383 
1908-9.] The Systematic Motions of the Stars. 
If the velocity of Stream II be v', then at a distance 0' from B the 
resolved part of this perpendicular to the line of sight is v sin O'. Assum- 
ing that the accidental distribution of velocities is the same in the two 
streams, the distribution of stars in the two streams should be the same 
when v sin 0 = v' sin O'. 
Using this argument, the agreement between the numbers 87 and 82 of 
the last table and between 65 and 64 leads to an equation 
*92 v = '82 v ; 
while the agreement between 42 and 41 and between 32 and 29 leads to 
•82 v — *52 v. 
7. These results are very rough, and would be altered considerably if 
the stars whose proper motions are between 18" and 23" were omitted. The 
results suggest that, by a more careful division of the stars into the two 
streams and by better grouping, it will be possible to determine the relative 
velocities of the streams. 
Dividing the figures on p. 381 by *508, ‘264, and *1 71, we obtain 
Distance from Apex. 
0°-9°. 
10°-19°. 
20°-29°. 
30°-39°. 
0 
0 
1 
CO 
0 
50°-59°. 
( 60°-120° 
49 
38 
26 
20 
9 
3 
I { 40°-59° and 121°-140° 
28 
20 
16 
8 
7 
3 
( 20°-39° and 141°-160° 
18 
7 
5 
8 
9 
4 
( 60°-120° 
27 
20 
19 
13 
5 
3 
II \ 40°-59° and 121°-140° 
15 
9 
7 
6 
3 
0 
( 20°-39° and 141°-160° 
2 
4 
4 
1 
1 
1 
With this table as a guide the original assortment of the stars into the 
two streams was revised, and the doubtful cases decided. E.g., No. 56 in 
Table I. A = 49° a = 130°. B = 33° 6 = 49°. If belonging to Stream I this 
star will fall in the last group but one of the second line : interpolating 
with the number in the last column of the second line we get 6. If the 
star belongs to Stream II it will fall in the 4th column of line 5, and we 
again have the number 6. The star is equally likely to belong to either 
stream, and it is treated as if '5 belongs to Stream I and ’o to Stream II. 
After this revision a table like Table II. was again formed. The follow- 
ing changes were made, however. Stars of proper motion 18" and 19" 
were omitted. These stars were included originally before the proper 
motions in B.A. and Dec. were combined, so as to make sure of getting all 
the stars of p.m. > 20" 
