Jury 30, 1914) 
in direction. Some signs of irregularity in the direc- 
tions were first detected by Sir William Herschel, 
who found that the movement of seven quick-moving 
stars situated in different parts of the sky were 
approximately directed to one point. He observed 
that this would result if the proper motions arose not 
from the movement of the stars themselves but from 
that of the point of observation in an opposite direc- 
tion, and concluded that the solar system was moving 
towards a point in the constellation Hercules. This 
conclusion was not universally admitted for some 
time, but researches by Argelander, Airy, Bessel, and 
others demonstrated a regular drift among the stars, 
such as would arise if on their otherwise irregular 
movements were superposed this common motion. A 
large number of researches have been made on the 
exact direction of the sun’s motion, and it is now 
established with some certainty that it is towards a 
point in right ascension 18h. and declination 35° N., 
not far in direction from the bright star Vega. The 
speed of the sun’s motion through space has been 
determined by spectroscopic observations. On _ the 
average, stars near Vega appear to be approaching 
us, stars in the opposite direction to be receding 
from us. In this way Prof. Campbell has found from 
the observed velocities of 1500 stars that the solar 
system is moving at the rate of 195 km. a second. 
/ 
Fic. 1 
The fact that the sun is moving with a velocity of 
195 km. a second in a known direction supplies us 
with a means of determining the average distances 
of groups of stars. This velocity carries the sun 
forward in a century a distance equal to 412 times 
the sun’s distance from the earth. It-at the beginning 
of the century the sun is at S, and at the end has 
moved to S/, the angular distance of a star situated 
at P, and having no motion of its own, will have 
increased from ASP to AS’P. The difference of these 
angles, which is the proper motion of the star, is 
SPS’, and it follows that the distance (SP) can readily 
be deduced. We cannot, however, say that any 
individual star is at rest, but if we take a sufficiently 
large group of stars it is legitimate to suppose that 
in the average the peculiar movements of the separate 
stars are eliminated, and the mean distance of the 
group can be inferred. 
During the last twenty or thirty years the proper 
motions of many stars hive been determined by the 
comparison ot modern with earlier observations. 
Particularly the reduction by Dr. Auwers of Bradley’s 
observations made in 1755 led to the accurate deter- 
mination of the angular movements of the brighter 
stars. The proper motions of fainter stars have been 
found by comparison with observations made in the 
first half of the nineteenth century. These have all 
NO. 2335, VOL. 93] . 
NAIURE 
aS 
| been utilised to determine the direction and angular 
amount of the dritt produced in the stars by the 
motion of the solar system through space. ‘lhe results 
were very puzzling, because aitlerent mathematical 
methods and different groups of stars gave widely 
ditterent directions for the solar motion. ‘lhe cause 
was discovered about ten years ago by Prof. Kapteyn, 
who found in the proper motions ot the stars another 
indication of regularity, or perhaps it might be called 
a systematic irregularity smaller than the one dis- 
covered by Herschel, but unmistakable when once 
pointed out. He interpreted these systematic irre- 
gularities to mean that the stars are divisible into two 
groups streaming through one another in opposite 
directions in space. Prof. Kapteyn’s discovery has 
been submitted to mathematical analysis by Prof. 
Eddington and Prof. Schwarzschild. Their researches 
have illuminated the whole subject of stellar motions ; 
and though they are not in entire agreement, they 
leave no doubt of the existence of a preferential move- 
ment among the stars towards the north part of 
Orion and the diametrically opposite direction in the 
constellation of the Serpent. 
We must next consider the motus peculiares—the 
irregular movements of the stars themselves. From 
observations of the velocities of stars in the line of 
sight, especially from those made at the Lick 
Observatory under Prof. Campbell’s direction, it is 
known that a few stars are moving with great 
velocities, such as 109 km. a _ second, while 
others are moving very slowly. The following 
analysis of Campbell’s results for one class of stars 
—those of spectral type A—(taken from a paper by 
Prof. Eddington) shows the proportion of slow- 
moving, moderate, and quick-moving stars :— 
Tasce II. 
Velocities Number of stars Number of stars 
observed given by error law 
o—5 kil/sec_... 55 oes 534 
5—10 bce 47 13s 46°2 
1o—16 she 30 fe 38°3 
16—25 at 30 aA 27°4 
25—4o soe 10 Soc 67 
> 40 ete fe) aa fo) 
Comparison with the third column of the table 
shows that the velocities are distributed in accord- 
ance with the law of errors. The law is identical with 
that found by Maxwell for the velocities of the 
molecules of a gas. In the case of a gas, this dis- 
tribution of velocities results from the frequent col- 
lisions. For the stars there is no evidence that it 
has resulted from their interaction. It must be regarded 
as an observational fact which permits us to say that 
the distribution of the velocities of the stars is stated 
concisely by this simple mathematical formula. 
The three movements—the movement of the solar 
| system in space, the streaming of the stars— and their 
irregular movements are all shown in their proper 
motions. The figure (taken from a paper by Mr. 
Jones—Monthly Notices of the RAGS nVOlamiextiver 
p. 196) exhibits the proper motions of some of the 
brighter stars situated near the North Pole. If the 
stars had all been placed at the origin they would in 
a century have spread out as shown in the figure. 
This spreading out has been caused by :— 
(i) The solar motion, which has shifted the centre 
of gravity of the swarm towards 180°. 
(ii) The peculiar motions of the stars themselves, 
which have spread them out in the directions towards 
| go° and 270°. 
" (iii) The streaming in the direction 0° to 180°, 
which, combined -vith the peculiar motions, has made 
the spreading out much greater in this than in the 
perpendicular direction. In this part of the sky the 
