600 
NATURE 
[AuGUST 6, 1914 
— 
The data only admit of a rough determination of 
the number of very faint stars and the number of 
very bright ones. The figures give a general indica- 
tion of the density of the stars in space and of their 
intrinsic brightness, and serve to direct attention to 
the fact that there are many stars much less luminous 
than the sun, and a certain proportion very much 
more luminous. 
The conclusions drawn up to this point have been 
based entirely on a consideration of the proper 
motions of the stars, irrespective of whether they are 
bright or faint; provided only that they are sufficiently 
bright to have been observed by Carrington. But as 
the apparent magnitude of a star depends on its 
distance as well as on its intrinsic brightness, we 
naturally expect some assistance in assigning the 
distances of these stars from their magnitudes. The 
brightest star in this small area round the North Pole 
is Polaris, the magnitude of which is 2. (It may be 
remarked incidentally that the distance of the pole 
star has been actually measured. It is twenty parsecs, 
or four million times the distance of the sun from the 
earth, and if it were at the same distance as the sun 
it would appear to be 100 times as bright.) Then 
there are about twenty stars which are visible to the 
naked eye. The following table gives the actual 
number of stars of different magnitudes (photo- 
graphic) :— 
TABLE V. 
Brighter than 7’om. ... 61 stars 
From 7‘om. to 8om. ... 124g, 
SE OLOLM SE. OOM wee: SOM 
“5, ORC -5 MKeNaONs 5 993); 
Fainter than 10'om. ... 2140 ,, 
Then, again, the stars may be divided into groups 
according to the physical characteristics revealed by 
the spectroscope. The researches of Kapteyn, Camp- 
bell, and others have shown—at any rate, for the 
brighter stars—remarkable relationships between the 
distances and velocities of the stars and the type of 
spectrum which they manifest. It is therefore 
desirable to examine the proper motions of stars of 
different spectral types separately. The spectra of 
many thousands of stars have been determined at 
Harvard College, under Prof. Pickering’s direction, 
by Miss Cannon. The different classes are indicated 
in the Harvard classification by the letters B, A, F, 
G, K, M, with further subdivisions. The B stars 
are characterised by the presence of helium, the A 
stars by series of broad hydrogen lines. In the F 
stars the hydrogen lines are thinner, and fine metallic 
lines are shown. The G stars are very like the sun, 
full of metallic lines, and with broad lines due to 
calcium. In the K stars the two calcium lines are 
still broader, and there are many fine metallic lines. 
The M stars are characterised by broad absorption 
bands. This arrangement places the stars in the 
order of their temperatures; the B stars are the 
bluest and hottest, and the M stars the reddest and 
coolest. The character of the spectra of about 800 
of the stars in Carrington’s Catalogue is given by 
the Harvard observations. 
For the fainter stars the spectra have not been 
determined, but they can be inferred in another way. 
As the blue stars are more active photographically 
than the red stars, if a red and a blue star have the 
same visual magnitude, the magnitudes estimated 
from the images on a photograph will differ consider- 
ably, and this difference is an index of the colour, 
and thus of the type of spectrum. Now the visual 
magnitudes of most of these faint stars have been 
very accurately determined at Potsdam by Messrs. 
Miller and Kron (and have been kindly communicated 
in manuscript), and the photographic magnitudes 
NO. 2336, VOL, 93) 
have been determined at Greenwich. The differences 
have been taken between the photographic and visual 
magnitudes, and serve to classify the stars according 
to their temperature. ; 
Separating the stars into two groups, those which 
are brighter than 9’°5 magnitude on the Potsdam scale 
of magnitudes, and those which are fainter than 9°5 
magnitude, and dividing each group into four classes 
according to the colour index, the parallactic motion, 
i.e. the mean angular movement per century arising 
from the motion of the sun through space, is deter- 
mined for each class. The results are exhibited in the 
following table :— 
Tas.e VI. 
Stars brighter than Stars fainter than 
Spectral colar oism: aie ena Bae 
] i araliactic arallactic 
eae cad Number motion Number motion 
“ “ 
K—M >8 175 0°65 269 0°36 
G—-K 4to8 168 1°31 428 0°95 
F—G = 1a tOrd, 264 2°58 959 1°53 
A—F <—I 240 1‘97 460 1°28 
In this table the red stars are on the top line; the 
third line consists of stars which are in the same 
stage of development as the sun; those in the second 
line are somewhat cooler and redder; those in the 
last line hotter and bluer. The last line includes a 
few, but only a few, B stars, as there are not many 
in this part of the sky. The quantities in the fourth 
and six columns of the table are a gauge of the 
distance of the stars to which they refer. [t is only 
necessary to divide these into 337”, which is the angle 
through which a star distant 1 parsec would have been 
displaced in the solar motion in one hundred years, to 
obtain the distances in parsecs. Thus the 240 stars 
belonging to types A-F, and brighter than 9:5 mag- 
nitude, are at an average distance of 170 parsecs. 
The first point to notice is that parallactic motions 
of stars fainter than 95 magnitude are always con- 
siderably less than the corresponding quantities for 
stars brighter than 9'5 magnitude. This is, of course, 
because the faint stars are, on the whole, further 
away. The average distance of stars of magnitude 
100 1S approximately 13 times as great as for a star 
of 80 magnitude. 
The next point is the very great distance of the 
red stars. The 269 faint red stars are very nearly 
1000 parsecs away, or 200 million times as distant 
as the sun. At this great distance the sun would 
appear as of magnitude 15°5, but these stars vary in 
magnitude from o9'5 to 110, and are therefore 
intrinsically from 250 to 63 times as bright as the 
sun. Now it happens that among the stars nearest 
to the sun the distances of which have been actually 
measured there are several red stars, and these are 
all very much fainter than the sun. It has been 
suggested by Prof. Russell and Prof. Hertzsprung 
independently that the red stars are of two distinct 
classes, which they call the giants and the dwarfs, 
and that, in accordance with Sir Norman Lockyer’s 
views, the giant red stars are in an early stage of 
evolution, and are increasing in temperature; while 
the dwarf stars are at the other end of the series, and 
are growing colder and darker. 
Leaving the red stars, it is seen that the stars 
the colour indexes of which lie between —1 and +4 
are nearer to us than the groups on either side of 
them. These stars are those the spectra of which 
are of the types F and G in the Harvard notation, 
and are the stars most like the sun. The mean 
distances of these stars is only 130 parsecs for the 
stars brighter than 9's magnitude, and 215 parsecs 
for the stars fainter than 9's magnitude. At this 
distance the sun would be of magnitude 12'1. It 
