388 
Proceedings of the Royal Society of Edinburgh. [Sess. 
Multiplying the numbers 111*2, 805, etc. of § 10 by 4'30, so that 
they may refer to the same fraction of the sphere as the numbers 
in the above table, we obtain for the density of stars whose proper motions 
are >19"*5 at different distances from the apices of the streams — 
0 . 
Sin 6 . 
I. 
II. 
73° 
•957 
478 
248 
55 
•818 
346 
201 
37 
•606 
247 
91 
24 
•404 
104 
60 
Interpolation from the previous table shows that between the distances 
65°-115° from A and B respectively there are belonging to the two 
streams — 
I. 
// 
II. 
478 stars p.m. 
> 
19-5 
248 stars p.m. 
> 
19-5 
346 
55 
> 
25*2 
201 
5 i 
> 
22-4 
247 
55 
> 
31-0 
91 
55 
> 
36*6 
104 
5 5 
> 
00 
60 
55 
> 
47*5 
Comparison of this table with the previous one shows that there are in 
Stream I as many stars per unit with p.m. >25 //- 2 at mean distance 73° from 
the apex, as there are at mean distance 55° with p.m. 19 //, 2, and so on. 
If the accidental velocity is small compared with the stream velocity 
and the stars are uniformly distributed, then at a distance 0 from A the 
number of stars per unit area whose p.m. >v will equal the number per 
unit area 90° from A, whose p.m. >v cosec 0. 
Multiplying by the corresponding values of sin 0 we obtain — 
I. 
II. 
18*7 
u 
18*7 
20'6 
18-3 
18-8 
22*2 
19-6 
19-2 
The accordance of these figures may be regarded as a check on the 
uniformity of the distribution of the stars. 
As there are 247 stars of Stream I between 65° and 115° from A with 
p.m. >3T /- 0, and 248 of Stream II between 65° and 115° from B with p.m. 
>19 //- 5, the stream velocities are in the ratio of 31 : 195 or 3 : 2, confirming 
the previous result. 
