386 
Proceedings of the Royal Society of Edinburgh. [Sess. 
9. Taking the sums of the columns in the preceding table and giving the 
sums for the small groups which are not given in detail, we find — 
Stream 1. 
Limits of Dist. from 
Fraction of 
Area of 
Sphere. 
; 
Number of Stars whose Directions diverge. 
Apex. 
0°-9°. 
10°-19°. 
20°-29°. 
30°-39 o . 
40°-49°. 
50°-59°. 
65°-115° . . . . 
•430 
211 
162 
105 
77 
45 
22-9 
45°-64°, 116°-135° 
•283 
88-5 
73 
66-3 
37-8 
28-2 
11-1 
30°-44°, 136°-150° 
•157 
4L4 
25 
23-6 
17-2 
16-5 
10-6 
18°-29°, 151°-162° 
•084 
10-5 
5-8 
4-1 
7*0 
63 
2-5 
12°-17°, 163°-168° 
•026 
1-8 
3-4 
1 
1-6 
0-2 
Stream II. 
65°-] 15°. . . . 
•430 
108 
71 
68-8 
573 
22-1 
20-5 
45°-64°, 116°-135° 
•283 
50-4 
45-9 
35-9 
27-4 
20*1 
7-6 
30°-44°, 136°-150° 
18°-29°, 151°-162° 
•157 
11-7 
9-9 
11-4 
8-3 
3-7 
2-0 
•084 
2-6 
5-2 
3-9 
o-i 
2d 
1-2 
Dividing by the areas, the proportional number of stars per unit area 
belonging to the different groups is obtained, the mean value of the sine 
of the angular distance from the apex being given in first column. 
Stream I. 
Sin (dist.). 
0°-9°. 
10°-19°. 
20°-29°. 
30°-39°. 
40°-49°. 
50°-59°. 
•957 
49-1 
27*7 
24-4 
17-9 
10-5 
5 3 
•818 
31-3 
25-8 
23-4 
13-4 
io-o 
3-9 
•606 
26-4 
16-0 
15-1 
11-0 
10-5 
6-8 
•404 
12-5 
6-9 
4-9 
8-3 
8-7 
3-0 
Stream II. 
« 
•957 
25-1 
16-5 
16-0 
133 
5-2 
4*8 
•818 
17-8 
16-2 
12-7 
9-7 
7-1 
2-7 
•606 
7-5 
6*3 
7 3 
5 3 
2-4 
1-3 
•404 
34 
6*2 
4-7 
0-2 
2-5 
1-4 
The above figures show that stars of Stream I whose mean distance 
from the apex of Stream I is sin -1 '606 are distributed similarly to the 
stars of Stream II at mean distance sin ~ *957 from their apex. 
10. If the numbers of stars belonging to the two streams are equal, and 
