubtful. 
1924 Total. 
Kapteyn and Eddington, using stars of large and small proper motions, 
found an equal number in the two streams. The above result is not at 
variance with this, for if Stream I has a larger stream velocity, a greater 
proportion of stars belonging to Stream I will naturally be obtained by 
limiting the stars to those of large proper motion. 
5. The number of stars at different distances from the two apices, 
moving in directions within 60° and 30° of the two apices, are as follows : — 
Distance from 
Apex. 
Fraction of 
Area of whole 
Sphere in- 
cluded. 
Number in 
Stream I 
within 60°. 
Number in 
Stream II 
within 60°. 
Number in 
Stream I 
within 30°. 
Number in 
Stream II 
within 30°. 
60°-120° 
•508 
736 
440 
574 
330 
40°-59° and 120°-140° 
•264 
216 
111 
170 
84 
20°-39° and 141°-160° 
•171 
71 
23 
49 
18 
The relative density of the stars of the two streams at different distances 
from the apices, moving within 60° and 30° of the directions of the streams, 
are therefore : — 
Distance from 
Apex. 
Within 60°. 
Within 30°. 
I. 
i — i 
hH 
I. 
II. 
60°-120° 
145 
87 
113 
65 
40°-59° and 121°-140° 
82 
42 
64 
32 
20°-39° and 141°-160° 
41 
13 
29 
10 
6. If the velocity of Stream I be v, then at a distance 0 from A the resolved 
part of this perpendicular to the line of sight is v sin 0. The mean value 
of this for stars between 60° and 120° from A (more accurately 59 and 
120|°) is *92 v ; for stars from 40° to 60° and 1 20° to 140° from A is - 82 v. 
