576 
NAT ORE 
[JuLy 30, 1914 
streaming happens to be in the direction of and 
opposite to the solar motion. 
Let us now consider the proper motions of the 
3700 stars observed by Carrington in the light of 
these discoveries. The shift of the centre of gravity 
caused by the solar motion is 1°44” a century. As we 
know how far the sun has moved in a century, this 
gives the average distance of these stars as fifty 
270° 
90° 
fic. 2.—Proper Motions of Group A5-F9. 
When suitable allowance is made for the accidental 
error in these observations, it is found that the number 
less than any given amount 7 can be represented by 
the following algebraical formula :— 
‘e 
3700 == oe 
ee ea) 
The distribution of the angular velocities is 
shown in Fig. 3 (A), the total 
number being represented by 
the area of the curve; the num- 
ber, for example, between 2” 
and 3” a century is given by 
the shaded portion. 
Now suppose that all these 
stars were actually moving 
with the same velocity, say 
10 km. .a second, then their 
distance could be calculated, 
those with proper motion 1’ 
a century being forty million 
times as distant as the sun, 
those with proper motion 2” 
a century twenty million times, 
those of 4” a century ten million 
times, and so on, the larger the 
proper motion the nearer the 
star to us. 
This is only an_ illustration ; 
the velocities of the stars are 
not all the same, but are dis- 
tributed according to the law 
of errors. If the distance of 
each star were known, then by 
180 
million times the distance of the sun from the earth. | dividing the velocity by the distance the proper 
Turning now to the proper motions in a direction | motion would be found. We have to find 
perpendicular to that of the sun’s motion, which arise | how many are at one distance, how many at 
from the moius peculiares of the stars themselves. | another, so that the proper motions will be 
Counting these cross proper motions, we find them | distributed in accordance with the law found 
divided as shown in Table III. from the observations. 
o! i" 2" 3" a" 5" 6" 7" PER CENTURY. 0 10 20 30 40 50 oy [he SEC 
A.—Distribution of angular velocities. Fic. 3. B.—Distribution of linear velocities. 
Tas_e III. Fig. 3 (B) shows the distribution of linear veloci- 
are greater than 15'0’ a century 
lie between 10°0” and 150” a century 
<1) 
33.05) 9 80 ” ikeme) ss 
GGmrs a (ko) So : 
IQI |, > AOS 5, 7) OO : 
873 ’ ” 2°0 % 40 a 
2504 ,, As Clon. 2°0 Fic 
NO:/ 2335.) VOlLu Gal 
ties, the shaded portion, for example, giving the 
| proportion moving between 30 and 4o km. a second. 
Now the distribution of angular velocities is shown in 
(A), and the question arises: How must the stars be 
_ distributed in distance for these twe laws to har- 
| monise ? 
(To be continued.) 
